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.

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• Publication Date: March 20, 2021
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