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随着科学技术的迅猛发展，具有复杂分层结构的数据在现实生活中很普遍。能完全剖析这类数据，发觉该类数据表象下的潜在规律性对于统计学等科研领域很有意义。《分层分位模拟——理论、方法及以应用（英文版）》致力于介绍复杂分层数据分析前沿知识，侧重于分层分位回归理论、方法及其应用研究。内容主要包括三大块：分层数据建模、分位回归与分层-分位回归。主要涉及到线性分层分位回归模拟、非参数分层分位回归模拟、适应性分层分位回归模拟、可加性分层分位回归模拟、变系数分层分位回归模拟、单指数分层分位回归模拟、分层分位自回归模拟、复合分层分位回归模拟、高维分层分位回归模拟、分层分位回归模拟、分层样条分位回归模拟、分层线性分位回归模拟、分层半参数分位回归模拟、复合分层线性分位回归模拟、复合分层半参数分位回归模拟等。
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ContentsPrefacePartI QUANTILE REGRESSION MODELLINGChapter1 INEAR QUANTILE REGRESSION 31.1 Education: Mathematical Achievements 31.1.1 Introduction 31.1.2 Data51.1.3 Estimation Results 71.1.4 Confidence Intervals and Related Interpretations 111.1.5 Conclusion 161.2 Large Sample Properties 161.3 Bibliographic Notes 19Chapter2 NONPARAMETRIC QUANTILE REGRESSION 202.1 Robust Local Approximation Method 202.1.1 Introduction 202.1.2 Consistency 222.1.3 Rate of Convergence 262.1.4 Asymptotic Distribution 332.1.5 Optimization of Estimate 372.1.6 Bibliographic Notes 392.2 Nonparametric Function Estimation 402.2.1 Introduction 402.2.2 Asymptotic Properties 422.2.3 Applications 522.2.4 Bibliographic Notes 542.3 Local Linear Quantile Regression 552.3.1 Introduction 552.3.2 Local Linear Check Function Minimization 582.3.3 Local Linear Double-Kernel Smoothing 622.3.4 Bibliographic Notes 68Chapter3 ADAPTIVE QUANTILE REGRESSION 693.1 Locally Constant Adaptive Quantile Regression 693.1.1 Introduction 693.1.2 Adaptive Estimation 723.1.3 Implementation 733.1.4 Theoretical Properties 753.1.5 Bibliographic Notes 823.2 Locally Linear Adaptive Quantile Regression 823.2.1 Introduction 823.2.2 Local Linear Adaptive Estimation 843.2.3 Algorithm 853.2.4 Theoretical Properties 863.2.5 Bibliographic Notes 89Chapter4 ADAPTIVE QUANTILES REGRESSION 914.1 Additive Conditional Quantiles with High-Dimensional Covariates 914.1.1 Introduction 914.1.2 Methodology 934.1.3 Asymptotic Behavior 984.1.4 Concluding Remarks 1054.1.5 Bibliographic Notes 1054.2 Nonparametric Estimation 1054.2.1 Introduction 1064.2.2 Estimator 1084.2.3 Asymptotic Results 1104.2.4 Conclusions 1264.2.5 Bibliographic Notes 126Chapter5 QUANTILE REGRESSION BASED ON VARYINGCOEFFICIENT MODELS 1275.1 Adaptive Quantile Regression Based on Varying-coefficient Models 1275.1.1 Introduction 1275.1.2 Adaptive Estimation 1295.1.3 Theoretical Properties 1355.1.4 Conclusion 1425.1.5 Bibliographic Notes 1435.2 Varying-coefficient Models with Heteroscedasticity 1435.2.1 Introduction 1445.2.2 Local Linear CQR-AQR Estimation 1465.2.3 Local Quadratic CQR-AQR Estimation 1565.2.4 Bandwidth Selection 1575.2.5 Hypothesis Testing 1585.2.6 Local m-polynomial CQR-AQR Estimation 1595.2.7 Discussion 1605.2.8 Bibliographic Notes 161Chapter6 SINGLE-INDEX QUANTILE REGRESSION 1636.1 Single Index Models 1636.1.1 Introduction 1636.1.2 The Model and Estimation 1656.1.3 Large Sample Properties 1686.1.4 Conclusions 1786.1.5 Bibliographic Notes 1786.2 CQR for Varying Coefficient Single-index Models 1796.2.1 Introduction 1796.2.2 Quantile Regression 1816.2.3 Composite Quantile Regression 1846.2.4 Discussion 1946.2.5 Bibliographic Notes 194Chapter7 QUANTILE AUTOREGRESSION 1967.1 Introduction 1967.2 The Model 1977.2.1 Description of The Model 1977.2.2 Properties 1997.3 Estimation 2037.4 Quantitle Monotonicity 2087.5 Inference 2097.5.1 Wald Process and Related Tests 2097.5.2 Testing for Asymmetric Dynamics 2107.5.3 Bibliographic Notes 212Chapter8 COMPOSITE QUANTILE REGRESSION 2138.1 Composite Quantile and Model Selection 2138.1.1 Introduction and Motivation 2138.1.2 Composite Quantile Regression 2168.1.3 Asymptotic Relative Efficiency 2208.1.4 The CQR-oracular Estimator 2258.1.5 Concluding Remarks 2288.1.6 Bibliographic Notes 2298.2 Local Quantile Regression 2298.2.1 Introduction 2298.2.2 Estimation of Regression Function 2318.2.3 Estimation of Derivative 2358.2.4 Local p-polynomial CQR Smoothing 2388.2.5 Discussion 2468.2.6 Bibliographic Notes 246Chapte9 HIGH DIMENSIONAL QUANTILE REGRESSION 2489.1 Diagnostic for Ultra High Heterogeneity 2489.1.1 Introduction 2489.1.2 Nonconvex Penalized Quantile Regression 2519.1.3 Discussion 2629.1.4 Bibliographic Notes 2639.2 Bayesian Quantile Regression 2649.2.1 Introduction 2649.2.2 Asymmetric Laplace Distribution 2659.2.3 Bayesian Approach 2669.2.4 Improper Priors for Parameters 2679.2.5 Discussion 2699.2.6 Bibliographic Notes 270PartII HIERARCHICAL MODELINGChapter10 HIERARCHICAL LINEAR MODELS 27310.1 Bayes Estimates 27310.1.1 Introduction 27310.1.2 Exchangeability 27410.1.3 General Bayesian Linear Model 27710.1.4 Estimation 28110.1.5 Bibliographic Notes 28310.2 Maximum Likelihood from Incomplete Data 28310.2.1 Introduction 28310.2.2 Definitions of the EM Algorithm 28610.2.3 General Properties 29010.2.4 Bibliographic Notes 29610.3 EM-algorithm 29610.3.1 Introduction 29710.3.2 Covariance Components Models 29810.3.3 Estimation of
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