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FIGURES FOR

CHAPTER 2

STATISTICAL INFERENCE

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Section 2.1 Example 1


Figure 2.1

The normal distribution: Y N(,2).


Figure 2.2An unbiased estimator has a sampling distribution that is centered over the population parameter. Y is unbiased because its sampling distribution is centered over .


Figure 2.3The estimator is asymptotically unbiased; its sampling distribution becomes centered over 2 as n→∞.


Figure 2.4

The variance of Y decreases as the sample size increases.


Figure 2.5

The comparative efficiency of three estimators.


Figure 2.6

Simulated samplingdistributions (uniformpopulation).


Figure 2.7

Yi i.i.d.(,2).


Figure 2.8The least squares estimator is the value of that minimizes the sum of squares function S.


Figure 2.9

p-value for Example 10.


Figure 2.10

Rejection regions.


Figure 2.12

Y is lognormally distributed: ln Y N(, 2).


Figure 2.13

Simulated samplingdistributions for the statistic t = √n(Y − )/sunder nonnormality.


Figure 2.14A histogram of the monthly return on IBM stock, July 1963–June 1968.


Figure 2.15Deterministic and stochastic trends.


Figure 2.16The rate of return on IBM stock, July 1963–June 1968.