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The exhaustive list of topics in Statistical Inference in which we provide Help with Homework Assignment and Help with Project is as follows:

  • Basic concepts of point estimation: unbiasedness, consistency and efficiency of estimators, examples.
  • Finding Estimators: method of moments and maximum likelihood estimators, properties of maximum likelihood estimators, problems.
  • Lower Bounds for the Variance: Frechet-Rao-Cramer, Bhattacharya, Chapman-Robbins-Kiefer inequalities, generalization of Frechet-Rao-Cramer to higher dimensions, problems.
  • Data Reduction: Sufficiency, Factorization Theorem, Rao-Blackwell Theorem, minimal sufficiency, completeness, Lehmann-Scheffe Theorem, applications in deriving uniformly minimum variance estimators, Ancillary statistics, Basu’s Theorem, problems.
  • Invariance: Best equivariant estimators, problems.
  • Bayes and Minimax Estimation: Concepts and applications.
  • Testing of Hypotheses: Basic concepts, simple and composite hypotheses, critical region, types of error, most powerful test, Neyman-Pearson Lemma, applications.
  • Tests for Composite Hypotheses: Families with monotone likelihood ratio, uniformly most powerful tests, applications.
  • Unbiasedness: Unbiased tests, similarity and completeness, UMP unbiased tests.
  • Likelihood Ratio Tests - applications to one sample and two sample problems.
  • Invariant Tests.
  • Contingency Tables & Chi-square tests.
  • Wald’s sequential probability ratio test.
  • Interval estimation: methods for finding confidence intervals, shortest length confidence intervals, problems.