Download DEPARTMENT OF STATISTICS UNDERGRADUATE COURSES

DEPARTMENT OF STATISTICS
UNDERGRADUATE COURSES
Statistics (1)(2): 4 credits/1st yr.
This course contain the following topics: a first look at statistics; descriptive
graphs; descriptive measures; probability concepts; discrete probability
distributions; statistical inference and sampling; hypotheses testing for the mean
and variance of a population; inference procedures for two populations; estimation
and testing for population proportions; analysis of variance; quality control;
applications of the Chi-square statistic; correlation and simple linear regression;
multiple linear regression; time series analysis and index number.
Economics (1)(2): 3 credits/1st yr.
The content of this course includes equilibrium analysis of demand and supply,
price elasticity, consumption theory, production and cost analysis, market analysis,
combination of factors and income distribution, determination of income, kenyesian
theory, classical theory, monetarism theory, rational expectation theory,
international trade and finance, economic growth and economic systems.
Calculus (1)(2): 4 credits/1st yr.
The content of this course includes limit concepts, the application and definition
of derivatives, the properties of definite integral, the fundamental theory of calculus,
the method and application of integral, the introduction of transcendental functions
and its application, infinite series, power series, Taylor series, polar coordinate,
vector analysis, and the application of multivariate functions.
Linear Algebra: 3 credits/1st yr.
Matrices and their Algebra; Linear Equations; Vector Spaces; Eigenvectors and
their Applications Orthogonality; Linear Transformation.
Introduction to Computer Science: 3 credits/1st yr.
The content of this course includes: (1) a first look at the computer, (2)
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introduction to MS-DOS, (3) introduction to IBM PC BASIC programming, (4)
introduction to random number and its applications in statistics, (5) numerical
functions and string functions, (6) introduction to sequential files and random
access files, and (7) introduction to computer graphics.
Statistical Software and Graphics: 3 credits/2nd yr.
Introducing the use of statistical computer packages/softwares, training the
programming and designing ability, and preparing the know-how for future use in
statistical applications.
The content of this course includes data collection, data processing, rules of table
construction, rules of the graphical representation, curve chart, bar chart, surface
diagram, volume chart, figurative chart, statistical map, and organization chart.
Advanced Calculus: 3 credits/2nd yr.
Properties such as continuity and differentiability of functions of one variable
and functions of several variables are discussed. Riemann integral and Lebesgue
integral for functions of one and several variables are introduced. Fubini theorem
for iterated integral is given. The convergence of functions such as pointwise and
uniform convergence are discussed. Infinite series and Fourier analysis are also
introduced.
Outline of Civil Law: 3 credits/2nd yr.
The content of this course includes introduction, general provisions, debts,
general rules, summary in laws of debts, proprietary right, right of pledge, and right
to take possession of.
Sampling Survey: 3 credits/2nd yr.
The content of this course includes simple random sampling, stratified random
sampling, systematic sampling, cluster sampling, ratio estimates and regression
estimates, multi-stage sampling, double sampling, and replicates sampling.
Regression Analysis: 3 credits/2nd yr.
1. (1) Basic Statistics: Normal, t,  2 and F distributions, Estimation,
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Confidence interval, Testing hypotheses, (2) Matrix Algebra: Symmetry,
Orthogonality, Rank, Trace, Positive definite, Idempotent, Projection, Eigenvalue,
Eigenvector; 2. Simple Linear Regression: Estimation of parameters, Interval
estimation, Hypotheses testing, Prediction, Coefficient of determination, Residual
analysis; 3. Multiple Linear Regression: Estimation of parameters, Confidence
interval, Hypotheses testing, Prediction, Simultaneous inference, Weighted least
squares, Multicollinearity, Coefficients of partial determination; 4. Polynomial
Regression; 5. Indicator Variables; 6. Variable Selection and Model Building: All
possible regressions, Stepwise regression methods, Ridge regression.
Programming Language: 3 credits/2nd yr.
1. introduction to Computers and Programming, 2. problem solving and Fortran,
3. decisions and IF statement, 4. repetition and loops, 5. FORMAT statements, 6.
code view, 7. Array, 8. Subprograms, 9. Application, 10. IMSL.
Linear Programming: 3 credits/2nd yr.
The content of this course includes formulation of linear programs, the simplex
method, geometry of the complex method, duality in linear programming, revised
simplex method, the dual simplex method, parametric linear programs, sensitivity
analysis, bounded-variable linear programs, the transportation problem, the
assignment problem, and the integer problem.
Differential Equation: 3 credits/2nd yr.
The content of this course includes introduction, first order differential equations,
high order liner differential equations, series solutions, system of differential
equations, Laplace transformation, and partial differential equation.
Numerical Analysis: 3 credits/2nd yr.
The content of this course includes the solution of nonlinear equations,
interpolation by polynominal, differentiation and integration, systems of equations,
the solution of differential equations, and approximation.
Insurance Mathematics: 3 credits/2nd yr.
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This course is designed to introduce some basic ideas of compound interest,
application, and computation about various annuities: (1) interest rate; discount rate,
effective, nominal rate; (2) basic annuities; (3) general annuities; (4) yield rates; (5)
amortization and sinking fund; (6) supplementary.
Quality Control: 3 credits/2nd yr.
The content of this course includes: (1) off line quality control: total quality
control, quality control circle, and (2) on line quality control: control charts,
sampling plans.
International Trade: 3 credits/2nd yr.
This course is designed to introduce classical theory of international trade, new
classical theory of international trade, modern theory of international trade,
economic growth and international trade, policy of international trade, policy of
open trade, protection on international trade, theory of tariffs, non-tariff control,
market structure, and economic organization.
Practice of International Trade: 3 credits/2nd yr.
The content of this course includes introduction to international trade, practice
on export, trade claim, tax return in export, and telegrams in international trade.
Introduction to Probability: 3 credits/2nd yr.
1. probability, 2. mathematical expection, 3. functions of random variables, 4.
sampling distribution, 5. limit theorems.
Forecasting Methods: 3 credits/2nd yr.
The objective of the course is to learn how to observe data in details and how to
classify data correctly in our real life. We want to develop a statistical model that
can represent the information provided by data, like the data of regression
relationship or the data series of time. Furthermore, We try to explain, predict and
control the phenomenon, Also, We will make decision by using statistical
forecasting method.
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Finance: 3 credits/3rd yr.
Public Finance is public sector or government economics. It includes general
analysis, public expenditure theory, public revenue theory and the policy of public
finance; it also provides a broad perspective on the role of government in the
economy.
Money and Banking: 3 credits/3rd yr.
The content of this course includes the basic knowledge of money and banking,
money supply and commercial banking system, the central bank and money
controls, monetary theories and monetary policies, and the international monetary
system.
Experimental Design: 3 credits/3rd yr.
The content of this course includes: (1) Basic statistical concepts, (2) Completely
randomized design, (3) Completely randomized analysis of covariance, (4)
Random block design, (5) Latin square design and its related design, (6)
Orthogonal layout techniques.
Categorical Data Analysis: 3 credits/3rd yr.
The content of this course includes analysis of two-way contingency tables,
analysis of three-way contingency tables, model selection, analysis of high-way
contingency tables, logistic model, and loglinear model.
Microeconomics: 3 credits/3rd yr.
The content of this course includes: A. Introduction: (1) production and
operations management, (2) decision making; B. Forecasting: (3) forecasting; C.
Design of production systems: (4) capacity planning: facilities and equipment, (5)
location planning, (6) products and service design, (7) facilities layout, (8) design
of work systems; D. Operating and controlling the system: (9) aggregate planning,
(10) inventory management, (11) material requirements planning, (12) scheduling,
(13) project management, (14) Queuing, (15) Quality assurance.
Statistical Methods: 3 credits/3rd yr.
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The content of this course includes probability, sampling methods, descriptive
statistics, estimation methods, testing methods, regression analysis, analysis of
correlation, experimental design, covariance analysis, nonparametric statistics, and
quality control and reliability.
Mathematical Statistics (1)(2): 3 credits/3rd yr.
The content of this course includes: (1) Point estimations -- MLE, UMVUE,
Bayesian estimators, minimax, least square methods, and method of moments; (2)
Confidence intervals, testing statistical hypotheses, the Neyman-Pearson lemma, T
tests, F tests, the sequential probability ration tests, Chi-square tests, nonparamatric
tests, sufficient statistics, completeness, exponential families and their related
theorems, regression analysis, and analysis of variance.
Multivariate Analysis: 3 credits/3rd yr.
This course includes the application of multivariate regression and analysis,
analysis of variance, principal component analysis, factor analysis, MDS, AID,
cluster analysis, discriminant analysis, cannonical correlation analysis, and other
data analysis.
Macroeconomics: 3 credits/3rd yr.
The content of this course includes: (1) Introduction to macroeconomics: actual
and potential GNP, national income and product accounts; (2) Income
determination: the static equilibrium model, income determination, interest rate,
monetary and fiscal policy, equilibrium output and the price level, the classical case
and labor supply and the money wage, unemployment and wage regidity,
equilibrium in the basic static model; (3) Sectoral demand functions and extensions
of the basic model: comsumption and consumer expenditure, investment demand,
the demand for money, the supply of money, monetary and fiscal policy in the
extended model, inflation, productivity and the Phillips curve; (4) Extensions of the
basic model: the foreign sector and the balance of payments, economic growth,
inflation and unemployment.
Demography: 3 credits/3rd yr.
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The content of this course includes introduction, population census and sample
survey, history of population survey, methods of population survey, practice of
population survey, vital registration, population projection, stable population,
fertility, mortality, population growth, life table, and statistics on labor forces in our
country.
Practice of Quality Control: 3 credits/3rd yr.
The content of this course includes law, policy and organization in quality
control, techniques in quality control, control system, and case study.
Marketing Management: 3 credits/3rd yr.
The content of this course includes: (1) Social foundations of marketing: meeting
human needs, (2) The Marketing management process, (3) Marketing research and
Information systems, (4) The Marketing environment, (5) Consumer markets and
consumer, buyer behavior, (6) Organizational markets and organization buyer
behavior, (7) Market segmentation, targeting, and positioning, (8) Designing
products: products, brands, packing, and services, (9) Designing products:
new-product development and product life-cycle strategies, (10) Pricing products:
pricing objectives and policies, (11) Placing products: distribution channels and
physical distribution, (12) Promoting products: communication and promotion
strategy, (13) Strategy, planning and control, (14) International marketing, (15)
Statistical methods of marketing application.
Operations Research: 3 credits/3rd yr.
The content of this course includes: (1) The nature of operations research, (2)
Linear programming, (3) Network analysis, (4) Advanced topics in linear
programming, (5) Decision analysis, (6) Random process, (7) Queuing models, (8)
Inventory models, (9) Simulation, (10) Dynamic programming, (11) Nonlinear
programming.
Statistical Simulation: 3 credits/3rd yr.
1. Introduction and elements of probability, 2. Random numbers, 3. Generating
discrete random variables, 4. generating continuous random variables, 5.the
discrete event simulation approach, 6. statistical analysis of simulated data, 7.
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variance reduction techniques and statistical validation techniques (contingent upon
the time available).
Analysis of Time Series: 3 credits/3rd yr.
The content of this course includes building, estimating, testing and forecasting
ARIMA models, autocorrelation, partial autocorrelation, cross correlation
coefficients, exponential smoothing methods, transfer function models, and
seasonal time series analysis, and the use of SCA and SAS/ETS packages as
computing tools.
Practice of Experimental Design: 3 credits/3rd yr.
The content of this course includes completely randomized design, randomized
block design, factorial design, fractional factorial design, split design, orthogonal
array, Taguchi method on experimental design, SN ratio, and response surface.
Economic Statistics: 3 credits/3rd yr.
The content of this course includes: (1) The basis of input-output tables accounts for producers (2) Methods of surveying - censuses and samples (3)
Statistics of national income (4) Employment and distribution of income (5)
Forecasting of economics (6) The basis of index tables (7) Statistics of productivity
Nonparametrics Statistics: 3 credits/3rd yr.
Nonparametric methods based on ranks for one-sample location, two-sample
location and scale, and k-sample location (where k>3) are introduced . Pitman
relative efficiency for comparing several test statistics are discussed. Rank
regression is also introduced.
Statistical Data Analysis: 3 credits/4th yr.
Procedure in analysis of statistical data, important points in using statistical
methods, type of data, design effect, meaning of association, measurement of
association, measurement of attribute, reliability and validity, useful statistical
methods, case study.
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Statistical Decision Theory: 3 credits/4th yr.
The content of this course includes utilities of decision, prior information,
posterior analysis, sequential decision, linear programming, and simulation.
Estimation Theory: 3 credits/4th yr.
The content of this course includes sufficiency, completeness, unbiasedness,
point estimators, maximum likelihood estimators, Baysian estimation, confidence
interval, tolerence interval, estimation on linear statistics, estimation on
nonparametric statistics, and special topics.
Theory of Testing Hypotheses: 3 credits/4th yr.
The content of this course includes testing hypotheses, uniformly most powerful
test, uniformly most powerful unbiased test, likelihood ratio test, sequential
analysis, testing theory on nonparametric statistics, rank test, sign test, and special
topics.
Systems Analysis: 3 credits/4th yr.
The content of this course includes introduction, methods and restrictions, linear
programming, dynamic programming, PERT-CPM, Bayesian decision procedure,
Markov analysis, investment analysis, MIS, and case study.
Econometrics: 3 credits/4th yr.
The content of this course includes introduction, classical first order regression
model, dummy variables, autoregression and distributed lag models, generalized
linear regression model, instrumental variables, identified problems, simultaneous
equations model, model selection and application.
Measure Theory: 3 credits/4th yr.
The course is designed to introduce system of real numbers, lebesgue measure,
lebesgue integral, measure functions and integration, measurable space, and
probability space.
Statistical Analysis: 3 credits/4th yr.
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Confirming the learning of statistical methods and principles, training the basic
abilities of statistical analysis and introducing practical application examples.
Topics on Statistics: 3 credits/4th yr.
The course is designed to introduce point estimation, confidence interval, testing
hypotheses, regression analysis, ANOVA, experimental design, nonparametric
statistics, and time series.
Topics on probability: 3 credits/4th yr.
This course includes the definition of distribution functions, sequence of r.v.'s
and modes of convergence, distributions of random vector, sampling distribution.
GRADUATE COURSES
Theory and Application of Multivariate Analysis: 3 credits/1st yr.
1. Aspects of Multivariate Analysis, 2. Introduction of Elementary Linear
Algebra, 3. Introduction of Statistics, 4. Multivariate Normal Distributions, 5.
Inference and Comparisons, 6. Principal Component Analysis, 7. Factor Analysis, 8.
Discrimination and Classification, 9. Cluster Analysis, 10. Introduction of SAS and
Statgraphics.
Theory of Sample Surveys: 3 credits/1st yr.
Introduction; simple random sampling; the estimation of sample size; stratified
random sampling; ratio estimators and regression estimators; systematic sampling;
cluster sampling.
Theory and Application of Nonparametric Statistics: 3 credits/1st yr.
Nonparametric methods based on ranks for one-sample location, two-sample
location and scale, and k-sample location (where k>3) problems are introduced.
The techniques for verifying the properties of a test statistic such as consistency
and efficiency are given. Projection method for deriving asymptotic distributions
for the sum of dependent variables is applied. The techniques for edriving locally
most powerful rank test are introduced. Pitman relative efficiency for comparing
several test statistics are discussed. Rank regression is also introduced.
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Mathematical Statistics (1)(2): 3 credits/1st yr.
1. Basic Statistics: Conditional expectation,
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3.
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2
, F and t distributions,
Orthogonal transformations, The bivariate normal distribution, Variancestabilizing transforms, Edgeworth approximations.
Statistical Models: Sufficient statistics, Minimal sufficient statistics,
Complete statistics, Exponential families.
Methods of Estimation: Frequency substitution, Method of moments, The
method of least squares, maximum likelihood estimates, UMVUE, Bayes and
Minimax estimation.
Comparison of Estimates: Unbiased, The information inequality, Consistency,
Asymptotic normality, Asymptotic efficiency and optimality.
Confidence Intervals and Testing: Confidence regions, The p-value, Power
and sample size, The Neyman-Pearson Lemma, UMP test, GLR test,
Uniformly most accurate confidence bounds.
Time Series Analysis: 3 credits/1st yr.
1. Fundamental Concepts 2. Stationary Time Series Models 3. Nonstationary
Time Series Models 4. Forecasting 5. Model Inentification 6. Parameter
Estimation, Diagnostic Checking and Model Selection 7. Seasonal Time
Series Models.
Statistical Finance: 3 credits/2nd yr.
1. Basic statistical models used in Statistical Finance; capital asset pricing model;
efficient frontier; portfolio construction; sharpe- linfner method; Black-scholes
model; Efficient market; statistical estimation and test; value at risk; Applications in
Taiwan Stock Market and large refinement funds.
Multiple Comparisons and Decision procedures: 3 credits/2nd yr.
This course is designed to learn the theory and methods of multiple comparisons
of the parameters when the null hypothesis of homogeneity is rejected. That is, we
are going to study the multiple comparisons with the best, the multiple comparisons
with the average, the multiple comparisons with the control, ranking the
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populations and estimating the ranked parameters, selecting best of good
populations by indifference zone and subset selection, the theory of equivalency
test of several populations without the traditional hypothesis of equality, and so on.
These methods can be applied to pharmaceutical industry, medicine, financial
market, manufacturing industry, agriculture, poultry science, etc.
Ph.D. Courses
Statistical Finance: 3 credits/2nd yr.
1. Basic statistical models used in Statistical Finance; capital asset pricing model;
efficient frontier; portfolio construction; sharpe- linfner method; Black-scholes
model; Efficient market; statistical estimation and test; value at risk; Applications in
Taiwan Stock Market and large refinement funds.
Multiple Comparisons and Decision procedures: 3 credits/2nd yr.
This course is designed to learn the theory and methods of multiple comparisons
of the parameters when the null hypothesis of homogeneity is rejected. That is, we
are going to study the multiple comparisons with the best, the multiple comparisons
with the average, the multiple comparisons with the control, ranking the
populations and estimating the ranked parameters, selecting best of good
populations by indifference zone and subset selection, the theory of equivalency
test of several populations without the traditional hypothesis of equality, and so on.
These methods can be applied to pharmaceutical industry, medicine, financial
market, manufacturing industry, agriculture, poultry science, etc.
Advanced Statistical Inference (I): 3 credits/1st yr.
Brief review on Probability Theory; Sufficiency and Completeness; Evaluation
Criteria for Estimators; Global Properties (Decision Theoretical View); Large
Sample Theory (Asymptotic properties).
Advanced Probability Theory: 3 credits/1st yr.
Review on some topics in graduated Probability Theory; Convergence of
Sequences of Random Variables; CLT, Large Deviation and Related Topics;
Conditional Expectation and Conditional Probability, Stochastic Process;
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Martingale; Convergence of Random Sequences with Martingale Theory.
Theory of Sampling Survey: 3 credits/1st yr.
Selected topics in sampling and survey theory at an advanced level.
Advanced Statistical Inference (II): 3 credits/1st yr.
Elementary Concepts on Test; Neyman-Pearson Lemma, MP Test and
Admissibility; MLR family and Existence of UMP Tests; Unbiasedness, Invariance
and Tests and Confidence Sets; Minimaxity and other criteria; Conditional
Inference:
Advanced Multivariate Analysis: 3 credits/1st yr.
Selected topics in the theory of multivariate analysis at an advanced level.
Topics on Regression Analysis: 3 credits/2nd yr.
This course contains the following topics: the simple linear regression;
assumptions behind regression analyses; multiple regression; some problems and
remedies; model building; dummy variable and advanced statistical inferences;
remedies for violations of the regression assumptions.
Advanced Experimental Designs: 3 credits/2nd yr.
Selected topics in the field of experimental design.
Quality Engineering: 3 credits/2nd yr.
Probability models and statistical methods used in engineering and the natural
sciences, Principles of Quality Engineering, Matrix, Experiments using Orthogonal
Arrays, Steps in Robust Design, Signal-to-Noise Ratios, Computer-aided Robust
Design, Design of Dynamic Systems, Reliability Improvement.
Non-Linear Models: 3 credits/2nd yr.
Model building, estimation methods, commonly encountered problems, measures
of curvature and nonlinearity, statistical inference, autocorrelated errors, growth
models, compartmental models, multiphase and spline regression, error-in-variables
models, multiresponse nonlinear models, asymptotic theory.
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Time Series Analysis: 3 credits/2nd yr.
Stationary and nonstationary processes, properties of models, estimation of
model parameters, spectral analysis, forecasting.
Generalized Linear Models: 3 credits/2nd yr.
Linear Models, Non-Linear Models, and Generalized Linear Models.
Advanced Nonparametric Statistics: 3 credits/2nd yr.
Statistical procedures valid under unrestrictive assumptions; sign test; confidence
intervals; efficiency comparisons; signed rank procedures; Walsh sums; point
estimators; two sample rank tests; zeros; ties, and other problems of discrete data;
order statistics; Winsorized and truncated point estimators and connection with
gross error models; permutation procedures; combinatorial problems, and computer
applications.
Advanced Stochastic Processes: 3 credits/2nd yr.
Game theory and decision theory, the main theorems of decision theory,
conjugate prior distributions and limiting posterior distributions, sequential
decision problems, empirical Bayes method of estimation. Discrete and continuous
Markov processes, birth and death process, diffusion theory, and power spectra.
Topics on Statistical Consulting: 3 credits/2nd yr.
To develop statistical consulting skills ranging from basic concepts relating to
how to formulate the exact nature of the client’s problem, to solving it and
presenting the solution in the language of the client. Moreover, the course is
designed to develop advanced statistical consulting skills. The student will
complete major statistical consulting problems under supervision initially, and later
without supervision but to report to instructor; formal session on current problems;
better design of experiments; report preparation.
Advanced Bayesian Analysis: 3 credits/3rd yr.
Sampling theory and its critique, subjective probability, likelihood principles,
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Bayes theorem, Bayesian analysis of Normal theory inference problems, the
Behrens-Fisher problem, assessment of model assumptions, robustness of inference,
analysis of variance, estimation of variance components, empirical Bayes, some
aspects of multivariate problems.
Econometrics: 3 credits/3rd yr.
The Classical Inference Approach for the General Linear Model, Inference in
General Statistical Models and Time Series, Dynamic Specifications, Inference in
Simultaneous Equation Models, Further Model Extensions.
Sequential Analysis: 3 credits/3rd yr.
Sequential probability ratio test, two-sided tests, composite tests, truncated
sequential test, Brownian motion approximations, test with curved boundaries,
repeated significance test, secretary-type problems, sequential allocation of
treatments, armed-bandit problems, sequential interval estimation, sequential
estimation of points on regression functions, Robbins-Makov process,
Chow-Robbins method, Kiefer-Wolfowitz procedure.
Topics on Statistical Research (I)~(IV): 3 credits/3rd-4th
Theory for the Jackknife, and Bootstrap, Bootstrap Confidence sets and
Hypothesis Tests, Applications to Sample Surveys, Linear models, Nonlinear,
Nonparametric and Multivariate models, Applications to Time Series, Bayesian
Bootstrap.
Thesis
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