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分层分位模拟——理论、方法及应用(英文版)

作者：田茂再

出版社：科学出版社出版时间：2022-01-01

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分层分位模拟——理论、方法及应用(英文版) 版权信息

ISBN：9787030699039
条形码：9787030699039 ; 978-7-03-069903-9
装帧：一般胶版纸
册数：暂无
重量：暂无
所属分类：
自然科学
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数学
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数学理论

分层分位模拟——理论、方法及应用(英文版) 本书特色

适读人群：高等学校、科研院所的数学、统计学以及相关专业的高年级学生、研究生、教师,科技工作者本书内容详实，参考资料丰富，强烈推荐。

分层分位模拟——理论、方法及应用(英文版) 内容简介

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。能接近剖析这类数据，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。本书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。

分层分位模拟——理论、方法及应用(英文版) 目录

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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分层分位模拟——理论、方法及应用(英文版) 节选

Part I QUANTILE REGRESSION MODELLING Chapter 1 LINEAR QUANTILE REGRESSION 1.1 Education: Mathematical Achievements Family background factor can be a very important part of a person’s life. One ofthe main interests of this chapter is to investigate whether the family backgroundfactors alter performance on mathematical achievement of the stronger studentsthe same way that weaker students are affected. Using large sample of 2000， 2001and 2002 mathematics participation in Alberta， Canada， such questions have beeninvestigated by means of quantile regression approach. The findings suggest thatthere may be differential family-background-factor effects at different points in theconditional distribution of mathematical achievements. 1.1.1 Introduction Children’s mathematical achievements have long been a concern of society. Mastering mathematics has become more important than ever. Previous research indicates thata senior high school student with a strong grasp of mathematics has an advantage inacademics and in the job market， i.e.， mathematical achievement is a key to collegeentrance and success in the labor force. For several decades a number of studies have been focus on gathering andinvestigating information from many variables with effects on the mathematicalachievement. The social， economic， and cultural factors that are either in favorof or not conducive to children are not well understood. Among our main researchinterests here are the variables including family background factors， such as numberof parents， number of siblings， mother’s socioeconomic status， father’s socioeconomicstatus， gender， immigrants， language problem， native and minority， etc. As for gender difference in learning mathematics， evidence shows that femalesare not likely to believe that mathematics has utility in their lives (Fennema andSherman， 1978). They see mathematics as unconnected to a relationship model ofthinking. Even if females continue to take mathematical courses， they are apt tofind that they themselves do not like these courses. However， liking a subject is keyto succeeding at it (Lockhead et al.， 1985). Some researches on immigrants’ school performance suggest that their performanceis above averages (e.g.， Rumbaut， 1996; Viadero， 1997; Lapin， 1998). Whilethere is also evidence that immigrant children， especially Hispanics and others withimpoverished background， suffer poor academic achievement and lower educationalattainment (e.g.， McPartland， 1998; Vernez and Abrahamse， 1996). Also， morerecent studies of immigrant children’s academic achievement provide some insightsfor understanding the variation among immigrant children’s academic achievement.For example， Hao and Portes(1998) used the concept social capital to explainimmigrant children’s academic performance. It’s well known that language problem limits immigrant children’s learningon key subject areas such as mathematics and science. Living in socially andlinguistically isolated communities， poor immigrant children can hardly improvetheir new language skills and the language barriers persist over the school years.On the other hand， bilingual proficiency， defined as the mastery of both the mothertongue and a new language， is found to be a strength for immigrant children’scognitive growth (e.g.， Hao and Portes， 1998). Several authors have recognized that minorities may see mathematics as a Whitedomain， are less likely than Whites to understand its future value， and are negativelyinfluenced by the school staff’s attitudes toward them and their work (Mathews，1983). Educational reform advocated by the politicians and policy makers hasbeen performed in enhancing minority mathematical achievement including gooddiscipline and attendance， small class size， placement in advanced tracks， andmaterials that affirm the important role of minorities in mathematics (Mathews， 1983; Taylor， 1983). Generally speaking， studies mentioned above have primarily dependent onclassical mean regression methods such as ordinary least squares(OLS) or instrumentalvariables (IV). These methodology may miss crucial points such as howfamily background factors affect mathematical achievement differently at differentquantiles of the conditional test score distribution. What is worse， these approachescannot be used to characterize the entire conditional distribution of mathematicalachievement given high-dimensional covariates (family background factors) and theestimated coefficient vector (marginal effects) is not robust to outlier observation onmathematical achievement. Fortunately， the drawbacks mentioned above can be overcome by combinganother statistical method called quantile regression(QR)， which was proposed byKoenker and Bassett (1978) and has become a comprehensive approach to the useof linear and nonlinear response models for conditional quantile functions. Roughlyspeaking， QR， which is based on minimizing “check function” r

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