Why is consistency of an estimator important?

Why is consistency of an estimator important?

Consistency is important mainly with observational data where there is no possibility of repetition. Here, at least we want to know that if the sample is large the single estimate we will obtain will be really close to the true value with high probability, and it is consistency that guarantees that.

Why is consistency a desirable property for estimators?

This intuitively means that if a PE is consistent, its distribution becomes more and more concentrated around the real value of the population parameter involved. Therefore, we could say that as N increases, the probability that the estimator ‘closes in’ on the actual value of the parameter approaches 1.

What do you mean by consistency of an estimator?

If the sequence of estimates can be mathematically shown to converge in probability to the true value θ0, it is called a consistent estimator; otherwise the estimator is said to be inconsistent. Consistency as defined here is sometimes referred to as weak consistency.

Why do we need estimators in statistics?

In statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule (the estimator), the quantity of interest (the estimand) and its result (the estimate) are distinguished. For example, the sample mean is a commonly used estimator of the population mean.

What is consistency in statistical inference?

From Wikipedia, the free encyclopedia. In statistics, consistency of procedures, such as computing confidence intervals or conducting hypothesis tests, is a desired property of their behaviour as the number of items in the data set to which they are applied increases indefinitely.

What does consistency mean in statistics?

Consistency refers to logical and numerical coherence. Context: An estimator is called consistent if it converges in probability to its estimand as sample increases (The International Statistical Institute, “The Oxford Dictionary of Statistical Terms”, edited by Yadolah Dodge, Oxford University Press, 2003).

What makes an estimator a good estimator?

A good estimator must satisfy three conditions: Unbiased: The expected value of the estimator must be equal to the mean of the parameter. Consistent: The value of the estimator approaches the value of the parameter as the sample size increases.

Why is unbiased estimator important?

The theory of unbiased estimation plays a very important role in the theory of point estimation, since in many real situations it is of importance to obtain the unbiased estimator that will have no systematical errors (see, e.g., Fisher (1925), Stigler (1977)).

What does it mean for an estimator to be the most efficient estimator?

best possible
An efficient estimator is an estimator that estimates the quantity of interest in some “best possible” manner. The notion of “best possible” relies upon the choice of a particular loss function — the function which quantifies the relative degree of undesirability of estimation errors of different magnitudes.

What can you use to check consistency of an estimator?

The sample mean and sample variance are two well-known consistent estimators. The idea of consistency can also be applied to model selection, where you consistently select the “true” model with the associated “true” parameters. For example, a goodness of fit test can also be used as measure of consistency.