A Course in Large Sample Theory

Content: 
Front Matter....Pages i-ix
Front Matter....Pages 1-1
Modes of Convergence....Pages 3-7
Partial Converses to Theorem 1....Pages 8-12
Convergence in Law....Pages 13-18
Laws of Large Numbers....Pages 19-25
Central Limit Theorems....Pages 26-35
Front Matter....Pages 37-37
Slutsky Theorems....Pages 39-43
Functions of the Sample Moments....Pages 44-50
The Sample Correlation Coefficient....Pages 51-55
Pearson’s Chi-Square....Pages 56-60
Asymptotic Power of the Pearson Chi-Square Test....Pages 61-66
Front Matter....Pages 67-67
Stationary m-Dependent Sequences....Pages 69-74
Some Rank Statistics....Pages 75-86
Asymptotic Distribution of Sample Quantiles....Pages 87-93
Asymptotic Theory of Extreme Order Statistics....Pages 94-100
Asymptotic Joint Distributions of Extrema....Pages 101-104
Front Matter....Pages 105-105
A Uniform Strong Law of Large Numbers....Pages 107-111
Strong Consistency of Maximum-Likelihood Estimates....Pages 112-118
Asymptotic Normality of the Maximum-Likelihood Estimate....Pages 119-125
The Cramér—Rao Lower Bound....Pages 126-132
Asymptotic Efficiency....Pages 133-139
Front Matter....Pages 105-105
Asymptotic Normality of Posterior Distributions....Pages 140-143
Asymptotic Distribution of the Likelihood Ratio Test Statistic....Pages 144-150
Minimum Chi-Square Estimates....Pages 151-162
General Chi-Square Tests....Pages 163-171
Back Matter....Pages 172-214