1. HW 1 April 7: 7.2 (also get method of moments estimators, and use them to start a Newton-type optimizer in two variables such as nlm in R, and try to deal with the nonnegative constraints with a transformation ..., sample R commands), 7.3, 7.6 , 7.16cd (not correctly stated)
2. HW 2 April 14: 7.19, 7.20, 7.24, 7.33 (regression with intercept 0 is right for the original Hubble data from the 1929 paper showing expansion of the universe)
3. HW 3 April 21: 7.40, 7.44, 7.47, 7.49 (skip Section 7.3.4)
4. HW 4 April 28: 8.2 (good problem to review p-values), 8.6, 8.7 (For a), there is a very simple way to design the test using the beta distribution; R simulation, comments. For b), the likelihood ratio statistic does not simplify much beyond evaluation at the MLEs because the sufficient statistics are not simple -- not a problem since the main testing tool is Wilks' Theorem p. 490 which gives χ² (1) asymptotics on -2 log(lambda), and this can be used numerically: reject H_0 if -2 log(lambda) > 3.841. Note also that the R function "fitdistr" in the MASS library will fit the Weibull and exponential families, and provides the estimates, standard errors from asymptotic theory for MLEs for z-tests, and numerical values of the log-likelihood function for χ² tests.), 8.10 (scaling technique)
   Example of LRT and MLE testing for Weibull, quake time data
5. HW 5 May 12: 8.14, 8.22 (power plot), 8.31, 8.38, 8.42 (comments)
6. HW 6 May 19: 10.3 (how does the Delta method compare?), 10.9 (skip (b) and the other related parts), 10.34 (focus on Theorems 10.1.12 (Fisher) and 10.3.3 (Wilks) in this Chapter, for #34 try a simulation with n=20, p=1/3 for comparison, R code)
7. HW 7 May 26: 9.2 (does that look like a prediction interval?), 9.6
8. HW 8 May Jun 2: 9.8, 9.14 (lecture on confidence regions), 9.48, 9.52abde (the (d) interval comes from a simple pivot, invert the interval to get the test and compare with (a), R code for three confidence intervals for sigma, 9.52e )(not turned in!)

     April 2017     
Su Mo Tu We Th Fr Sa
                   1 
 2  3  4  5  6  7  8  first class, Satterthwaite application 
 9 10 11 12 13 14 15  intro to EM algorithm, EM simply
16 17 18 19 20 21 22  complete family
23 24 25 26 27 28 29  formal testing history 

      May 2017      
Su Mo Tu We Th Fr Sa
    1  2  3  4  5  6  midterm Friday  
 7  8  9 10 11 12 13  inconsistent MLE, numerical se values for mle
14 15 16 17 18 19 20  Example 10.3.2 Wilks' Theorem  
21 22 23 24 25 26 27  exponential example in book: Wald, LRT Wilks', LRT exact; recent paper on binomial case, R code for confidence of Wald, LRT, and score intervals
28 29 30 31           Memorial Day, exp pivots, unif(0, theta) pivot 
                     
      June 2017     
Su Mo Tu We Th Fr Sa
             1  2  3 
 4  5  6  7  8  9 10  binomial intervals, bootstrap se, last class
11 12 13 14 15 16 17 
18 19 20 21 22 23 24 
25 26 27 28 29 30