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Hardcover | 25 October 1999

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444 Pages

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This book systematically and thoroughly covers the vast literature on the nonparametric and semiparametric statistics and econometrics that has evolved over the last five decades. Within this framework this is the first book to discuss the principles of the nonparametric approach to the topics covered in a first year graduate course in econometrics, e.g. regression function, heteroskedasticity, simultaneous equations models, logit-probit and censored models. Nonparametric and semiparametric methods potentially offer considerable reward to applied researchers, owing to the methods' ability to adapt to many unknown features of the data. Professors Pagan and Ullah provide intuitive explanations of difficult concepts, heuristic developments of theory, and empirical examples emphasizing the usefulness of the modern nonparametric approach. The book should provide a new perspective on teaching and research in applied subjects in general and econometrics and statistics in particular.

Industry Reviews

'The authors of this well-produced volume merit high praise for their endeavours. This will be the most comprehensive summary of nonparametric statistics that we are likely to see for a long time. I can recommend it as a guide to recent work in an important area of mathematical statistics.' Short Book Reviews

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Non-Fiction Economics Econometrics

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Published: 25th October 1999

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Non-Fiction Economics Econometrics

Preface	p. xvii
Introduction	p. 1
Methods of Density Estimation	p. 5
Introduction	p. 5
Nonparametric Density Estimation	p. 7
A "Local" Histogram Approach	p. 7
A Formal Derivation of andfirac;[subscript 1] (x)	p. 9
Rosenblatt-Parzen Kernel Estimator	p. 9
The Nearest Neighborhood Estimator	p. 11
Variable Window-Width Estimators	p. 12
Series Estimators	p. 13
Penalized Likelihood Estimators	p. 15
The Local Log-Likelihood Estimators	p. 17
Summary	p. 19
Estimation of Derivatives of a Density	p. 19
Finite-Sample Properties of the Kernel Estimator	p. 20
The Exact Bias and Variance of the Estimator andfirac;	p. 21
Approximations to the Bias and Variance and Choices of h and K	p. 23
Reduction of Bias	p. 29
Asymptotic Properties of the Kernel Density Estimator andfirac; with Independent Observations	p. 32
Asymptotic Unbiasedness	p. 33
Consistency	p. 34
Asymptotic Normality	p. 39
Small-Sample Confidence Intervals	p. 42
Sampling Properties of the Kernel Density Estimator with Dependent Observations	p. 43
Unbiasedness	p. 43
Consistency	p. 43
Asymptotic Normality	p. 48
Bibliographical Summary (Approximate and Asymptotic Results)	p. 48
Choices of Window Width and Kernel: Further Discussion	p. 49
Choice of h	p. 49
Choice of Higher Order Kernels	p. 54
Choice of h for Density Derivatives	p. 56
Multivariate Density Estimation	p. 57
Testing Hypotheses about Densities	p. 60
Comparison with a Known Density Function	p. 61
Testing for Symmetry	p. 67
Comparison of Unknown Densities	p. 68
Testing for Independence	p. 69
Examples	p. 71
Density of Stock Market Returns	p. 71
Estimating the Dickey-Fuller Density	p. 74
Conditional Moment Estimation	p. 78
Introduction	p. 78
Estimating Conditional Moments by Kernel Methods	p. 79
Parametric Estimation	p. 80
Nonparametric Estimation: A "Local" Regression Approach	p. 81
Kernel-Based Estimation: A Formal Derivation	p. 83
A General Nonparametric Estimator of m(x)	p. 84
Unifying Nonparametric Estimators	p. 86
Estimation of Higher Order Conditional Moments	p. 95
Finite-Sample Properties	p. 95
Approximate Results: Stochastic x	p. 96
The Local Linear Regression Estimator	p. 104
Combining Parametric and Nonparametric Estimators	p. 106
Asymptotic Properties	p. 108
Asymptotic Properties of the Kernel Estimator with Independent Observations	p. 108
Asymptotic Properties of the Kernel Estimator with Dependent Observations	p. 115
Bibliographical Summary (Asymptotic Results)	p. 116
Implementing the Kernel Estimator	p. 118
Choice of Window Width	p. 118
Robust Nonparametric Estimation of Moments	p. 122
Estimating Conditional Moments by Series Methods	p. 123
Asymptotic Properties of Series Estimators with Independent Observations	p. 126
Asymptotic Properties of Series Estimators with Dependent Observations	p. 133
Implementing the Estimator	p. 133
Imposing Structure on the Conditional Moments	p. 137
Generalized Additive Models	p. 137
Projection Pursuit Regression	p. 139
Neural Networks	p. 140
Measuring the Affinity of Parametric and Nonparametric Models	p. 141
Examples	p. 150
A Model of Strike Duration	p. 150
Earnings-Age Profiles	p. 152
Review of Applied Work on Nonparametric Regression	p. 157
Nonparametric Estimation of Derivatives	p. 160
Introduction	p. 160
The Model and Partial Derivative Formulae	p. 161
Estimation	p. 164
Estimation of Partial Derivatives by Kernel Methods	p. 164
Estimation of Partial Derivatives by Series Methods	p. 167
Estimation of Average Derivatives	p. 167
Local Linear Derivative Estimators	p. 170
Pointwise Versus Average Derivatives	p. 172
Restricted Estimation and Hypothesis Testing	p. 173
Imposing Linear Equality Restriction on Partial Derivatives	p. 174
Imposing Linear Inequality Restrictions	p. 175
Hypothesis Testing	p. 176
Asymptotic Properties of Partial Derivative Estimators	p. 177
Asymptotic Properties of Kernel-Based Estimators	p. 178
Series-Based Estimators	p. 182
Higher Order Derivatives	p. 182
Local Linear Estimators	p. 183
Asymptotic Properties of Kernel-Based Average Derivative Estimators	p. 184
Implementing the Derivative Estimators	p. 189
Illustrative Examples	p. 190
A Monte Carlo Experiment with a Production Function	p. 190
Earnings-Age Relationship	p. 192
Review of Applied Work	p. 194
Semiparametric Estimation of Single-Equation Models	p. 196
Introduction	p. 196
Semiparametric Estimation of the Linear Part of a Regression Model	p. 198
General Results	p. 198
Diagnostic Tests after Nonparametric Regression	p. 208
Semiparametric Estimation of Some Macro Models	p. 210
The Asymptotic Covariance Matrix of SP Estimators without Asymptotic Independence	p. 212
Efficient Estimation of Semiparametric Models in the Presence of Heteroskedasticity of Unknown Form	p. 214
Conditions for Adaptive Estimation	p. 217
Efficient Estimation of Regression Parameters with Unknown Error Density	p. 225
Efficient Estimation by Likelihood Approximation	p. 225
Efficient Estimation by Kernel-Based Score Approximation	p. 227
Efficient Estimation by Moment-Based Score Approximation	p. 230
Estimation of Scale Parameters	p. 234
Optimal Diagnostic Tests in Linear Models	p. 234
Adaptive Estimation with Dependent Observations	p. 235
M-Estimators	p. 237
Estimation	p. 237
Diagnostic Tests with M-Estimators	p. 242
Sequential M-Estimators	p. 243
The Semiparametric Efficiency Bound for Moment-Based Estimators	p. 245
Approximating the SP Efficiency Bound by a Conditional Moment Estimator	p. 246
Applications	p. 248
Semiparametric Estimation of a Heteroskedastic Model	p. 248
Adaptive Estimation of a Model of House Prices	p. 250
Review of Other Applications	p. 251
Semiparametric and Nonparametric Estimation of Simultaneous Equation Models	p. 254
Introduction	p. 254
Single-Equation Estimators	p. 255
Parametric Estimation	p. 256
Rilstone's Semiparametric Two-Stage Least Squares Estimator	p. 258
Systems Estimation	p. 260
A Parametric Estimator	p. 260
The SP3SLS Estimator	p. 261
Newey's Estimator	p. 262
Newey's Efficient Distribution-Free Estimators	p. 264
Finite-Sample Properties	p. 267
Nonparametric Estimation	p. 269
Identification	p. 269
Nonparametric Two-Stage Least Squares (2SLS) Estimation	p. 270
Semiparametric Estimation of Discrete Choice Models	p. 272
Introduction	p. 272
Parametric Estimation of Binary Discrete Choice Models	p. 273
Semiparametric Efficiency Bounds for Binary Discrete Choice Models	p. 275
Semiparametric Estimation of Binary Discrete Choice Models	p. 279
Ichimura's Estimator	p. 280
Klein and Spady's Estimator	p. 283
The SNP Maximum Likelihood Estimator	p. 285
Local Maximum Likelihood Estimation	p. 286
Alternative Consistent SP Estimators	p. 286
Manski's Maximum Score Estimator	p. 286
Horowitz's Smoothed Maximum Score Estimator	p. 287
Han's Maximum Rank Correlation Estimator	p. 291
Cosslett's Approximate MLE	p. 292
An Iterative Least Squares Estimator	p. 293
Derivative-Based Estimators	p. 294
Models with Discrete Explanatory Variables	p. 295
Multinomial Discrete Choice Models	p. 296
Some Specification Tests for Discrete Choice Models	p. 297
Applications	p. 299
Semiparametric Estimation of Selectivity Models	p. 300
Introduction	p. 300
Some Parametric Estimators	p. 300
Some Sequential Semiparametric Estimators	p. 304
Cosslett's Dummy Variable Method	p. 306
Powell's Kernel Estimator	p. 306
Newey's Series Estimator	p. 308
Newey's GMM Estimator	p. 310
Maximum Likelihood-Type Estimators	p. 310
Gallant and Nychka's Estimator	p. 310
Newey's Estimator	p. 311
Estimation of the Intercept in Selection Models	p. 315
Applications of the Estimators	p. 315
Conclusions	p. 316
Semiparametric Estimation of Censored Regression Models	p. 317
Introduction	p. 317
Some Parametric Estimators	p. 319
Semiparametric Efficiency Bounds for the Censored Regression Model	p. 322
The Kaplan-Meier Estimator of the Distribution Function of a Censored Random Variable	p. 324
Semiparametric Density-Based Estimators	p. 326
The Semiparametric Generalized Least Squares Estimator (SGLS)	p. 327
Estimators Replacing Part of the Sample	p. 328
Maximum Likelihood Type Estimators	p. 329
Semiparametric Nondensity-Based Estimators	p. 329
Powell's Censored Least Absolute Deviation (CLAD) Estimator	p. 330
Powell's (1986a) Censored Quantile Estimators	p. 333
Powell's Symmetrically Censored Least Squares Estimators	p. 333
Newey's Efficient Estimator under Conditional Symmetry	p. 336
Comparative Studies of the Estimators	p. 337
Retrospect and Prospect	p. 339
Statistical Methods	p. 342
Probability Concepts	p. 342
Random Variable and Distribution Function	p. 345
Conditional Distribution and Independence	p. 347
Borel Measurable Functions	p. 348
Inequalities Involving Expectations	p. 350
Characteristic Function (c.f.)	p. 351
Results on Convergence	p. 352
Weak and Strong Convergence of Random Variables	p. 352
Laws of Large Numbers	p. 354
Convergence of Distribution Functions	p. 355
Central Limit Theorems	p. 357
Further Results on the Law of Large Numbers and Convergence in Moments and Distributions	p. 360
Convergence in Moments	p. 361
Some Probability Inequalities	p. 365
Order of Magnitudes (Small o and Large O)	p. 368
Asymptotic Theory for Dependent Observations	p. 370
Ergodicity	p. 371
Mixing Sequences	p. 372
Near-Epoch Dependent Sequences	p. 376
Martingale Differences and Mixingales	p. 377
Rosenblatt's (1970) Measure of Dependence [beta][subscript n]	p. 379
Stochastic Equicontinuity	p. 379
References	p. 383
Index	p. 419
Table of Contents provided by Syndetics. All Rights Reserved.

Nonparametric Econometrics

At a Glance

Hardcover

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