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Reduction of Data
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Contents
Statistical Inference
Subsections
Reduction of Data
Types of inference
Frequentist inference
Sufficient Statistics
Factorization Criterion
The Exponential Family of Distributions
Likelihood
Information in a Sample
Estimation
Some Properties of Estimators
Unbiasedness
Mean Square Error
Consistency
Efficiency
Cramér-Rao Lower Bound
Minimum Variance Estimation
When can the MVB be Attained?
Properties of Maximum Likelihood Estimates
Interval Estimates
Pivotal Method
Confidence Interval for Population Quantile
Hypothesis Testing
Basic Concepts and Notation
Introduction
Power Function and Significance Level
Relation between Hypothesis Testing and Confidence Intervals
Randomized Tests
Evaluation of and Construction of Tests
Unbiased and Consistent Tests
Certain Best Tests
Neyman Pearson Theorem
Uniformly Most Powerful (UMP) Test
Likelihood Ratio Tests
Background
The Likelihood Ratio Test Procedure
Some Examples
Asymptotic Distribution of
Bob Murison 2000-10-31
