Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Maximum Likelihood Estimation

In course

MATH-442: Statistical theory

This course gives a mostly rigourous treatment of some statistical methods outside the context of standard likelihood theory. ...

Description

This lecture covers the problem of point estimation, focusing on maximum likelihood estimators and their relationship with Kullback-Leibler divergence. It discusses the asymptotic properties of the MLE, including consistency and asymptotic normality. The lecture also explores examples such as the geometric and uniform distributions, illustrating the properties of MLEs. The asymptotic theory for MLEs is presented, emphasizing the regularity conditions required for consistency. The lecture concludes with a discussion on the asymptotic distribution of the MLE and the critical aspect of proving its consistency.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Instructor

Yoav Zemel

Official source

Ontological neighbourhood

Statistics

Statistical inference: Mathematical statistics

Related concepts (32)

Maximum likelihood estimation

In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable. The point in the parameter space that maximizes the likelihood function is called the maximum likelihood estimate. The logic of maximum likelihood is both intuitive and flexible, and as such the method has become a dominant means of statistical inference.

Asymptotic theory (statistics)

In statistics, asymptotic theory, or large sample theory, is a framework for assessing properties of estimators and statistical tests. Within this framework, it is often assumed that the sample size n may grow indefinitely; the properties of estimators and tests are then evaluated under the limit of n → ∞. In practice, a limit evaluation is considered to be approximately valid for large finite sample sizes too. Most statistical problems begin with a dataset of size n.

Asymptotic distribution

In mathematics and statistics, an asymptotic distribution is a probability distribution that is in a sense the "limiting" distribution of a sequence of distributions. One of the main uses of the idea of an asymptotic distribution is in providing approximations to the cumulative distribution functions of statistical estimators. A sequence of distributions corresponds to a sequence of random variables Zi for i = 1, 2, ..., I .

Estimator

In statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule (the estimator), the quantity of interest (the estimand) and its result (the estimate) are distinguished. For example, the sample mean is a commonly used estimator of the population mean. There are point and interval estimators. The point estimators yield single-valued results. This is in contrast to an interval estimator, where the result would be a range of plausible values.

Continuous uniform distribution

In probability theory and statistics, the continuous uniform distributions or rectangular distributions are a family of symmetric probability distributions. Such a distribution describes an experiment where there is an arbitrary outcome that lies between certain bounds. The bounds are defined by the parameters, and which are the minimum and maximum values. The interval can either be closed (i.e. ) or open (i.e. ). Therefore, the distribution is often abbreviated where stands for uniform distribution.

Related lectures (36)

Likelihood Ratio Test: Hypothesis Testing

Covers the Likelihood Ratio Test and hypothesis testing methods using Maximum Likelihood Estimators.

Continuous Random Variables

Covers continuous random variables, probability density functions, and distributions, with practical examples.

Confidence Intervals: Definition and Estimation

Explains confidence intervals, parameter estimation methods, and the central limit theorem in statistical inference.

Estimation and Confidence Intervals

Explores bias, variance, and confidence intervals in parameter estimation using examples and distributions.

Estimation Methods in Probability and Statistics