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Hierarchical Quantile Modeling: Theory, Methodology and Applications

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Language: English
Page: 735
Publication Date: 01/2022
ISBN: 9787030699039
Publisher: Science Press
Table of Contents
Contents
Preface
PartI QUANTILE REGRESSION MODELLING
Chapter1 INEAR QUANTILE REGRESSION 3
1.1 Education: Mathematical Achievements 3
1.1.1 Introduction 3
1.1.2 Data5
1.1.3 Estimation Results 7
1.1.4 Confidence Intervals and Related Interpretations 11
1.1.5 Conclusion 16
1.2 Large Sample Properties 16
1.3 Bibliographic Notes 19
Chapter2 NONPARAMETRIC QUANTILE REGRESSION 20
2.1 Robust Local Approximation Method 20
2.1.1 Introduction 20
2.1.2 Consistency 22
2.1.3 Rate of Convergence 26
2.1.4 Asymptotic Distribution 33
2.1.5 Optimization of Estimate 37
2.1.6 Bibliographic Notes 39
2.2 Nonparametric Function Estimation 40
2.2.1 Introduction 40
2.2.2 Asymptotic Properties 42
2.2.3 Applications 52
2.2.4 Bibliographic Notes 54
2.3 Local Linear Quantile Regression 55
2.3.1 Introduction 55
2.3.2 Local Linear Check Function Minimization 58
2.3.3 Local Linear Double-Kernel Smoothing 62
2.3.4 Bibliographic Notes 68
Chapter3 ADAPTIVE QUANTILE REGRESSION 69
3.1 Locally Constant Adaptive Quantile Regression 69
3.1.1 Introduction 69
3.1.2 Adaptive Estimation 72
3.1.3 Implementation 73
3.1.4 Theoretical Properties 75
3.1.5 Bibliographic Notes 82
3.2 Locally Linear Adaptive Quantile Regression 82
3.2.1 Introduction 82
3.2.2 Local Linear Adaptive Estimation 84
3.2.3 Algorithm 85
3.2.4 Theoretical Properties 86
3.2.5 Bibliographic Notes 89
Chapter4 ADAPTIVE QUANTILES REGRESSION 91
4.1 Additive Conditional Quantiles with High-Dimensional Covariates 91
4.1.1 Introduction 91
4.1.2 Methodology 93
4.1.3 Asymptotic Behavior 98
4.1.4 Concluding Remarks 105
4.1.5 Bibliographic Notes 105
4.2 Nonparametric Estimation 105
4.2.1 Introduction 106
4.2.2 Estimator 108
4.2.3 Asymptotic Results 110
4.2.4 Conclusions 126
4.2.5 Bibliographic Notes 126
Chapter5 QUANTILE REGRESSION BASED ON VARYINGCOEFFICIENT MODELS 127
5.1 Adaptive Quantile Regression Based on Varying-coefficient Models 127
5.1.1 Introduction 127
5.1.2 Adaptive Estimation 129
5.1.3 Theoretical Properties 135
5.1.4 Conclusion 142
5.1.5 Bibliographic Notes 143
5.2 Varying-coefficient Models with Heteroscedasticity 143
5.2.1 Introduction 144
5.2.2 Local Linear CQR-AQR Estimation 146
5.2.3 Local Quadratic CQR-AQR Estimation 156
5.2.4 Bandwidth Selection 157
5.2.5 Hypothesis Testing 158
5.2.6 Local m-polynomial CQR-AQR Estimation 159
5.2.7 Discussion 160
5.2.8 Bibliographic Notes 161
Chapter6 SINGLE-INDEX QUANTILE REGRESSION 163
6.1 Single Index Models 163
6.1.1 Introduction 163
6.1.2 The Model and Estimation 165
6.1.3 Large Sample Properties 168
6.1.4 Conclusions 178
6.1.5 Bibliographic Notes 178
6.2 CQR for Varying Coefficient Single-index Models 179
6.2.1 Introduction 179
6.2.2 Quantile Regression 181
6.2.3 Composite Quantile Regression 184
6.2.4 Discussion 194
6.2.5 Bibliographic Notes 194
Chapter7 QUANTILE AUTOREGRESSION 196
7.1 Introduction 196
7.2 The Model 197
7.2.1 Description of The Model 197
7.2.2 Properties 199
7.3 Estimation 203
7.4 Quantitle Monotonicity 208
7.5 Inference 209
7.5.1 Wald Process and Related Tests 209
7.5.2 Testing for Asymmetric Dynamics 210
7.5.3 Bibliographic Notes 212
Chapter8 COMPOSITE QUANTILE REGRESSION 213
8.1 Composite Quantile and Model Selection 213
8.1.1 Introduction and Motivation 213
8.1.2 Composite Quantile Regression 216
8.1.3 Asymptotic Relative Efficiency 220
8.1.4 The CQR-oracular Estimator 225
8.1.5 Concluding Remarks 228
8.1.6 Bibliographic Notes 229
8.2 Local Quantile Regression 229
8.2.1 Introduction 229
8.2.2 Estimation of Regression Function 231
8.2.3 Estimation of Derivative 235
8.2.4 Local p-polynomial CQR Smoothing 238
8.2.5 Discussion 246
8.2.6 Bibliographic Notes 246
Chapte9 HIGH DIMENSIONAL QUANTILE REGRESSION 248
9.1 Diagnostic for Ultra High Heterogeneity 248
9.1.1 Introduction 248
9.1.2 Nonconvex Penalized Quantile Regression 251
9.1.3 Discussion 262
9.1.4 Bibliographic Notes 263
9.2 Bayesian Quantile Regression 264
9.2.1 Introduction 264
9.2.2 Asymmetric Laplace Distribution 265
9.2.3 Bayesian Approach 266
9.2.4 Improper Priors for Parameters 267
9.2.5 Discussion 269
9.2.6 Bibliographic Notes 270
PartII HIERARCHICAL MODELING
Chapter10 HIERARCHICAL LINEAR MODELS 273
10.1 Bayes Estimates 273
10.1.1 Introduction 273
10.1.2 Exchangeability 274
10.1.3 General Bayesian Linear Model 277
10.1.4 Estimation 281
10.1.5 Bibliographic Notes 283
10.2 Maximum Likelihood from Incomplete Data 283
10.2.1 Introduction 283
10.2.2 Definitions of the EM Algorithm 286
10.2.3 General Properties 290
10.2.4 Bibliographic Notes 296
10.3 EM-algorithm 296
10.3.1 Introduction 297
10.3.2 Covariance Components Models 298
10.3.3 Estimation of
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Hierarchical Quantile Modeling: Theory, Methodology and Applications
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