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

Lecture

Sampling Theory: Statistics and Inference

Description

This lecture covers sampling theory, statistics, and inference, focusing on the sampling distribution of statistics under different distributions. It explains the concept of a statistic, sampling distribution, and ancillary statistic. The lecture also delves into sufficient statistics and their role in providing information about unknown parameters.

Official source

Ontological neighbourhood

Statistics

Statistical inference: Mathematical statistics

Related concepts (32)

Sampling (statistics)

In statistics, quality assurance, and survey methodology, sampling is the selection of a subset or a statistical sample (termed sample for short) of individuals from within a statistical population to estimate characteristics of the whole population. Statisticians attempt to collect samples that are representative of the population. Sampling has lower costs and faster data collection compared to recording data from the entire population, and thus, it can provide insights in cases where it is infeasible to measure an entire population.

Sufficient statistic

In statistics, a statistic is sufficient with respect to a statistical model and its associated unknown parameter if "no other statistic that can be calculated from the same sample provides any additional information as to the value of the parameter". In particular, a statistic is sufficient for a family of probability distributions if the sample from which it is calculated gives no additional information than the statistic, as to which of those probability distributions is the sampling distribution.

Ancillary statistic

An ancillary statistic is a measure of a sample whose distribution (or whose pmf or pdf) does not depend on the parameters of the model. An ancillary statistic is a pivotal quantity that is also a statistic. Ancillary statistics can be used to construct prediction intervals. They are also used in connection with Basu's theorem to prove independence between statistics. This concept was first introduced by Ronald Fisher in the 1920s, but its formal definition was only provided in 1964 by Debabrata Basu.

IPad

The iPad is a brand of iOS and iPadOS-based tablet computers that are developed by Apple Inc, first introduced on January 27, 2010. The iPad range consists of the original iPad lineup and the flagship products iPad Mini, iPad Air, and iPad Pro. The iPhone's iOS operating system (OS) was initially used for the iPad but in September 2019, its OS was switched to a fork of iOS called iPadOS that has better support for the device's hardware and its user interface is customized for the tablets' larger screens.

IPad Pro

The iPad Pro is a premium model of Apple's iPad tablet computer. It runs iPadOS, a tablet-optimized version of the iOS operating system. The original iPad Pro was introduced in September 2015, and ran iOS 9. It had an A9X chip, and came in two sizes: 9.7-inch and 12.9 inch. The second-generation iPad Pro, unveiled in June 2017, had an upgraded A10X Fusion chip and swapped the 9.7-inch screen for a larger 10.5-inch display. The third-generation iPad Pro, announced in October 2018, eliminated the home button, and featured Face ID; it came in 11-inch and 12.

Related lectures (53)

Sufficient Statistics: Understanding Data Compression

Explores sufficient statistics, data compression, and their role in statistical inference, with examples like Bernoulli Trials and exponential families.

Sampling Distributions: Understanding Ancillary Statistics

Explores ancillary statistics, sufficiency, and minimally sufficient statistics in sampling distributions.

Sampling Theory: Statistics for Mathematicians

Covers the theory of sampling, focusing on statistics for mathematicians.

Sampling Distributions: Theory and Applications

Explores sampling distributions, estimators' properties, and statistical measures for data science applications.

Entropy and Sampling Theory