Page 261 - Applied statistics and probability for engineers

7

Point Estimation of

Parameters and

Sampling Distributions

Introduction
Chapter Outline
7-1 Point Estimation Statistical methods are used to make decisions and draw
conclusions about populations. This aspect of statistics is
7-2 Sampling Distributions and the Central generally called statistical inference. These techniques uti-
Limit Theorem lize the information in a sample for drawing conclusions.
This chapter begins our study of the statistical methods used
7-3 General Concepts of Point Estimation in decision making.
7-3.1 Unbiased Estimators Statistical inference may be divided into two major areas:
7-3.2 Variance of a Point Estimator parameter estimation and hypothesis testing. As an exam-
7-3.3 Standard Error: Reporting a Point ple of a parameter estimation problem, suppose that an
Estimate engineer is analyzing the tensile strength of a component
7-3.4 Bootstrap Standard Error used in an air frame. This is an important part of assessing
7-3.5 Mean Squared Error of an the overall structural integrity of the airplane. Variability is
Estimator naturally present in the individual components because of
differences in the batches of raw material used to make the
7-4 Methods of Point Estimation components, manufacturing processes, and measurement
7-4.1 Method of Moments procedures (for example), so the engineer wants to estimate
7-4.2 Method of Maximum Likelihood the mean strength of the population of components. In prac-
7-4.3 Bayesian Estimation of tice, the engineer will use sample data to compute a number
Parameters
that is in some sense a reasonable value (a good guess) of
the true population mean. This number is called a point esti-
mate. We will see that procedures are available for develop-
ing point estimates of parameters that have good statistical
properties. We will also be able to establish the precision of
the point estimate.

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