## Applications to Statistical Inference under Normality

5.6.1. Estimation

Statistical inference is concerned with parameter estimation and parameter inference. The latter will be discussed next in this section.

In a broad sense, an estimator of a parameter is a function of the data that serves as an approximation of the parameter involved. For example, if X1, X2,Xn is a random sample from the N(д, a2)-distribution, then the sample mean X = (1 /n) Хд = Xj may serve as an estimator of the unknown parameter д (the population mean). More formally, given a data set {X1, X2,.Xn } for which the joint distribution function depends on an unknown parameter (vector) в, an estimator of в is a Borel-measurable function 6 = gn (X1,.Xn) of the data that serves as an approximation of в ...

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