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Lecture 8

STAT 2507 Lecture Notes - Lecture 8: Bias Of An Estimator, Interval Estimation, Point Estimation

Course Code
STAT 2507
Masoud Nasari

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STATS 2507
Chapter 8
Large Sample Estimation
In the previous chapters we have learned everything we need to understand statistical inference
and how it can be applied in practical situations. In this chapter we will learn more about
estimation and how to infer about population parameters using point estimators. Statistical
inference Statistical inference is the process employed to make decisions or predictions about
parameters. Examples of population parameters: Population mean, µ Population standard
deviation, σ Population proportion, p
Examples of applications of inference:
The prediction of short- and long-term interest rates
The forecasting of the behaviour of the stock market
A consumer wants to estimate the selling price of her house before putting it on the market
Deciding on the effectiveness of a new drug
Statistical Inference Definitions:
Estimation: is the process of estimating or predicting the value of a parameter of interest.
Hypothesis Testing: is the process of making decision about the value of a parameter based on
some preconceived idea about what its value might be.
Types of Estimators
Definition: an estimator is a rule, usually expressed as a formula, that tells us how to calculate an
estimate based on the information in the sample.
Estimators are used in two ways.
Point estimation: Based on sample data, a single number is calculated to estimate a population
parameter. The rule or formula that describes this calculation is called the point estimator, and
the resulting number is called a point estimate
Interval estimation: Based on sample data, two numbers are calculated to form an interval
within which the parameter is expected to lie. The rule or formula used in the calculation is
called an interval estimator, and the pair of numbers obtained is called an interval estimate or
confidence interval.
Point Estimation
In practice, there can be more than one point estimator that can be used to estimate a
population parameter of interest. The choice of which point estimator would depend on the
behaviour of the point estimator and its sampling distribution.
The first characteristic that is desired to have in a point estimator is that its sampling
distribution centres around the true value of the parameter. An estimator that has this
characteristic is called unbiased.
Point Estimation-Unbiased Estimators An estimator is said to be unbiased if its expected value
is equal to the population parameter it estimates. That is, the long-run average value of the
estimator is equal to the population parameter. NOTE: Every estimator we have seen so far is
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