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

Lecture

Probability and Statistics II: Estimation and Hypothesis Testing

In course

MATH-236: Probability and statistics II

Linear statistical methods, analysis of experiments, logistic regression. ...

Description

This lecture covers the Central Limit Theorem, confidence intervals, hypothesis testing for population mean, point estimation, qualities of estimators like bias and variance, and efficiency comparison of estimators. It emphasizes the importance of unbiased estimators.

Instructor

Darlene Goldstein

Official source

Ontological neighbourhood

Statistics

Statistical inference: Mathematical statistics, Statistical hypothesis testing

Related concepts (32)

Minimum-variance unbiased estimator

In statistics a minimum-variance unbiased estimator (MVUE) or uniformly minimum-variance unbiased estimator (UMVUE) is an unbiased estimator that has lower variance than any other unbiased estimator for all possible values of the parameter. For practical statistics problems, it is important to determine the MVUE if one exists, since less-than-optimal procedures would naturally be avoided, other things being equal. This has led to substantial development of statistical theory related to the problem of optimal estimation.

Efficiency (statistics)

In statistics, efficiency is a measure of quality of an estimator, of an experimental design, or of a hypothesis testing procedure. Essentially, a more efficient estimator needs fewer input data or observations than a less efficient one to achieve the Cramér–Rao bound. An efficient estimator is characterized by having the smallest possible variance, indicating that there is a small deviance between the estimated value and the "true" value in the L2 norm sense.

Estimation theory

Estimation theory is a branch of statistics that deals with estimating the values of parameters based on measured empirical data that has a random component. The parameters describe an underlying physical setting in such a way that their value affects the distribution of the measured data. An estimator attempts to approximate the unknown parameters using the measurements.

Density estimation

In statistics, probability density estimation or simply density estimation is the construction of an estimate, based on observed data, of an unobservable underlying probability density function. The unobservable density function is thought of as the density according to which a large population is distributed; the data are usually thought of as a random sample from that population. A variety of approaches to density estimation are used, including Parzen windows and a range of data clustering techniques, including vector quantization.

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.

Related lectures (58)

Estimation and Confidence Intervals

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

Confidence Intervals: Gaussian Estimation

Explores confidence intervals, Gaussian estimation, Cramér-Rao inequality, and Maximum Likelihood Estimators.

Estimation Methods in Probability and Statistics

Discusses estimation methods in probability and statistics, focusing on maximum likelihood estimation and confidence intervals.

Statistics for Data Science: Introduction to Statistical Methods

Covers the fundamental concepts of statistics and their application in data science.

Statistics: Hypothesis Testing & Confidence Intervals