The TA will have some material for the tutorial. The handouts used for the tutorial are here .
Old term tests and exams are posted on the course OWL page (this is different than the page I used last year).
Handouts used in the lectures.
Jan 8, 2018 : course outline and ch8-2intro.pdf
This uses data from the text, It comes with a CD with the text. The data set is also available from http://www.stat.berkeley.edu/~rice/Book3ed/ where you click on the Data Sets link. It comes in various formats. Often csv format is most useful as many statsitical packages can read these, including R. ASCII is also a useful version in the same sense.
illinois60.txt this is a data set that we use for some gamma fit data examples later in the course.
Jan 10 : Ch8-StatModels.pdf This material is not from the text, but some background material to Chapters 8 and 9.
Jan 12 : Continue with example from Jan 10 handout.
brief introduction to empirical distribution function (edf) with an R example. edf1.R
This R script is an Rgui file, but you can copy these commands to an Rstudio script if you prefer to use Rstudio
January 15, 2018 :
The student can work through the first at home, and the second we will look at in class. At this point only part of these R scripts can be used. It also includes some methods on how to find the approximate variance and its estimator, of
sqrt(n)*( theta.hat_n – theta)
which is based on the so called delta method to be discussed later in the course.
Jan 17, 2018 : continue with
ch8-3-estimator-prop.pdf Some handout files are named to indicate they are based on or give examples for sections in the Rice text. Here the handout refers to Chapter 8 section 3.
Jan 22, 2018
The next two files give a review of two main methods of constructing estimators, the method of moments and maximum likelihood. In this course we also find how to obtain their approximate distributions.
Ch8-4MethodofMoments.pdf This is a review of a topic in the second year course Stat 2858
Ch8-5-MLE-I.pdf Most of this handout is also a review of material from Stat 2858
Jan 24, 2018
Continue with MLE-I handout from Jan 22
FisherInfoComments.pdf relation between Fisher’s information for Binomial and iid Bernoulli experiments
gamma fit with method of moments R script
Some data sets for which a gamma model is appropriate
illinois60 , illinois61 , illinois62 , illinois63 , illinois64
Also the coal data set earlier in this file follows a gamma distribution
January 31, 2018
Normal CI normalCI.r This file considers CI for the parameters for a normal model. It also introduces the idea of confidence interval coverage rates.
Reminder there is a test next week on February 7 during the tutorial time. It will be held in WSC 240 (tutorial room) and WSC 248 (since there are too many students for exam writing in WSC 240). About 20 student will write in WSC 248.
Material covered : The lecture material in the handouts up to today’s class, but not including the delta method. Material in the text Sections 8.2 , 8.3 , 8.4 , 8.5. There will be no questions on R coding or implementation, even though this is important for statistical applications.
The exam will include a formula sheet, which is given here formulae-Stat3858.pdf
It will also include the statistical tables, as needed, from the Appendix in Rice’s text.
Normal table normal table
February 2, 2018 : I the previous couple of lectures we obtained a method to approximate the distribution of the nomalized MLE in the regular case.
Generally for the method of moments estimators there is also a normal approximation for normalized estimators.
DeltaMethod.pdf This allows us to find a normal approximation for the distribution of method of moments estimators in many cases – look at this after Fisher’s information
gamma method of moments R script examples
Some files for next week
Sect 8.7 and 8.8 Cramer Rao These are the beginning of understanding why MLE is the best estimator, at least in the regular case.
February 9, 2018 : Continue with Sec 8.7-8 handout
Feb 12, 2018 :
There is one other method based on simulation to approximate the (sampling) distribution of some “test statstistic” - ie the type needed to construct confidence intervals. These methods are bootstrap methods. For now we consider the parametric bootstrap, and then later in the course the nonparametric bootstrap.
Bootstrap.pdf and review the later part of Ch8-5-MLE-II.pdf
Here is an R script example to describe this method, so we can see how it is related to simulation methods described earlier. This material is briefly described in Rice Secion 8.5, page 284-85.
February 12 and 14, 2018
Chapter 9.1 hypothesis testing
Neyman Pearson lemma
February 16, 2018
material related to chapter 9 Rice.