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Related Concept Videos

Weighted Mean00:57

Weighted Mean

While taking the arithmetic, geometric, or harmonic mean of a sample data set, equal importance is assigned to all the data points. However, all the values may not always be equally important in some data sets. An intrinsic bias might make it more important to give more weightage to specific values over others.
For example, consider the number of goals scored in the matches of a tournament. While computing the average number of goals scored in the tournament, it may be more important to...
What are Estimates?01:06

What are Estimates?

It isn't easy to measure a parameter such as the mean height or the mean weight of a population. So, we draw samples from the population and calculate the mean height or mean weight of the individuals in the sample. This sample data acts as a representative measure of the population parameter. These sample statistics are known as estimates. 
The estimate for the mean of a sample is denoted by ͞x, whereas the mean of the population is designated as μ. Further, parameters such as the mean,...
Estimating Population Mean with Unknown Standard Deviation01:22

Estimating Population Mean with Unknown Standard Deviation

In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
William S. Gosset (1876–1937) of the Guinness...
Prediction Intervals01:03

Prediction Intervals

The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y. 
The...
Distributions to Estimate Population Parameter01:26

Distributions to Estimate Population Parameter

The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...
Estimating Population Mean with Known Standard Deviation01:16

Estimating Population Mean with Known Standard Deviation

To construct a confidence interval for a single unknown population mean μ, where the population standard deviation is known, we need sample mean as an estimate for μ and we need the margin of error. Here, the margin of error (EBM) is called the error bound for a population mean (abbreviated EBM). The sample mean is the point estimate of the unknown population mean μ.
The confidence interval estimate will have the form as follows:
(point estimate - error bound, point estimate + error bound)
The...

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Related Experiment Video

Updated: May 9, 2026

Inverse Probability of Treatment Weighting (Propensity Score) using the Military Health System Data Repository and National Death Index
06:55

Inverse Probability of Treatment Weighting (Propensity Score) using the Military Health System Data Repository and National Death Index

Published on: January 8, 2020

Information estimators for weighted observations.

Hideitsu Hino1, Noboru Murata

  • 1Department of Computer Science, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki, 305-8573, Japan. hinohide@cs.tsukuba.ac.jp

Neural Networks : the Official Journal of the International Neural Network Society
|July 18, 2013
PubMed
Summary
This summary is machine-generated.

This study introduces new information estimators for probability distributions, particularly for weighted data. These improved methods are computationally efficient and applicable to data compression and regression.

Keywords:
Entropy estimationInformation estimationWeighted data

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Area of Science:

  • Statistics
  • Information Theory
  • Machine Learning

Background:

  • Shannon information content is crucial for probability distributions.
  • Estimating information content from data is vital in statistics, information theory, and machine learning.

Purpose of the Study:

  • Propose novel information estimators for probability distributions.
  • Develop estimators capable of handling weighted data.
  • Enhance computational efficiency and remove tuning parameters from existing methods.

Main Methods:

  • Developed weighted information estimators for probability distributions.
  • Modified estimators for computational efficiency and parameter-free operation.
  • Extended methods to estimate cross-entropy, entropy, and Kullback-Leibler divergence.

Main Results:

  • Proposed information estimators effectively handle weighted data.
  • Modified estimators demonstrate improved computational efficiency and no tuning parameter requirement.
  • Numerical experiments confirm the proper functioning of the developed estimators.

Conclusions:

  • The proposed information estimators are effective for analyzing probability distributions, especially with weighted data.
  • The enhanced, parameter-free estimators offer computational advantages.
  • Applications include distribution-preserving data compression and ensemble regression weight optimization.