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Title Introduction to The Theory of Statistics. Code Local Credit ECTS Lecture (hour/week) Practical (hour/week) Laboratory (hour/week) 0236126 3 7.5 3 0 0 Prerequisite None Semester Not set Course Language Not set Level Of Course Third Cycle Course Type Elective @ Statistics Division - Statistics PhD. Program Course Category Major Area Courses Mode Of Delivery Face-to-Face Owner Academic Unit Statistics Course Coordinator Atıf Evren Instructor(s) Asistant(s) Course Objectives Fundamentals of statistical theory Course Content Probability, random variables,expectations,limit theorems,some parametric families,sampling and reduction of data,estimation, testing hypotheses. Recommended Or Required Reading Recommended Optional Program Components - Lecture notes. - MOOD, A.M. vd (1974) Introduction to the Theory of Statistics, McGrawHill International Editions, (3rd edition) - LINDGREN, B.W., Statistical Theory, Chapman&Hall, 4th edition - SHAO, J., Mathematical Statistics, Springer None Course Learning Outcomes 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Essentials of probability theory. Multivariate distributions. Functions of random variables. Sampling distributions. Statistical estimation. Properties of estimators. Bayes estimators. Methods for finding confidence intervals. Hypothesis tests. Generalized likelihood ratio test. Weekly Subjects and Related Preparation Studies Week 1 2 3 4 5 Subjects Probability. Random variables. Probability functions. Distribution functions and expectation. Moments and moment generating functions. Special parametric families of univariate distributions. Joint and conditional distributions. Stochastic independence. Expectation. Covariance and correlation coefficient. Cauchy-Schwarz Inequality. Bivariate normal distribution. Distributions of functions Related Preparation Mood, Graybill, Boes, Chapter I Mood, Graybill, Boes, Chapter II-III Mood, Graybill, Boes, Chapter IV Mood, Graybill, Boes, Chapter IV Mood, Graybill, Boes, Chapter IV-V 6 7 8 9 10 11 12 13 14 15 16 of random variables. Cumulative-distribution-function technique. Momentgenerating-function technique. Transformations. Sampling and sampling distributions. Sampling from the normal distribution. Midterm examination. Parametric point estimation. Methods for finding estimators. Method of moments. Maximum likelihood. Other methods. Properties of point estimators. Sufficiency. Unbiased estimation. Lower bound for variance. Sufficiency and completeness. Location or scale invariance. Bayes estimators. Posterior distribution. Loss-function approach. Minimax estimator. Parametric interval estimation. Confidence intervals. Sampling from the normal distribution.Methods of finding confidence intervals. Hypothesis tests. Generalized likelihood-ratio test. Uniformly most powerful tests. Unbiased tests. Methods of finding tests. Sampling from the normal distribution. Chi-square tests. Asymptotic distribution of generalized likelihood ratio. Chi-square goodness of fit test. Test of the equality of two multinomial distributions. Tests of independence in contingency tables. Final examination. Mood, Graybill, Boes, Chapter V Mood, Graybill, Boes, Chapter VI General review Mood, Graybill, Boes, Chapter VII Mood, Graybill, Boes, Chapter VII Mood, Graybill, Boes, Chapter VII Mood, Graybill, Boes, Chapter VIII Mood, Graybill, Boes, Chapter IX Mood, Graybill, Boes, Chapter IX Mood, Graybill, Boes, Chapter IX General review Evaluation System Activities Number Attendance/Participation Laboratory Application Field Work Special Course Internship (Work Placement) Quizzes/Studio Critics Homework Assignments 2 Presentations/Jury Project Seminar/Workshop Mid-Terms 1 Final 1 Percentage of In-Term Studies Percentage of Final Examination TOTAL Percentage of Grade 20 40 40 60 40 100 ECTS Workload Table Activities Number Duration(Hour) Total Workload Course Hours (Including Exam Week: 16 x Total Hours) Laboratory Application Field Work Study Hours Out of Class Special Course Internship (Work Placement) Homework Assignments Quizzes/Studio Critics Project Presentations / Seminar Mid-Terms Final Extra Notes 14 3 42 14 8 112 2 15 30 1 1 20 20 Total Workload : Total Workload / 30(h) : ECTS Credit : None 20 20 224 7.47 7.5