STA 4322 Introduction to Statistical Theory (4445)

STA 5328 Fundamentals of Statistical Theory (7620)

Syllabus Homework

Lecture: 1:55 pm – 2:45 pm | MWF | Griffin-Floyd Hall 100

Instructor: Jorge Román Email: jcroman7@stat.ufl.edu Office: Griffin-Floyd Hall 115A Office Hours: T Th 10:40-11:30am

Teaching Assistant: Long Zhang Email: longzhang@ufl.edu Office: Griffin-Floyd Hall 117D Office Hours: 11:00am-12:00pm

Below is a tentative course schedule:

Date	Day	Material
Aug 24	M	Syllabus, Introduction[7.1 ]
Aug 26	W	Sampling distributions related to the Normal distribution [7.2]
Aug 28	F	Central Limit Theorem [7.3]
Aug 31	M	The Normal approximation to the Binomial distribution [7.5]
Sep 2	W	The Bias and the Mean Square Error of point estimators [8.1-8.3]
Sep 4	F	Evaluating the goodness of a point estimator [8.4]
Sep 7	M	Labor Day
Sep 9	W	Confidence intervals [8.5] HW1 due
Sep 11	F	Large Sample Confidence intervals [8.6] Selecting the sample size [8.7]
Sep 14	M	Small-Sample Confidence Intervals [8.8]
Sep 16	W	Confidence intervals for the Variance [8.9] HW2 due
Sep 18	F	Introduction [9.1] Relative Efficiency [9.2]

Sep 21	M	Exam 1 Review \ Exam 1 will be on Tuesday, Sept 22^nd at 6:30pm
Sep 23	W	Consistency [9.3]
Sep 25	F	Sufficiency [9.4]
Sep 28	M	Rao-Blackwell Theorem [9.5]
Sep 30	W	The Method of Moments [9.6]/The Method of Maximum Likelihood [9.7]
Oct 2	F	Introduction [10.1] Elements of a Statistical Test [10.2]
Oct 5	M	Common Large Sample Tests [10.3]
Oct 7	W	Type II error [10.4] HW3 due
Oct 9	F	Relationship between tests and CI’s [10.5]
Oct 12	M	Another way of reporting the results [10.6]
Oct 14	W	Some comments on the theory of testing [10.7]/ Small sample tests [10.8]
Oct 16	F	Homecoming
Oct 19	M	Tests for Variances [10.9]
Oct 21	W	Power of tests and the Neyman-Pearson Lemma [10.10]
Oct 23	F	Exam 2 Review \ Exam 2 will be on Tuesday, Oct 27th at 7:20pm Griffin Floyd 100
Oct 26	M	Normal MLE’s
Oct 28	W	Likelihood Ratio Tests [10.11]
Nov 2	M	Likelihood Ratio Tests [10.11]
Nov 4	W	Introduction to Linear Models, Method of least squares [11.1-11.3]
Nov 6	F	Properties of the LS estimators [11.4]
Nov 9	M	Inferences Concerning the Beta parameters [11.5]
Nov 11	W	No Class Veteran’s Day
Nov 13	F	Inferences Concerning Linear Functions of the Model Parameters [11.6]
Nov 16	M	Predictions [11.7]
Nov 18	F	Correlation [11.8]

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Tentative Topic Coverage:

Chapter	Section
Chapter 7 Sampling Distributions and the Central Limit Theorem	7.1 Introduction 7.2 Sampling Distributions Related to the Normal Distribution 7.3 The Central Limit Theorem 7.5 The Normal Approximation to the Binomial Distribution
Chapter 8 Estimation	8.1 Introduction 8.2 The Bias and Mean Square Error of Point Estimators 8.3 Some Common Unbiased Point Estimators 8.4 Evaluating the goodness of a point estimator 8.5 Confidence intervals 8.6 Large-Sample Confidence Intervals 8.7 Selecting the Sample Size 8.8 Small-Sample Confidence Intervals 8.9 Confidence intervals for the Variance
Chapter 9 Properties of Point Estimators and Methods of Estimation	9.1 Introduction 9.2 Relative Efficiency 9.3 Consistency 9.4 Sufficiency 9.5 Rao-Blackwell Theorem 9.6 The Method of Moments 9.7 The Method of Maximum Likelihood
Chapter 10 Hypothesis Testing	10.1 Introduction 10.2 Elements of a Statistical Test 10.3 Common Large-Sample Tests 10.4 Type II error 10.5 Relationships Between Hypothesis Testing Procedures and Confidence Intervals 10.6 Another Way to Report the Results of a Statistical Test 10.7 Some Comments on the Theory of Hypothesis Testing 10.8 Small Sample Hypothesis Testing 10.9 Testing Hypothesis Concerning Variances 10.10 Power of tests and the Neyman – Pearson Lemma 10.11 Likelihood Ratio Tests
Chapter 11 Linear Models and Estimation by Least Squares	11.1 Introduction 11.2 Linear Statistical Models 11.3 The Method of Least Squares 11.4 Properties of the LS estimators 11.5 Inferences Concerning the Beta parameters 11.6 Inferences Concerning Linear Functions of the Model Parameters 11.7 Predictions 11.8 Correlation