Narrow Results

The following sections are included:

• INTRODUCTION

• POINT ESTIMATION
  • Point Estimate, Estimator, and Estimation
  • Four Important Properties of Estimators
  • Mean-Squared Error for Choosing Point Estimator

• INTERVAL ESTIMATION

• INTERVAL ESTIMATES FOR μ WHEN IS KNOWN
  • Confidence Intervals in Terms of 20 Samples
  • Sandbags We Can Have Real Confidence In: 95 Percent and 99 Percent Confidence Intervals
  • 95 Percent Confidence Interval for the Sandbag Sample with a Smaller Sample Size
  • 95 Percent Confidence Interval for the Mean External Audit Fees for 32 Diverse Companies

• CONFIDENCE INTERVALS FOR μ WHEN IS UNKNOWN
  • 95 Percent Confidence Interval for the Average Weight of Football Players
  • 90 Percent Confidence Interval for the Average Weight of Football Players
  • Estimate for Waiting Time at a Bank
  • 95 Percent Confidence Interval for the True Mean Incremental Profit of “Successful” Trade Promotion

• CONFIDENCE INTERVALS FOR THE POPULATION PROPORTION
  • 95 Percent Confidence Interval for Voting Proportion
  • 95 Percent Confidence Interval for Commodity Preference Proportion
  • 95 Percent Confidence Interval for the Proportion of Working Adults Who Use Computer Equipment

• CONFIDENCE INTERVALS FOR THE VARIANCE
  • Confidence Intervals for

• AN OVERVIEW OF STATISTICAL QUALITY CONTROL⁵
  • The Sample Size of an Inspection
  • Acceptance Sampling and Its Alternative Plans
  • Process Control

• CONTROL CHARTS FOR QUALITY CONTROL
  • -Chart
  • -Chart and S-Chart

• FURTHER APPLICATIONS
  • Using Interval Estimates to Evaluate Donors and Donations Models
  • Shoppers’ Attitudes Toward Shoplifting and Shoplifting Prevention Devices

• Summary

• Appendix 10A Control Chart Approach for Cash Management¹⁶

• Appendix 10B Using MINITAB to Generate Control Charts

• Questions and Problems

One of the most important objectives of statistical inference is to estimate unknown model parameters based on an observed data. In this chapter, we will introduce some fundamental estimation methods for distributional model parameters. In particular, the maximum likelihood estimation and the method of moments estimation/generalized method of moments estimation are discussed, and their asymptotic properties investigated. Then we will discuss the methods for evaluating parameter estimators using the mean squared error criterion. The Lagrange multiplier method and the Cramer-Rao lower bound are used to derive the best unbiased estimators.