Let P be a probability distribution on some space \(\mathcal {X}\) . A random sample from P is a collection of independent random variables X 1, …, X n , all with the same distribution P. We then also call X 1, …, X n independent copies of a population random variable X, where X has distribution P. In statistics, the probability measure P is not known, and the aim is to estimate aspects of P using the observed sample X 1, …, X n . Formally, an estimator, say T, is any given known function of the data, i.e., T = T( X 1, …, X n ).

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Estimation: Overview

  • Sara van de Geer

摘要

Let P be a probability distribution on some space \(\mathcal {X}\) . A random sample from P is a collection of independent random variables X 1, …, X n , all with the same distribution P. We then also call X 1, …, X n independent copies of a population random variable X, where X has distribution P. In statistics, the probability measure P is not known, and the aim is to estimate aspects of P using the observed sample X 1, …, X n . Formally, an estimator, say T, is any given known function of the data, i.e., T = T( X 1, …, X n ).