# Class Notes for STATS 426 at University of Michigan - Ann Arbor (U OF M)

U OF MSTATS 426Moulinath BanerjeeFall

## STATS 426 Lecture Notes - Lecture 1: Bernoulli Distribution, Bayes Estimator, Fair Coin

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9 Mar 2016
22
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U OF MSTATS 426Moulinath BanerjeeFall

## STATS 426 Lecture Notes - Lecture 3: Multivariate Random Variable, Random Variable, Open Set

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9 Mar 2016
9
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U OF MSTATS 426Moulinath BanerjeeFall

## STATS 426 Lecture Notes - Lecture 13: Bias Of An Estimator, Taylor Series, Independent And Identically Distributed Random Variables

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9 Mar 2016
8
Large sample properites of the mle and variance. In this section we study some of the large sample properties of the mle in standard parametric models
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U OF MSTATS 426Moulinath BanerjeeFall

## STATS 426 Lecture Notes - Lecture 5: Probability Distribution, Universal Windows Platform Apps, Standard Deviation

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9 Mar 2016
4
Some inequalities and the weak law of large numbers. We rst introduce some very useful probability inequalities. Markov"s inequality: let x be a non-ne
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U OF MSTATS 426Moulinath BanerjeeFall

## STATS 426 Lecture Notes - Lecture 11: Maximum Likelihood Estimation, Likelihood Function, Independent And Identically Distributed Random Variables

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9 Mar 2016
11
We discuss (a) estimation by the method of moments and (b) maximum likelihood. As before, our set-up is the following: x1, x2, . , xn are i. i. d. obse
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U OF MSTATS 426Moulinath BanerjeeFall

## STATS 426 Lecture Notes - Lecture 9: Nuisance Parameter, Independent And Identically Distributed Random Variables, Random Variable

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9 Mar 2016
6
In statistical jargon, the set of plausible values will be called a con dence set and the degree of plausibility will be called the level of con dence.
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U OF MSTATS 426Moulinath BanerjeeFall

## STATS 426 Lecture Notes - Lecture 8: Gamma Distribution, Independent And Identically Distributed Random Variables, Orthogonal Matrix

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9 Mar 2016
6
The gamma distribution: the gamma function is a real-valued non-negative function de ned on (0, ) in the following manner. ( ) =z x 1 e x dx , > 0 . Tw
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U OF MSTATS 426Moulinath BanerjeeFall

## STATS 426 Lecture Notes - Lecture 7: Simple Random Sample, Random Variable, Independent And Identically Distributed Random Variables

OC5495645 Page
9 Mar 2016
11
The goal is to estimate the mean and the variance of a variable of interest in a nite population by collecting a random sample from it. Suppose there a
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U OF MSTATS 426Moulinath BanerjeeFall

## STATS 426 Lecture Notes - Lecture 12: Bias Of An Estimator, Multivariate Random Variable, Exponential Family

OC5495646 Page
9 Mar 2016
9
We saw in the above section that for a variety of di erent models one could di erentiate the log likelihood function with respect to the parameter and
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U OF MSTATS 426Moulinath BanerjeeFall

## STATS 426 Lecture 6: Chapter 6

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9 Mar 2016
9
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U OF MSTATS 426Moulinath BanerjeeFall

## STATS 426 Lecture 2: Chapter 2

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9 Mar 2016
12
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