SUFFICIENT STATISTIC Meaning and
Definition
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A "sufficient statistic" is a statistical measure that captures all the necessary information about a given data sample for making inferences about a parameter or a population. In other words, it summarizes the data in a concise manner while retaining all the relevant information needed for statistical analysis.
A sufficient statistic is capable of representing the entire sample information as it contains all the inferential knowledge about the underlying population distribution. It reduces the complexity of the data while still providing enough details to estimate parameters accurately. By using sufficient statistics, one can make inferences and draw conclusions about a population without needing to examine the entire dataset.
To be considered sufficient, a statistic must satisfy two primary conditions: (1) it must retain all the information relevant to the parameter being estimated, and (2) conditional on the sufficient statistic, the data should be independent of the parameter itself. In simpler terms, the value of a sufficient statistic should not depend on any other information or statistical observation apart from the sample itself.
Sufficient statistics are extensively used in statistical inference, hypothesis testing, and parameter estimation. They play a crucial role in various fields such as economics, biology, engineering, and social sciences, where it is necessary to draw meaningful conclusions from a limited amount of data.
Etymology of SUFFICIENT STATISTIC
The word "sufficient" comes from the Latin word "sufficiens", which means "sufficient" or "adequate". It was derived from the verb "sufficere", which combines "sub" (under) and "facere" (to make).
The term "sufficient statistic" was coined in the field of statistics to describe a statistic that contains all the relevant information about a parameter of interest in a statistical model. It was first introduced by British statistician Sir Ronald A. Fisher in 1922. The term "sufficient" is used to convey that the statistic provides enough information to make accurate inferences about the parameter without using the full data set.
