Statistical Inference

Paper I : Statistical Inference

UNIT – I

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.

UNIT – II

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.

UNIT – III

Neyman-Pearson’s lemma and its applications for finding most powerful tests for simple
hypothesis against simple alternative. Tests based on t, F and χ2 distributions.

UNIT-IV

Likelihood ratio tests and their reduction to standard tests. Large sample tests, variance –
stabilizing transformations. Interval estimation, Pivotal quantity and its use in finding
confidence intervals, concept of best confidence intervals.