Page 368 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Unit 29: Methods of Point Estimation and Interval Estimation
Dilfraz Singh, Lovely Professional University

Unit 29: Methods of Point Estimation and Notes

Interval Estimation

CONTENTS
Objectives
Introduction
29.1 Methods of Point Estimation
29.2 Interval Estimation
29.3 Summary
29.4 Key-Words
29.5 Review Questions
29.6 Further Readings

Objectives

After reading this unit students will be able to:
• Discuss the Methods of Point Estimation.
• Explain the Interval Estimation.
Introduction

The object of sampling is to study the features of the population on the basis of sample observations.
A carefully selection sample is expected to reveal these features, and hence we shall infer about the
population from a statistical analysis of the sample. This process is known as Statistical Inference.
There are two types of problems. Firstly, we may have no information at all about some characteristics
of the population, especially the values of the parameters involved in the distribution, and it is required
to obtain estimates of these parameters. This is the problem of Estimation. Secondly, some information
or hypothetical values of the parameters may be available, and it is required to test how far the
hypothesis is tenable in the light of the information provided by the sample. This is the problem of
Test of Hypothesis or Test of Significance.
Suppose we have a random sample x , x , ... x on a variable x, whose distribution in the population
1 2 n
involves an unknown parameter θ . It is required to find an estimate of θ on the basis of sample
values. The estimation is done in two different ways: (i) Point Estimation, and (ii) Interval Estimation.
In point estimation, the estimated value is given by a single quantity, which is a function of sample
observations (i.e. statistic). This function is called the ‘estimator’ of the parameter, and the value of the
estimator in a particular sample is called an ‘estimate’. In interval estimation, an interval within which
the parameter is expected to lie is given by using two quantities based on sample values. This is
known as Confidence Interval, and the two quantities which are used to specify the interval, are known
as Confidence Limits.
29.1 Methods of Point Estimation

(1) Method of Maximum Likelihood
This is a convenient method for finding an estimator which satisfies most of the criteria discussed
earlier. Let x , x , ... x be a random sample from a population with p.m.f. (for discrete case) or
1 2 n
p.d.f. (for continuous case) ( θ,fx ) , where θ is the parameter. Then the joint distribution of the
sample observations viz.

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