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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) 6-9 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, 6-10 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. 6-11 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. 6-12 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. 6-13 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. 6-14 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. 6-15 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. 6-16 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. 6-17 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. 6-18 Mathematical Statistics (1)(2): 3 credits/1st yr. 1. Basic Statistics: Conditional expectation, 2. 3. 4. 5. 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 6-19 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; 6-20 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. 6-21 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, 6-22 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 6-23