Page 13 - Fundamentals of Probability and Statistics for Engineers

x Contents

9 PARAMETER ESTIMATION 259
9.1 Samples and Statistics 259
9.1.1 Sample Mean 261
9.1.2 Sample Variance 262
9.1.3 Sample Moments 263
9.1.4 Order Statistics 264
9.2 Quality Criteria for Estimates 264
9.2.1 Unbiasedness 265
9.2.2 Minimum Variance 266
9.2.3 Consistency 274
9.2.4 Sufficiency 275
9.3 Methods of Estimation 277
9.3.1 Point Estimation 277
9.3.2 Interval Estimation 294
References 306
Further Reading and Comments 306
Problems 307

10 MODEL VERIFICATION 315
10.1 Preliminaries 315
10.1.1 Type-I and Type-II Errors 316
10.2 Chi-Squared Goodness-of-Fit Test 316
10.2.1 The Case of Known Parameters 317
10.2.2 The Case of Estimated Parameters 322
10.3 Kolmogorov–Smirnov Test 327
References 330
Further Reading and Comments 330
Problems 330

11 LINEAR MODELS AND LINEAR REGRESSION 335
11.1 Simple Linear Regression 335
11.1.1 Least Squares Method of Estimation 336
11.1.2 Properties of Least-Square Estimators 342
11.1.3 Unbiased Estimator for 2 345
11.1.4 Confidence Intervals for Regression Coefficients 347
11.1.5 Significance Tests 351
11.2 Multiple Linear Regression 354
11.2.1 Least Squares Method of Estimation 354
11.3 Other Regression Models 357
Reference 359
Further Reading 359
Problems 359

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