Modern Series Methods in Econometrics and Statistics.pdf
大小:(8.64 MB)

只需: RMB 17元  马上下载

计量经济学与统计学中的现代序列方法资料
内容非常丰富380多页，内容特别新2026新。

1 Motivations .................................................... 1
1.1 How Do Series Methods Come into Play? ...................... 1
1.2 Why Do We Choose Series Methods? ......................... 2
1.2.1 Advantages and Disadvantages ......................... 3
1.2.2 Rough Comparison with Kernel Methods ................ 5
1.3 Examples: Applications of Series Methods ..................... 6
1.3.1 Density Estimation in Finance ......................... 6
1.3.2 Average Treatment Effect ............................. 7
1.3.3 Machine Learning .................................... 8
References ..................................................... 9
Part I Series Methods
2 Conditional Expectations ....................................... 15
2.1 Probability Spaces .......................................... 15
2.2 Random Variables and Expectations ........................... 19
2.3 Conditional Expectation Given Variable ....................... 23
2.4 Conditional Expectation with Projection Viewpoint .............. 33
2.5 Conditional Expectation Given Sigma Field .................... 37
References ..................................................... 41
3 Regressions and Series Estimation ............................... 43
3.1 Regressions from Conditional Expectation Viewpoint ............ 44
3.2 Classification of Regressions ................................. 47
3.3 Series Methods ............................................. 50
3.3.1 Procedure of Series Estimation ......................... 51
3.3.2 Selection Criteria of Truncation Parameter ............... 59
3.3.3 Orthogonal Series Versus Power Functions .............. 65
References ..................................................... 69
Part II Applications of Series Methods
4 Density Estimation and Its Applications .......................... 73
4.1 Nonparametric Density Estimation ............................ 74
4.1.1 General Approach .................................... 74
4.1.2 Estimates of the Derivatives of Density .................. 80
4.1.3 Guaranteed Positivity of Density Estimates .............. 85
4.2 Applications of Density Estimation ........................... 87
4.2.1 Estimation of Parameters in Diffusion Process by MLE .... 87
4.2.2 Exponential Series Estimator for Multivariate
Densities ........................................... 89
4.2.3 Thick-Tailed Density Estimation in Finance .............. 91
4.2.4 Series Estimation of Option-Implied State Price
Density ............................................. 93
References ..................................................... 100
5 Partially Linear Single-Index Regression Models .................. 103
5.1 Single-Index Models ........................................ 104
5.1.1 Identifiability ........................................ 105
5.1.2 Estimation of Single-Index Models ..................... 106
5.2 Single-Index Models with Nonstationarity ..................... 108
5.2.1 Estimation Procedure ................................. 110
5.2.2 Asymptotic Theory ................................... 113
5.3 Partially Linear Single-Index Models .......................... 119
5.4 Partially Linear Single-Index Models with Nonstationarity ....... 121
5.4.1 Estimation Procedure ................................. 122
5.4.2 Asymptotic Theory ................................... 122
5.4.3 Extension to the General H-Regular Class ............... 124
5.5 Monte Carlo Simulations .................................... 126
5.5.1 Simulations for a Single-Index Model ................... 127
5.5.2 Simulations for a Partially Linear Single-Index Model ..... 128
5.6 Empirical Study ............................................ 129
5.7 Mathematical Details ....................................... 133
References ..................................................... 138
6 Additive Nonparametric Models ................................. 141
6.1 Identification and Estimation ................................. 142
6.2 Cointegrating Additive Nonparametric Models .................. 145
6.2.1 Estimation Procedure ................................. 146
6.2.2 Asymptotic Theory ................................... 148
6.3 Monte Carlo Simulations .................................... 152
6.4 Empirical Study ............................................ 154
6.5 Mathematical Details ....................................... 160
6.6 Discussions ................................................ 166
References ..................................................... 172
7 Semiparametric Moment Restriction Models ..................... 175
7.1 Parametric MRMs .......................................... 175
7.2 Semiparametric MRMs ...................................... 182
7.2.1 Conditional MRMs Estimated Through Conditional
Density ............................................. 182
7.2.2 Conditional MRMs Estimated Through SMD ............ 183
7.2.3 An Optimal Comparison of Misspecified MRMs .......... 184
7.3 High-Dimensional Semiparametric MRMs ..................... 187
7.3.1 SMRMs Without Single-Index Structure ................ 189
7.3.2 SMRMs with Single-Index Structure .................... 194
7.3.3 Statistical Inference .................................. 196
7.3.4 Ultra-High-Dimensional SMRMs ...................... 199
7.3.5 Simulation Experiments ............................... 202
7.3.6 Mathematical Details ................................. 205
7.4 Panel Data SMRMs ......................................... 211
7.4.1 High-Dimensional Panel Data SMRMs .................. 212
7.4.2 Asymptotic Theory ................................... 216
7.4.3 Monte Carlo Experiments ............................. 217
7.4.4 Mathematical Details ................................. 223
References ..................................................... 226
Appendix A: Abstract Spaces ....................................... 231
Appendix B: Approximation in Space C ............................. 247
Appendix C: Approximation in Hilbert Space ........................ 261
Appendix D: Comparison Between Series and Kernel Methods ........ 347
Subject Index ..................................................... 365
Author Index ...................................................... 369