STAT 135,  FALL 06
Ani  Adhikari

Week 1.  Review of most-needed probability facts, in the context of estimating the population mean (or proportion, in the dichotomous case) from a random sample drawn with replacement. Confidence intervals.
Week 2.   As above, when the sampling is  without replacement.  Careful derivation of unbiased estimates of the population mean/proportion, and population variance.  Confidence intervals, again.  [Chapter 7 Sections 1-3.]
Week 3.  Estimating parameters in a distribution: the method of moments.  [Chapter 8 Sections 1-4.] Review of how to compute with gamma densities, and the special case of the chi-squared. Also, some basic technique: moment generating functions.  [Chapter 4 Section 5.]
Week 4.  Approximation by the delta-method, or propagation of error.  [Chapter 4 Section 6.] This ends the discussion on method of moments.  A more powerful way of estimating parameters in a distribution: the method of maximum likelihood, and good properties of the MLE when the sample is large. [Chaper 8 Section 5.]
Week 5.  Proofs (sort of) of the large sample properties of the MLE. [Chapter 8 Section 5.]  Efficiency [Chapter 8 Section 7] and sufficiency [Chapter 8 Section 8].
Week 6.  The language of testing, likelihood ratio tests, Neyman-Pearson Lemma [Chapter 9 Sections 1-3]. Duality of tests and confidence intervals [Chapter 9 Section 3.] Generalized likelihood ratio tests [Chapter 9 Section 4]. Calculating power [lecture, homework 6].
Week 7.  Parametric tests for means [Chapter 9 Section 4, Chapter 11 Sections 1-2.2, 3.1].  This includes tests for proportions [lecture, homework].  Uniformly most powerful tests [Chapter 9 Section 2.3].  Chi-squared test (theory) for the multinomial [Chapter 9 Section 5].
Week 8.  Chi-squared tests (method) for the multinomial [Chapter 9 Section 5 and Chapter 13 Sections 3-4].  Brief review and midterm.  What you need to know for the midterm is listed here.
Week 9. Paired comparisons:  McNemar's test [Chapter 13 Section 5], Wilcoxon's signed-rank test [Chapter 11 Sec 3.2].  Nonparametric tests for comparing two independent samples: Wilcoxon's rank-sum test, also known as the Mann-Whitney test [Chapter 11 Section 2.3].
Week 10. Comparing several samples: Bonferroni's method [page 487, numbered 12.2.2.2!].  One-way ANOVA: decomposition of sum of squares, F-test for equality of means (based on normality and other assumptions) [Chapter 12 Section 2]; Kruskal-Wallis nonparametric test for equality of distributions [Chapter 12 Section 2.3].
Week 11.  The least-squared predictor of Y given X [Chapter 4 Section 4.2].  The least-squares linear predictor of y given x [Chapter 14 Section 1], and the regression effect [Chapter 14 Section 2.3].  The bivariate normal distribution (review of 134 material) and inference in the simple linear regression [Chapter 14 Section 2, handout].
Week 12.  Complete the discussion of inference in simple linear regression [Chapter 14 Section 2, handout; which, along with the results of HW 9, includes most of the answers to Problems 10-14 of Chapter 14]. Parallels and differences between multiple regression and simple regression [Chapter 14 Section 4.5 (ignore the matrices for now) and Section 5].  Begin the mathematics of multiple regression [Chapter 14 Section 3].
Week 13. Inference in multiple regression [Chapter 14 Section 4].  The proofs we did look different from those in the text but they cover the same ground: Theorems A and B of 14.4.1, Theorems A and B of 14.4.2, Theorem A of 14.4.3, Theorem A of 14.4.4, the t-test of 14.4.5.  In addition we have the sum of squares decomposition and the F-test of whether all the slopes are 0.
Week 14.  The partial F-test of whether a subset of the slopes is 0.  Then on to Bayesian estimation [Chapter 8 Section 6 and Example E of 3.5.2].
Week 15. Review.