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Statistical Inference 2.1 | code- 693 | 200 +Pages
SYLLABUS- STATISTICAL INFERENCE 2.1, Chapter – 1
Point Estimation. Characteristics of a good estimator: Unbiasedness, consistency,
sufficiency and efficiency. Method of maximum likelihood and properties of maximum
likelihood estimators (without proof). Method of minimum Chi-square. Method of Least
squares and method of moments for estimation of parameters. Problems and examples.
Chapter – 2
Sufficient Statistics, Cramer-Rao inequality and its use in finding MVU estimators.
Statistical Hypothesis (simple and composite). Testing of hypothesis. Type I and Type II
errors, significance level, p-values, power of a test. Definitions of Most Powerful (MP),
Uniformly Most Powerful (UMP) and Uniformly Most Powerful Unbiased (UMPU) tests.
Chapter – 3
Neyman-Pearson's lemma and its applications for finding most powerful tests for simple
hypothesis against simple alternative. Tests based on t, F and _2 distributions.
Chapter – 4
Likelihood ratio tests and their reduction to standard tests. Large sample tests. Interval
estimation, Pivotal quantity and its use in finding confidence intervals, concept of best
confidence intervals.
Point Estimation. Characteristics of a good estimator: Unbiasedness, consistency,
sufficiency and efficiency. Method of maximum likelihood and properties of maximum
likelihood estimators (without proof). Method of minimum Chi-square. Method of Least
squares and method of moments for estimation of parameters. Problems and examples.
Chapter – 2
Sufficient Statistics, Cramer-Rao inequality and its use in finding MVU estimators.
Statistical Hypothesis (simple and composite). Testing of hypothesis. Type I and Type II
errors, significance level, p-values, power of a test. Definitions of Most Powerful (MP),
Uniformly Most Powerful (UMP) and Uniformly Most Powerful Unbiased (UMPU) tests.
Chapter – 3
Neyman-Pearson's lemma and its applications for finding most powerful tests for simple
hypothesis against simple alternative. Tests based on t, F and _2 distributions.
Chapter – 4
Likelihood ratio tests and their reduction to standard tests. Large sample tests. Interval
estimation, Pivotal quantity and its use in finding confidence intervals, concept of best
confidence intervals.
Kindle Edition
Published March 20, 2021
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