Mathematical Statistics

Published

18 October 2026

A course in mathematical statistics: from the basic notions of point estimation to linear regression and statistical hypothesis testing. The first part of the course is devoted to estimation theory β€” statistics, consistency and unbiasedness, methods for constructing estimators (moments, maximum likelihood), comparison of estimators, sufficient statistics, and confidence intervals. The second part covers the Bayesian approach, linear regression, and hypothesis testing, including in linear models, goodness-of-fit tests, and correlation coefficients.

Prerequisites

The course builds on β€œProbability Theory”: random variables and vectors, modes of convergence, the central limit theorem.

Assessment format

Assessment follows the current rules of the semester (tests, colloquium, exam); see the department’s current schedule.

Contents

Part I

  1. Introduction. Statistics, estimators
  2. Modes of convergence of vectors. The delta method
  3. Methods for constructing estimators
  4. Comparison of estimators
  5. Sufficient statistics. Optimal estimators
  6. Confidence intervals

Part II

  1. Bayesian estimation
  2. Linear regression: introduction
  3. Hypothesis testing: introduction
  4. Hypothesis testing in linear models
  5. Goodness-of-fit tests
  6. Correlation coefficients

See also the exam questions.

About this text

This text was prepared based on notes from seminar sessions.

Author: M.A. Nedoshivin
Email: nedoshivin.ma@phystech.edu

Found a typo or an error? Email the address above.

The materials are distributed under the CC BY-NC-SA 4.0 license; see the β€œAbout the project” page for details.