Page 357 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics Hitesh Jhanji, Lovely Professional University

Notes Unit 28: Theory of Estimation: Point Estimation,

Unbiasedness, Consistency, Efficiency and Sufficiency

CONTENTS
Objectives
Introduction
28.1 Point Estimation
28.2 Unbiasedness, Consistency, Efficiency and Sufficiency
28.3 Application of Point Estimation
28.4 Summary
28.5 Key-Words
28.6 Review Questions
28.7 Further Readings

Objectives

After reading this unit students will be able to:
• Explain Point Estimation and Unbiasedness.
• Discuss Consistency, Efficiency and Sufficiency.
• Know the Application of Point Estimation.
Introduction

The topic of estimation in Statistics deals with estimation of population parameters like mean of a
statistical distribution. It is assumed, that the concerned variable of the population follows a certain
distribution with some parameter(s). For instance, it may be assumed that the life of the electric bulbs
σ
follows a normal distribution which has two parameters viz. mean (m) and standard deviation () .
While one of the parameters, say, standard deviation is known to be equal to 200 hours from past
experience, the other parameter, viz. the mean life of the bulbs, is not known, and which we wish to
estimate.
Given a sample of observations x , x , x , ..., x , one is required to determine with the aid of these
n
3
1
2
observations, an estimate in the form of a specific number like 2500 hrs., in the above case. This
number can be taken to be the best value of the unknown mean. Such single value estimate is called
‘Point’ estimate. The estimation could also be in the form of an interval, say 2,300 to 2,700 hrs. This
can be taken to include the value of the unknown mean. This called ‘Interval Estimation’. An example
of point and interval estimation could be provided from our day-to-day conversation when we talk
about commuting time to office. We do make statements like “It takes about 45 minutes ranging from
40 to 50 minutes depending on the traffic conditions.” The statistical details of these two types of
estimation are described below.
28.1 Point Estimation

A point estimate is a single value, like 10, analogous to a point in a geometrical sense. It is used to
estimate a population parameter, like mean, with the help of a sample of observations.
It may be noted that the observations x , x , x , ... x are random variables, and therefore, any function
3
n
1
2
of these observations will also be a random variable. Any function of the sample observations is
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