14.1 Introduction

Chapters in this book

1. Frontmatter i
2. Preface iii
3. Contents vii
4. Part I QUANTILE REGRESSION MODELLING
5. Chapter 1 LINEAR QUANTILE REGRESSION
6. 1.1 Education: Mathematical Achievements 3
7. 1.2 Large Sample Properties 16
8. 1.3 Bibliographic Notes 19
9. Chapter 2 NONPARAMETRIC QUANTILE REGRESSION
10. 2.1 Robust Local Approximation Method 20
11. 2.2 Nonparametric Function Estimation 40
12. 2.3 Local Linear Quantile Regression 55
13. Chapter 3 ADAPTIVE QUANTILE REGRESSION
14. 3.1 Locally Constant Adaptive Quantile Regression 69
15. 3.2 Locally Linear Adaptive Quantile Regression 82
16. Chapter 4 ADAPTIVE QUANTILES REGRESSION
17. 4.1 Additive Conditional Quantiles with High-Dimensional Covariates 91
18. 4.2 Nonparametric Estimation 105
19. Chapter 5 QUANTILE REGRESSION BASED ON VARYING-COEFFICIENT MODELS
20. 5.1 Adaptive Quantile Regression Based on Varying-coefficient Models 127
21. 5.2 Varying-coefficient Models with Heteroscedasticity 143
22. Chapter 6 SINGLE-INDEX QUANTILE REGRESSION
23. 6.1 Single Index Models 163
24. 6.2 CQR for Varying Coefficient Single-index Models 179
25. Chapter 7 QUANTILE AUTOREGRESSION
26. 7.1 Introduction 196
27. 7.2 The Model 197
28. 7.3 Estimation 203
29. 7.4 Quantitle Monotonicity 208
30. 7.5 Inference 209
31. Chapter 8 COMPOSITE QUANTILE REGRESSION
32. 8.1 Composite Quantile and Model Selection 213
33. 8.2 Local Quantile Regression 229
34. Chapter 9 HIGH DIMENSIONAL QUANTILE REGRESSION
35. 9.1 Diagnostic for Ultra High Heterogeneity 248
36. 9.2 Bayesian Quantile Regression 264
37. Part II HIERARCHICAL MODELING
38. Chapter 10 HIERARCHICAL LINEAR MODELS
39. 10.1 Bayes Estimates 273
40. 10.2 Maximum Likelihood from Incomplete Data 283
41. 10.3 EM-algorithm 296
42. 10.4 Iterative Generalized Least Squares 310
43. 10.5 Scoring Algorithm 324
44. 10.6 Newton-Raphson Algorithm 337
45. Chapter 11 HIERARCHICAL GENERALIZED LINEAR MODELS
46. 11.1 Hierarchical Likelihood 354
47. 11.2 A Gibbs Sampling Approach 383
48. Chapter 12 HIERARCHICAL NONLINEAR MODELS
49. 12.1 Conditional Second-Order Generalized Estimating Equations 394
50. 12.2 A Hybrid Estimator 407
51. Chapter 13 HIERARCHICAL SEMIPARAMETRIC MODELS
52. 13.1 Hierarchical Semiparametric Nonlinear Mixed-Effects Models 429
53. 13.2 Simultaneously Modeling for Mean-Covariance 444
54. Chapter 14 HIERARCHICAL SPLINE MODELS
55. 14.1 Introduction 463
56. 14.2 Nonparametric Estimation 465
57. 14.3 WALD Tests for Regression Quantile Models 467
58. 14.4 Conclusions 470
59. 14.5 Bibliographic Notes 470
60. Chapter 15 HIERARCHIAL LINEAR QUANTILE MODELING
61. 15.1 Introduction 473
62. 15.2 The Hierarchical Quantile Regression Model 474
63. 15.3 EQ Algorithm 475
64. 15.4 Asymptotic Properties 477
65. 15.5 Bibliographic Notes 483
66. Chapter 16 HIERARCHICAL SEMIPARAMETRIC QUANTILE MODELING 16.1 Introduction
67. 16.1 Introduction 485
68. 16.2 The Models and Estimation 487
69. 16.3 Asymptotic Results 492
70. 16.4 Conclusion 499
71. 16.5 Bibliographic Notes 499
72. Chapter 17 COMPOSITE HIERARCHICAL LINEAR QUANTILE MODELING
73. 17.1 Introduction 501
74. 17.2 The Models 502
75. 17.3 Estimation 504
76. 17.4 Asymptotic Properties 506
77. 17.5 Discussion 511
78. 17.6 Bibliographic Notes 511
79. Chapter 18 COMPOSITE HIERARCHICAL SEMIPARAMETRIC QUANTILE MODELING
80. 18.1 Introduction 513
81. 18.2 The Models 515
82. 18.3 Estimation and Algorithm 516
83. 18.4 Asymptotic Properties 517
84. 18.5 Discussion 522
85. 18.6 Bibliographic Notes 523
86. Part IV LARGE SCALE APPLICATIONS TO REAL DATA
87. Chapter 19 APPLICATIONS OF QUANTILE REGRESSION 527
88. 19.1 Introduction 527
89. 19.2 Applications to Mathematical Education Based on LQR 540
90. 19.3 Application of Local LQR 556
91. 19.4 The Widening Gap between the Rich and the Poor 560
92. 19.5 Boston Housing Analysis Using AQR 561
93. 19.6 The Analysis of Japanese Firms in the Chemical Industry by Employing AQR 565
94. 19.7 The Analysis of Norwegian Air Pollution Bying Quantile Varying-coefficient Regression 568
95. 19.8 Empirical Application to Air Pollution Based HVCMs 570
96. 19.9 Boston Pricing by Single-index Quantile Regression 571
97. 19.10 Boston Pricing Using VCSIM 575
98. 19.11 Two Economic Time Series Basedbon the Quantile Autoregression 576
99. 19.12 The UK Family Expenditure Using Local CQR Methodology 579
100. 19.13 Analysis of Microarray Dataset 581
101. 19.14 Analysis of Two Data Sets Through Bayesian Quantile Autoregression 585
102. Chapter 20 APPLICATIONS OF HIERARCHICAL REGRESSION MODELS
103. 20.1 Two-factor Experimental Designs and Multiple Regression 588
104. 20.2 Examples of EM Algorithms 599
105. 20.3 Law Schools, Field Mice and Professional Football Teams 613
106. 20.4 A Longitudinal Study of Educational Achievements 624
107. 20.5 Ovarian Follicle and Calcium Supplement 627
108. 20.6 Applications of Hierarchical Generalized Linear Models 630
109. 20.7 Infectious Disease Data of Indonesia 642
110. 20.8 Epileptic Seizure 646
111. 20.9 Eight Guinea Pigs 648
112. 20.10 Canadian Temperature 653
113. 20.11 CD4 Cell 656
114. Chapter 21 APPLICATIONS OF HIERARCHICAL QUANTILE REGRESSION MODELING
115. 21.1 Household Electricity Demands 661
116. 21.2 Mathematics Education in Canada 673
117. 21.3 The Mean Pixel Intensity of Lymphnodes in the CT Scan 679
118. 21.4 Applications of Composite Hierachical Linear Quantile Regression 685
119. 21.5 Applications of Semi-HCQR Method to Partial HIV Monitoring Data 688
120. Bibliographic Notes 692
121. Bibliography 693
122. Index 734