Micro-Econometrics：Methods of Moments and Limited Dependent Variables

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收藏 2009-12-30

书名：《Micro-Econometrics: Methods of Moments and Limited Dependent Variables 》，作者：Myoung i.Lee，Springer，2nd edition (October 14, 2009)

非扫描版，原版，共计 788 页。非常好的一本计量著作，研究级别。

Product Description

The classical econometric approach to modelling has been to specify a model up to a finite-dimensional parameter vector, and estimation and testing techniques have been widely used on these finite-dimensional parameter spaces. In the last fifteen years or so however, new methods have been developed to allow more flexible models which utilise infinite-dimensional parameters. Simultaneously, methods of moments estimation have also become more widely used and applied. In this book, the author provides a survey of these modern techniques and how they are applied to limited dependent variable (LDV) models. As well as covering many classical approaches, the topics covered include: instrumental variable estimation, the generalized method of moments, extremum estimators, methods of simulated moments, minimum distance estimation, nonparametric density and regression function estimation, and semiparametric methods for LDV. As a result, many graduate students and research workers will appreciate this up-to-date account. An appendix describes the use of the software package GAUSS to implement these methods in conjunction with some real data sets.

Amazon 评论：

Ph.D students and researchers in applied microeconomics will enjoy this book, because this book is, to my knowledge, the first reasonably coherent and complete overview of semi-(non)parametric microeconometrics.

The book does a very good job of surveying the literature on semiparametric methods for modeling choice. This is an important field, and is not well covered in other textbooks. Of course the book requires some sophistication on the part of the user, namely a graduate level backround in econometrics.

详细参见：

http://www.amazon.com/Micro-Econometrics-Methods-Moments-Dependent-Variables/dp/0387953760/ref=sr_1_1?ie=UTF8&s=books&qid=1262178952&sr=1-1

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lkylelj

2009-12-30 21:48:55

Chapter 1 Methods of Moments for Single Linear Equation
Models 1
1 Least Squares Estimator (LSE) 1
1.1 LSE as aMethod ofMoment (MOM) . . . . . . . . . . . . . 1
1.1.1 Linear Model . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.2 LSE and Moment Conditions . . . . . . . . . . . . . . 2
1.1.3 Zero Moments and Independence . . . . . . . . . . . . 3
1.2 Asymptotic Properties of LSE . . . . . . . . . . . . . . . . . . 4
1.2.1 LLN and LSE Consistency . . . . . . . . . . . . . . . 5
1.2.2 CLT and
√
N-Consistency . . . . . . . . . . . . . . . . 6
1.2.3 LSE Asymptotic Distribution . . . . . . . . . . . . . . 7
1.3 Matrices and Linear Projection . . . . . . . . . . . . . . . . . 8
1.4 R2 and Two Examples . . . . . . . . . . . . . . . . . . . . . . 10
1.5 Partial Regression . . . . . . . . . . . . . . . . . . . . . . . . 13
1.6 Omitted Variable Bias . . . . . . . . . . . . . . . . . . . . . . 15
2 Heteroskedasticity and Homoskedasticity 17
2.1 Heteroskedasticity Sources . . . . . . . . . . . . . . . . . . . . 18
2.1.1 Forms of Heteroskedasticity . . . . . . . . . . . . . . . 18
2.1.2 Heteroskedasticity due to Aggregation . . . . . . . . . 19
2.1.3 Variance Decomposition . . . . . . . . . . . . . . . . . 20
2.1.4 Analysis of Variance (ANOVA)* . . . . . . . . . . . . 21
2.2 Weighted LSE (WLS) . . . . . . . . . . . . . . . . . . . . . . 23
2.3 Heteroskedasticity Examples . . . . . . . . . . . . . . . . . . 24
3 Testing Linear Hypotheses 25
3.1 Wald Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2 Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.3 Empirical Examples . . . . . . . . . . . . . . . . . . . . . . . 28
4 Instrumental Variable Estimator (IVE) 31
4.1 IVE Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.1.1 IVE in Narrow Sense . . . . . . . . . . . . . . . . . . . 31
4.1.2 Instrumental Variable (IV) qualifications . . . . . . . . 32
4.1.3 Further Remarks . . . . . . . . . . . . . . . . . . . . . 34
4.2 IVE Examples . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.3 IVE with More than Enough Instruments . . . . . . . . . . . 39
4.3.1 IVE in Wide Sense . . . . . . . . . . . . . . . . . . . . 39
4.3.2 Various Interpretations of IVE . . . . . . . . . . . . . 40
4.3.3 Further Remarks . . . . . . . . . . . . . . . . . . . . . 41
5 Generalized Method-of-Moment Estimator (GMM) 42
5.1 GMMBasics . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
5.2 GMMRemarks . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5.3 GMMExamples . . . . . . . . . . . . . . . . . . . . . . . . . 46
6 Generalized Least Squares Estimator (GLS) 48
6.1 GLS Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
6.2 GLS Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
6.3 Efficiency of LSE, GLS, and GMM . . . . . . . . . . . . . . . 50
Chapter 2 Methods of Moments for Multiple Linear Equation
Systems 53
1 System LSE, IVE, and GMM 53
1.1 System LSE . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
1.1.1 Multiple Linear Equations . . . . . . . . . . . . . . . . 53
1.1.2 System LSE and Motivation . . . . . . . . . . . . . . . 54
1.1.3 Asymptotic Variance . . . . . . . . . . . . . . . . . . . 55
1.2 System IVE and Rank Condition . . . . . . . . . . . . . . . . 56
1.2.1 Moment Conditions . . . . . . . . . . . . . . . . . . . 56
1.2.2 System IVE and Separate IVE . . . . . . . . . . . . . 57
1.2.3 Identification Conditions . . . . . . . . . . . . . . . . . 59
1.3 System GMMand Link to Panel Data . . . . . . . . . . . . . 60
1.3.1 System GMM . . . . . . . . . . . . . . . . . . . . . . . 60
1.3.2 System GMM and Panel Data . . . . . . . . . . . . . 62
2 Simultaneous Equations and Identification 66
2.1 Relationship Between Endogenous Variables . . . . . . . . . . 66
2.2 Conventional Approach to Rank Condition . . . . . . . . . . 68
2.3 Simpler Approach to Rank Condition . . . . . . . . . . . . . 69
2.4 Avoiding Arbitrary Exclusion Restrictions* . . . . . . . . . . 71
2.4.1 Grouping and Assigning . . . . . . . . . . . . . . . . . 71
2.4.2 Patterns in Reduced-Form Ratios . . . . . . . . . . . . 72
2.4.3 Meaning of Singular Systems . . . . . . . . . . . . . . 74
3 Methods of Moments for Panel Data 75
3.1 Panel LinearModel . . . . . . . . . . . . . . . . . . . . . . . . 76
3.1.1 Typical Panel Data Layout . . . . . . . . . . . . . . . 76
3.1.2 Panel Model with a Cross-Section Look . . . . . . . . 78
3.1.3 Remarks* . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.2 Panel GMMand Constructing Instruments . . . . . . . . . . 81
3.2.1 Panel IVE and GMM . . . . . . . . . . . . . . . . . . 81
3.2.2 Instrument Construction . . . . . . . . . . . . . . . . . 82
3.2.3 Specific Examples of Instruments . . . . . . . . . . . . 82
3.3 Within-Group and Between-Group Estimators . . . . . . . . 84
3.3.1 Within Group Estimator (WIT) . . . . . . . . . . . . 84

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2009-12-30 21:49:33

3.3.2 Between Group Estimator (BET) and Panel LSE
and GLS . . . . . . . . . . . . . . . . . . . . . . . . . 86
3.3.3 WIT as Fixed-Effect Estimator* . . . . . . . . . . . . 87
Chapter 3 M-Estimator and Maximum Likelihood Estimator
(MLE) 91
1 M-Estimator 91
1.1 Four Issues andMain Points . . . . . . . . . . . . . . . . . . . 91
1.2 Remarks for Asymptotic Distribution . . . . . . . . . . . . . . 92
1.3 Computation . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
2 Maximum Likelihood Estimator (MLE) 96
2.1 MLE Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
2.2 MLE Identification . . . . . . . . . . . . . . . . . . . . . . . . 99
2.3 Asymptotic Variance Relative to M-estimator . . . . . . . . . 100
3 M-Estimator with Nuisance Parameters 102
3.1 Two-Stage M-Estimator Basics . . . . . . . . . . . . . . . . . 102
3.2 Influence Function and Correction Term . . . . . . . . . . . . 103
3.3 Various Forms of Asymptotic Variances . . . . . . . . . . . . 105
3.4 Examples of Two-Stage M-Estimators . . . . . . . . . . . . . 106
3.4.1 No First-Stage Effect . . . . . . . . . . . . . . . . . . . 106
3.4.2 First-Stage Effect . . . . . . . . . . . . . . . . . . . . . 108
4 Method-of-Moment Tests (MMT) 108
4.1 Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
4.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.3 Conditional Moment Tests . . . . . . . . . . . . . . . . . . . . 112
5 Tests Comparing Two Estimators 112
5.1 Two Estimators for the Same Parameter . . . . . . . . . . . . 113
5.2 Two Estimators for the Same Variance . . . . . . . . . . . . . 115
6 Three Tests for MLE 117
6.1 Wald Test and Nonlinear Hypotheses . . . . . . . . . . . . . . 118
6.2 Likelihood Ratio (LR) Test . . . . . . . . . . . . . . . . . . . 119
6.2.1 Restricted LSE . . . . . . . . . . . . . . . . . . . . . . 119
6.2.2 Restricted MLE and LR Test . . . . . . . . . . . . . . 121
6.3 Score (LM) Test and Effective Score Test . . . . . . . . . . . 122
6.4 Further Remarks and an Empirical Example . . . . . . . . . . 124
7 Numerical Optimization and One-Step
Efficient Estimation 127
7.1 Newton–Raphson Algorithm . . . . . . . . . . . . . . . . . . . 127
7.2 Newton–Raphson Variants and Other Methods . . . . . . . . 129
7.3 One-Step Efficient Estimation . . . . . . . . . . . . . . . . . . 131
Chapter 4 Nonlinear Models and Estimators 133
1 Nonlinear Least Squares Estimator (NLS) 133
1.1 Various NonlinearModels . . . . . . . . . . . . . . . . . . . . 134
1.1.1 Index Models . . . . . . . . . . . . . . . . . . . . . . . 134
1.1.2 Transformation-of-Variable Models . . . . . . . . . . . 135
1.1.3 Mean, Median, and More Nonlinear Models . . . . . . 136
1.2 NLS and Its Asymptotic Properties . . . . . . . . . . . . . . . 138
1.3 Three Tests for NLS . . . . . . . . . . . . . . . . . . . . . . . 141
1.4 Gauss–Newton Algorithm . . . . . . . . . . . . . . . . . . . . 143
1.5 NLS-LMTest for LinearModels* . . . . . . . . . . . . . . . . 144
2 Quantile and Mode Regression 145
2.1 Median Regression . . . . . . . . . . . . . . . . . . . . . . . . 146
2.2 Quantile Regression . . . . . . . . . . . . . . . . . . . . . . . 147
2.2.1 Asymmetric Absolute Loss and Quantile
Function . . . . . . . . . . . . . . . . . . . . . . . . . . 147
2.2.2 Quantile Regression Estimator . . . . . . . . . . . . . 150
2.2.3 Empirical Examples . . . . . . . . . . . . . . . . . . . 151
2.3 Mode Regression . . . . . . . . . . . . . . . . . . . . . . . . . 153
2.4 Treatment Effects . . . . . . . . . . . . . . . . . . . . . . . . . 154
3 GMM for Nonlinear Models 156
3.1 GMM for Single Nonlinear Equation . . . . . . . . . . . . . . 157
3.2 Implementation and Examples . . . . . . . . . . . . . . . . . 159
3.3 Three Tests in GMM . . . . . . . . . . . . . . . . . . . . . . . 163
3.4 Efficiency of GMM . . . . . . . . . . . . . . . . . . . . . . . . 164
3.5 Weighting Matrices for Dependent Data . . . . . . . . . . . . 165
3.6 GMM for Multiple Nonlinear Equations* . . . . . . . . . . . . 166
4 Minimum Distance Estimation (MDE) 168
4.1 MDE Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
4.2 VariousMDE Cases . . . . . . . . . . . . . . . . . . . . . . . 171
4.3 An Empirical Example from Panel Data . . . . . . . . . . . . 174
Chapter 5 Parametric Methods for Single Equation
LDV Models 177
1 Binary Response 177
1.1 Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
1.2 Logit and Probit . . . . . . . . . . . . . . . . . . . . . . . . . 179
1.3 Marginal Effects . . . . . . . . . . . . . . . . . . . . . . . . . 183
1.4 Willingness to Pay and Treatment Effect . . . . . . . . . . . . 185
1.4.1 Willingness to Pay (WTP) . . . . . . . . . . . . . . . 185
1.4.2 Remarks for WTP Estimation . . . . . . . . . . . . . 187
1.4.3 Comparison to Treatment Effect . . . . . . . . . . . . 188
2 Ordered Discrete Response 189
2.1 Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
2.2 Digression on Re-parametrization in MLE . . . . . . . . . . . 191
2.3 Ordered Probit . . . . . . . . . . . . . . . . . . . . . . . . . . 192
2.4 An Empirical Example: Contingent Valuation . . . . . . . . . 194
3 Count Response 198
3.1 Basics and PoissonMLE . . . . . . . . . . . . . . . . . . . . . 198
3.2 Poisson Over-dispersion Problem and Other Estimators . . . 200
3.2.1 Negative Binomial (NB) MLE . . . . . . . . . . . . . . 200
3.2.2 Zero-Inflated Count Responses . . . . . . . . . . . . . 202
3.2.3 Methods of Moments . . . . . . . . . . . . . . . . . . . 202
3.3 An Empirical Example: Inequality Effect on Crime . . . . . . 203
3.4 IVE for Count or Positive Responses . . . . . . . . . . . . . . 204
4 Censored Response and Related LDV Models 206
4.1 CensoredModels . . . . . . . . . . . . . . . . . . . . . . . . . 206
4.2 Censored-Model MLE . . . . . . . . . . . . . . . . . . . . . . 208
4.3 Truncated Regression and Fractional Response . . . . . . . . 210
4.4 Marginal Effects for Censored/Selection Models . . . . . . . . 211
4.5 Empirical Examples . . . . . . . . . . . . . . . . . . . . . . . 213
5 Parametric Estimators for Duration 216
5.1 Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
5.1.1 Survival and Hazard Functions . . . . . . . . . . . . . 216
5.1.2 Log-Likelihood Functions . . . . . . . . . . . . . . . . 218
5.2 Exponential Distribution for Duration . . . . . . . . . . . . . 219
5.3 Weibull Distribution for Duration . . . . . . . . . . . . . . . . 221
5.4 Unobserved Heterogeneity and Other Parametric
Hazards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
5.5 Invariances and Extreme Value Distributions* . . . . . . . . . 225
Chapter 6 Parametric Methods for Multiple Equation LDV
Models 229
1 Multinomial Choice Models 229
1.1 Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
1.2 Multinomial Probit (MNP) . . . . . . . . . . . . . . . . . . . 231
1.2.1 Choice Probabilities and Identified
Parameters . . . . . . . . . . . . . . . . . . . . . . . . 231
1.2.2 Log-Likelihood Function and MOM . . . . . . . . . . 233
1.2.3 Implementation . . . . . . . . . . . . . . . . . . . . . . 234
1.3 Multinomial Logit (MNL) . . . . . . . . . . . . . . . . . . . . 235
1.3.1 Choice Probabilities and Implications . . . . . . . . . 235
1.3.2 Further Remarks . . . . . . . . . . . . . . . . . . . . . 237

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2009-12-30 21:50:09

1.3.4 An Empirical Example: Presidential
Election . . . . . . . . . . . . . . . . . . . . . . . . . . 239
1.4 Nested Logit (NES) . . . . . . . . . . . . . . . . . . . . . . . 242
2 Methods of Simulated Moments (MSM) 244
2.1 Basic Idea with Frequency Simulator . . . . . . . . . . . . . . 244
2.2 GHK Smooth Simulator . . . . . . . . . . . . . . . . . . . . . 247
2.3 Methods of Simulated Likelihood (MSL) . . . . . . . . . . . . 250
3 Sample-Selection Models 252
3.1 Various Selection Models . . . . . . . . . . . . . . . . . . . . . 253
3.2 Selection Addition, Bias, and Correction Terms . . . . . . . . 255
3.3 MLE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257
3.4 Two-Stage Estimator . . . . . . . . . . . . . . . . . . . . . . . 258
3.5 Selection Models for Some LDV’s . . . . . . . . . . . . . . . . 262
3.5.1 Binary-Response Selection MLE . . . . . . . . . . . . 262
3.5.2 Count-Response Zero-Inflated MLE . . . . . . . . . . 265
3.5.3 Count-Response Selection MOM . . . . . . . . . . . . 266
3.6 Double and Multiple Hurdle Models . . . . . . . . . . . . . . 267
4 LDV’s with Endogenous Regressors 269
4.1 Five Ways to Deal with Endogenous LDV’s . . . . . . . . . . 270
4.2 A Recursive System . . . . . . . . . . . . . . . . . . . . . . . 273
4.3 Simultaneous Systems in LDV’s and Coherency
Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
4.3.1 Incoherent System in Binary Responses . . . . . . . . 275
4.3.2 Coherent System in Censored Responses . . . . . . . . 275
4.3.3 Control Function Approach with a Censored
Response . . . . . . . . . . . . . . . . . . . . . . . . . 277
4.4 Simultaneous Systems in Latent Continuous
Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
4.4.1 Motivations and Justifications . . . . . . . . . . . . . . 278
4.4.2 Individual RF-Based Approach with MDE . . . . . . . 280
4.4.3 An Empirical Example . . . . . . . . . . . . . . . . . . 283
5 Panel-Data Binary-Response Models 285
5.1 Panel Conditional Logit . . . . . . . . . . . . . . . . . . . . . 285
5.1.1 Two Periods with Time-Varying
Intercept . . . . . . . . . . . . . . . . . . . . . . . . . 286
5.1.2 Three or More Periods . . . . . . . . . . . . . . . . . . 288
5.1.3 Digression on Sufficiency . . . . . . . . . . . . . . . . . 289
5.2 Unrelated-Effect Panel Probit . . . . . . . . . . . . . . . . . . 291
5.3 Dynamic Panel Probit . . . . . . . . . . . . . . . . . . . . . . 293
6 Competing Risks* 296
6.1 Observed Causes and Durations . . . . . . . . . . . . . . . . . 296
6.2 Latent Causes and Durations . . . . . . . . . . . . . . . . . . 298
6.3 Dependent Latent Durations and Identification . . . . . . . . 300
Chapter 7 Kernel Nonparametric Estimation 303
1 Kernel Density Estimator 303
1.1 Density Estimators . . . . . . . . . . . . . . . . . . . . . . . . 303
1.2 Density-Derivative Estimators . . . . . . . . . . . . . . . . . . 307
1.3 Further Remarks . . . . . . . . . . . . . . . . . . . . . . . . . 309
1.4 Adaptive Kernel Estimator . . . . . . . . . . . . . . . . . . . 312
2 Consistency and Bandwidth Choice 313
2.1 Bias and Order of Kernel . . . . . . . . . . . . . . . . . . . . 313
2.2 Variance and Consistency . . . . . . . . . . . . . . . . . . . . 316
2.3 Choosing Bandwidth with MSE . . . . . . . . . . . . . . . . . 318
2.4 Choosing Bandwidth with Cross-Validation . . . . . . . . . . 320
3 Asymptotic Distribution 322
3.1 Lindeberg CLT . . . . . . . . . . . . . . . . . . . . . . . . . . 323
3.2 Confidence Intervals . . . . . . . . . . . . . . . . . . . . . . . 324
3.3 Confidence Bands . . . . . . . . . . . . . . . . . . . . . . . . . 326
3.4 An Empirical Example of Confidence Bands . . . . . . . . . . 327
4 Finding Modes* 329
4.1 Graphical Detection . . . . . . . . . . . . . . . . . . . . . . . 329
4.2 A Multimodality Test . . . . . . . . . . . . . . . . . . . . . . 330
4.3 An Empirical Example: World Income
Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332
5 Survival and Hazard Under Random Right-Censoring* 333
5.1 Nelson–Aalen Cumulative-Hazard Estimator . . . . . . . . . . 333
5.2 Survival-Function Estimators . . . . . . . . . . . . . . . . . . 336
5.2.1 Cumulative-Hazard-Based Estimator . . . . . . . . . . 336
5.2.2 Kaplan–Meier Product Limit Estimator . . . . . . . . 338
5.3 Density and Hazard Estimators . . . . . . . . . . . . . . . . . 340
5.3.1 Kernel Density Estimator . . . . . . . . . . . . . . . . 340
5.3.2 Kernel Hazard Estimator . . . . . . . . . . . . . . . . 342
6 Kernel Nonparametric Regression 344
6.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344
6.2 Consistency . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347
6.3 Asymptotic Distribution . . . . . . . . . . . . . . . . . . . . . 348
6.4 Choosing Smoothing Parameter and Kernel . . . . . . . . . . 350
7 Topics in Kernel Nonparametric Regression 353
7.1 Mixed Regressors and Structural Breaks . . . . . . . . . . . . 353
7.2 Estimating Derivatives . . . . . . . . . . . . . . . . . . . . . . 356
7.3 Nonparameric MLE and Quantile Regression . . . . . . . . . 359
7.4 Local Linear Regression . . . . . . . . . . . . . . . . . . . . . 360
Chapter 8 Bandwidth-Free Semiparametric Methods 363
1 Quantile Regression for LDV models 363
1.1 Binary and Multinomial Responses . . . . . . . . . . . . . . . 364
1.2 Ordered Discrete Responses . . . . . . . . . . . . . . . . . . . 367
1.3 Count Responses . . . . . . . . . . . . . . . . . . . . . . . . . 369
1.3.1 Main Idea . . . . . . . . . . . . . . . . . . . . . . . . . 369
1.3.2 Quantile Regression of a Transformed Variable . . . . 371
1.3.3 Further Remarks . . . . . . . . . . . . . . . . . . . . . 372
1.4 Censored Responses . . . . . . . . . . . . . . . . . . . . . . . 373
1.4.1 Censored Quantile Estimators . . . . . . . . . . . . . . 373
1.4.2 Two-Stage Procedures and Unobserved
Censoring Point . . . . . . . . . . . . . . . . . . . . . 375
1.4.3 An Empirical Example . . . . . . . . . . . . . . . . . . 379
1.4.4 Median Rational Expectation* . . . . . . . . . . . . . 381
2 Methods Based on Modality and Symmetry 383
2.1 Mode Regression for Truncated Model
and Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . 384
2.2 Symmetrized LSE for Truncated and CensoredModels . . . . 386
2.2.1 Symmetrically Trimmed LSE . . . . . . . . . . . . . . 386
2.2.2 Symmetrically Censored LSE . . . . . . . . . . . . . . 388
2.3 Partial-Symmetry-Based Estimators . . . . . . . . . . . . . . 389
2.3.1 Quadratic Mode Regression Estimator (QME) . . . . 389
2.3.2 Remarks for QME . . . . . . . . . . . . . . . . . . . . 391
2.3.3 Winsorized Mean Estimator (WME) . . . . . . . . . . 393
2.4 Estimators for Censored-Selection Models . . . . . . . . . . . 396
3 Rank-Based Methods 397
3.1 Single Index Models (SIM) . . . . . . . . . . . . . . . . . . . 398
3.1.1 Single Index and Transformation of Variables . . . . . 398
3.1.2 Simple Single-Index Model Estimator . . . . . . . . . 399
3.1.3 Double or Multiple Indices . . . . . . . . . . . . . . . 400
3.2 Kendall Rank Correlation Estimator (KRE) . . . . . . . . . . 401
3.2.1 Estimator and Identification . . . . . . . . . . . . . . . 402
3.2.2 Asymptotic Distribution . . . . . . . . . . . . . . . . . 404
3.2.3 Randomly Censored Duration with Unknown
Transformation . . . . . . . . . . . . . . . . . . . . . . 406
3.3 Spearman Rank Correlation Estimator (SRE) . . . . . . . . . 408

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lkylelj

2010-1-10 12:32:17

自己顶下～！

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hebinjlu

2010-1-11 09:14:50

谢谢楼主分享好书！Myoung i.Lee写了好几本书，都非常有特色！

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