Statistical Inference II

Unit 1- Consistency and asymptotic normality (CAN) of real and vector parameters. Invariance of
consistency under continuous transformation. Invariance of CAN estimators under differentiable
transformations, generation of CAN estimators using central limit theorem.
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Unit 2- Method of moments, method of maximum likelihood, Special cases such as exponential class of
densities and multinomial distribution, Cramer-Huzurbazar theorem, method of scoring.
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Unit 3- Tests based on MLEs. Likelihood ratio tests, asymptotic distribution of log likelihood ratio, Wald
Test, Score Test, locally most powerful tests. Applications to categorical data analysis, three
dimensional contingency tables, Pearson’s chi-square test and LR test.
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Unit 4- Asymptotic comparison of tests. Asymptotic Relative Efficiency (Pitman’s). Introduction to
Nonparametric Methods, one sample tests
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Unit 5- chapter 5View Link

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