Observed Confidence Levels Theory and Application

Alan M. Polansky1584888024, 9781584888024, 9781584888031

Observed Confidence Levels: Theory and Application provides a fundamental theoretical roadmap for the application of this relatively new methodology to many of the common problems that occur in the field of statistical inference. Presenting practical applications from the fields of engineering, biology, and medicine, this book features in-depth discussions of how observed confidence levels can be computer in the R environment. Observed confidence levels are also compared and contrasted with other well-established statistical methodologies such as bootstrapping. Additional chapters review the problem of regions and highlight the use observed confidence levels to answer applied problems.

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Table of contents :
OBSERVED CONFIDENCE LEVELS: Theory and Application……Page 2
Contents……Page 5
Preface……Page 10
APPENDIX A: Review of Asymptotic Statistics……Page 246
References……Page 261
1.2 The Problem of Regions……Page 14
1.2.1 Normal Mean Example……Page 18
1.3.1 A Problem from Biostatistics……Page 19
1.3.2 A Problem from Statistical Quality Control……Page 20
1.3.3 A Problem from Biostatistics……Page 22
1.3.4 A Problem from Ecology……Page 24
1.3.5 A Problem from Biostatistics……Page 28
1.3.6 A Problem from Astronomy……Page 29
1.3.7 A Problem from Geophysics……Page 30
1.4 About This Book……Page 31
2.1 Introduction……Page 35
2.2 The General Case……Page 36
2.2.1 Normal Mean and Variance……Page 37
2.2.2 Correlation Coefficient……Page 38
2.2.3 Population Quantile……Page 39
2.2.4 Poisson Rate……Page 40
2.3 Smooth Function Model……Page 41
2.3.1 Univariate Mean……Page 46
2.3.2 Univariate Variance……Page 47
2.3.3 Correlation Coefficient……Page 48
2.4 Asymptotic Comparisons……Page 49
2.4.1 Univariate Mean……Page 57
2.4.2 Univariate Variance……Page 58
2.5 Empirical Comparisons……Page 59
2.6.1 A Problem from Biostatistics……Page 61
2.6.2 A Problem from Ecology……Page 64
2.6.3 A Problem from Astronomy……Page 66
2.6.4 A Problem from Anthropometric Studies……Page 68
2.7 Computation Using R……Page 70
2.8.1 Theoretical Exercises……Page 76
2.8.2 Applied Exercises……Page 77
3.1 Introduction……Page 80
3.2 Smooth Function Model……Page 81
3.2.1 Multivariate Mean……Page 84
3.3 Asymptotic Accuracy……Page 86
3.4 Empirical Comparisons……Page 92
3.5.1 A Problem from Biostatistics……Page 94
3.5.2 A Problem in Statistical Quality Control……Page 97
3.5.3 A Problem from Environmental Science……Page 99
3.6 Computation Using R……Page 101
3.7.1 Theoretical Exercises……Page 107
3.7.2 Applied Exercises……Page 108
4.1 Introduction……Page 114
4.2 Statistical Framework……Page 115
4.2.1 Simple Linear Regression……Page 118
4.2.2 One-Way Layout……Page 121
4.3 Asymptotic Accuracy……Page 122
4.4 Empirical Comparisons……Page 125
4.5.1 A Problem from Analytical Chemistry……Page 127
4.5.2 A Problem in Experimental Archaeology……Page 130
4.5.3 A Problem from Biostatistics……Page 134
4.5.4 A Problem from Biostatistics……Page 135
4.6.1 Model Selection……Page 136
4.7 Computation Using R……Page 140
4.8.1 Theoretical Exercises……Page 145
4.8.2 Applied Exercises……Page 146
5.1 Introduction……Page 152
5.2.1 Methods for Nonparametric Density Estimation……Page 153
5.2.2 Search The for Modes……Page 157
5.2.3 An Empirical Study……Page 166
5.3.1 A Problem from Astronomy……Page 168
5.3.2 A Problem from Ecology……Page 170
5.4 Solving Density Estimation Problems Using R……Page 176
5.5.1 Methods for Nonparametric Regression……Page 180
5.5.2 Observed Confidence Levels for theta (x)……Page 184
5.5.3 An Empirical Study……Page 191
5.6.2 A Problem from Chemistry……Page 193
5.7 Solving Nonparametric Regression Problems Using R……Page 194
5.8.1 Theoretical Exercises……Page 198
5.8.2 Applied Exercises……Page 199
6.1 Classical Nonparametric Methods……Page 204
6.2 Generalized Linear Models……Page 207
6.3 Multivariate Analysis……Page 210
6.4 Survival Analysis……Page 213
6.5 Exercises……Page 216
7.2 Statistical Hypothesis Testing……Page 224
7.3 Multiple Comparisons……Page 227
7.4 Attained Confidence Levels……Page 235
7.5 Bayesian Confidence Levels……Page 239
7.6 Exercises……Page 242
A.2 Modes of Convergence……Page 247
A.3 Central Limit Theorem……Page 252
A.4 Convergence Rates……Page 254
A.5 Exercises……Page 258