The most important target of Statistics is to draw inferences
about a population from the analysis of a sample drawn from that
population. The theory of estimation was set up by Prof. R. A.
Fisher. What is a parameter space? Consider X = random variable
with p.d.f f (x ,θ ), where θ∈Θ. The set Θ, which is the set of
all possible values of θ, is called the parameter space.
Characteristics of Estimators: A good estimator should satisfy
the following criteria: Let us now explain briefly the first
criteria Consistency estimator: An estimator is said to be
sufficient for a parameter, if it contains all the information
in the sample regarding the parameter. If S= s(x1, x2.... xn) is
an estimator of a parameter θ, based on a sample x1, x2.... xn
of size n from the population with density function f (x, θ)
such that the conditional distribution of x1, x2.... xn given S
is independent of θ, then S is sufficient estimator for θ.
Theorems Based on Sufficiency: The necessary and sufficient
condition for a distribution to