Preface |
Introduction / 1: |
Methods of Density Estimation / 2: |
Nonparametric Density Estimation / 2.1: |
A "Local" Histogram Approach / 2.2.1: |
A Formal Derivation of andfirac;[subscript 1] (x) / 2.2.2: |
Rosenblatt-Parzen Kernel Estimator / 2.2.3: |
The Nearest Neighborhood Estimator / 2.2.4: |
Variable Window-Width Estimators / 2.2.5: |
Series Estimators / 2.2.6: |
Penalized Likelihood Estimators / 2.2.7: |
The Local Log-Likelihood Estimators / 2.2.8: |
Summary / 2.2.9: |
Estimation of Derivatives of a Density / 2.3: |
Finite-Sample Properties of the Kernel Estimator / 2.4: |
The Exact Bias and Variance of the Estimator andfirac; / 2.4.1: |
Approximations to the Bias and Variance and Choices of h and K / 2.4.2: |
Reduction of Bias / 2.4.3: |
Asymptotic Properties of the Kernel Density Estimator andfirac; with Independent Observations / 2.5: |
Asymptotic Unbiasedness / 2.5.1: |
Consistency / 2.5.2: |
Asymptotic Normality / 2.5.3: |
Small-Sample Confidence Intervals / 2.5.4: |
Sampling Properties of the Kernel Density Estimator with Dependent Observations / 2.6: |
Unbiasedness / 2.6.1: |
Bibliographical Summary (Approximate and Asymptotic Results) / 2.6.2: |
Choices of Window Width and Kernel: Further Discussion / 2.7: |
Choice of h / 2.7.1: |
Choice of Higher Order Kernels / 2.7.2: |
Choice of h for Density Derivatives / 2.7.3: |
Multivariate Density Estimation / 2.8: |
Testing Hypotheses about Densities / 2.9: |
Comparison with a Known Density Function / 2.9.1: |
Testing for Symmetry / 2.9.2: |
Comparison of Unknown Densities / 2.9.3: |
Testing for Independence / 2.9.4: |
Examples / 2.10: |
Density of Stock Market Returns / 2.10.1: |
Estimating the Dickey-Fuller Density / 2.10.2: |
Conditional Moment Estimation / 3: |
Estimating Conditional Moments by Kernel Methods / 3.1: |
Parametric Estimation / 3.2.1: |
Nonparametric Estimation: A "Local" Regression Approach / 3.2.2: |
Kernel-Based Estimation: A Formal Derivation / 3.2.3: |
A General Nonparametric Estimator of m(x) / 3.2.4: |
Unifying Nonparametric Estimators / 3.2.5: |
Estimation of Higher Order Conditional Moments / 3.2.6: |
Finite-Sample Properties / 3.3: |
Approximate Results: Stochastic x / 3.3.1: |
The Local Linear Regression Estimator / 3.3.2: |
Combining Parametric and Nonparametric Estimators / 3.3.3: |
Asymptotic Properties / 3.4: |
Asymptotic Properties of the Kernel Estimator with Independent Observations / 3.4.1: |
Asymptotic Properties of the Kernel Estimator with Dependent Observations / 3.4.2: |
Bibliographical Summary (Asymptotic Results) / 3.5: |
Implementing the Kernel Estimator / 3.6: |
Choice of Window Width / 3.6.1: |
Robust Nonparametric Estimation of Moments / 3.7: |
Estimating Conditional Moments by Series Methods / 3.8: |
Asymptotic Properties of Series Estimators with Independent Observations / 3.9: |
Asymptotic Properties of Series Estimators with Dependent Observations / 3.10: |
Implementing the Estimator / 3.11: |
Imposing Structure on the Conditional Moments / 3.12: |
Generalized Additive Models / 3.12.1: |
Projection Pursuit Regression / 3.12.2: |
Neural Networks / 3.12.3: |
Measuring the Affinity of Parametric and Nonparametric Models / 3.13: |
A Model of Strike Duration / 3.14: |
Earnings-Age Profiles / 3.14.2: |
Review of Applied Work on Nonparametric Regression / 3.14.3: |
Nonparametric Estimation of Derivatives / 4: |
The Model and Partial Derivative Formulae / 4.1: |
Estimation / 4.3: |
Estimation of Partial Derivatives by Kernel Methods / 4.3.1: |
Estimation of Partial Derivatives by Series Methods / 4.3.2: |
Estimation of Average Derivatives / 4.3.3: |
Local Linear Derivative Estimators / 4.3.4: |
Pointwise Versus Average Derivatives / 4.3.5: |
Restricted Estimation and Hypothesis Testing / 4.4: |
Imposing Linear Equality Restriction on Partial Derivatives / 4.4.1: |
Imposing Linear Inequality Restrictions / 4.4.2: |
Hypothesis Testing / 4.4.3: |
Asymptotic Properties of Partial Derivative Estimators / 4.5: |
Asymptotic Properties of Kernel-Based Estimators / 4.5.1: |
Series-Based Estimators / 4.5.2: |
Higher Order Derivatives / 4.5.3: |
Local Linear Estimators / 4.5.4: |
Asymptotic Properties of Kernel-Based Average Derivative Estimators / 4.6: |
Implementing the Derivative Estimators / 4.7: |
Illustrative Examples / 4.8: |
A Monte Carlo Experiment with a Production Function / 4.8.1: |
Earnings-Age Relationship / 4.8.2: |
Review of Applied Work / 4.8.3: |
Semiparametric Estimation of Single-Equation Models / 5: |
Semiparametric Estimation of the Linear Part of a Regression Model / 5.1: |
General Results / 5.2.1: |
Diagnostic Tests after Nonparametric Regression / 5.2.2: |
Semiparametric Estimation of Some Macro Models / 5.2.3: |
The Asymptotic Covariance Matrix of SP Estimators without Asymptotic Independence / 5.2.4: |
Efficient Estimation of Semiparametric Models in the Presence of Heteroskedasticity of Unknown Form / 5.3: |
Conditions for Adaptive Estimation / 5.4: |
Efficient Estimation of Regression Parameters with Unknown Error Density / 5.5: |
Efficient Estimation by Likelihood Approximation / 5.5.1: |
Efficient Estimation by Kernel-Based Score Approximation / 5.5.2: |
Efficient Estimation by Moment-Based Score Approximation / 5.5.3: |
Estimation of Scale Parameters / 5.6: |
Optimal Diagnostic Tests in Linear Models / 5.7: |
Adaptive Estimation with Dependent Observations / 5.8: |
M-Estimators / 5.9: |
Diagnostic Tests with M-Estimators / 5.9.1: |
Sequential M-Estimators / 5.9.3: |
The Semiparametric Efficiency Bound for Moment-Based Estimators / 5.10: |
Approximating the SP Efficiency Bound by a Conditional Moment Estimator / 5.10.1: |
Applications / 5.11: |
Semiparametric Estimation of a Heteroskedastic Model / 5.11.1: |
Adaptive Estimation of a Model of House Prices / 5.11.2: |
Review of Other Applications / 5.11.3: |
Semiparametric and Nonparametric Estimation of Simultaneous Equation Models / 6: |
Single-Equation Estimators / 6.1: |
Rilstone's Semiparametric Two-Stage Least Squares Estimator / 6.2.1: |
Systems Estimation / 6.3: |
A Parametric Estimator / 6.3.1: |
The SP3SLS Estimator / 6.3.2: |
Newey's Estimator / 6.3.3: |
Newey's Efficient Distribution-Free Estimators / 6.3.4: |
Nonparametric Estimation / 6.4: |
Identification / 6.5.1: |
Nonparametric Two-Stage Least Squares (2SLS) Estimation / 6.5.2: |
Semiparametric Estimation of Discrete Choice Models / 7: |
Parametric Estimation of Binary Discrete Choice Models / 7.1: |
Semiparametric Efficiency Bounds for Binary Discrete Choice Models / 7.3: |
Semiparametric Estimation of Binary Discrete Choice Models / 7.4: |
Ichimura's Estimator / 7.4.1: |
Klein and Spady's Estimator / 7.4.2: |
The SNP Maximum Likelihood Estimator / 7.4.3: |
Local Maximum Likelihood Estimation / 7.4.4: |
Alternative Consistent SP Estimators / 7.5: |
Manski's Maximum Score Estimator / 7.5.1: |
Horowitz's Smoothed Maximum Score Estimator / 7.5.2: |
Han's Maximum Rank Correlation Estimator / 7.5.3: |
Cosslett's Approximate MLE / 7.5.4: |
An Iterative Least Squares Estimator / 7.5.5: |
Derivative-Based Estimators / 7.5.6: |
Models with Discrete Explanatory Variables / 7.5.7: |
Multinomial Discrete Choice Models / 7.6: |
Some Specification Tests for Discrete Choice Models / 7.7: |
Semiparametric Estimation of Selectivity Models / 7.8: |
Some Parametric Estimators / 8.1: |
Some Sequential Semiparametric Estimators / 8.3: |
Cosslett's Dummy Variable Method / 8.3.1: |
Powell's Kernel Estimator / 8.3.2: |
Newey's Series Estimator / 8.3.3: |
Newey's GMM Estimator / 8.3.4: |
Maximum Likelihood-Type Estimators / 8.4: |
Gallant and Nychka's Estimator / 8.4.1: |
Estimation of the Intercept in Selection Models / 8.4.2: |
Applications of the Estimators / 8.6: |
Conclusions / 8.7: |
Semiparametric Estimation of Censored Regression Models / 9: |
Semiparametric Efficiency Bounds for the Censored Regression Model / 9.1: |
The Kaplan-Meier Estimator of the Distribution Function of a Censored Random Variable / 9.4: |
Semiparametric Density-Based Estimators / 9.5: |
The Semiparametric Generalized Least Squares Estimator (SGLS) / 9.5.1: |
Estimators Replacing Part of the Sample / 9.5.2: |
Maximum Likelihood Type Estimators / 9.5.3: |
Semiparametric Nondensity-Based Estimators / 9.6: |
Powell's Censored Least Absolute Deviation (CLAD) Estimator / 9.6.1: |
Powell's (1986a) Censored Quantile Estimators / 9.6.2: |
Powell's Symmetrically Censored Least Squares Estimators / 9.6.3: |
Newey's Efficient Estimator under Conditional Symmetry / 9.6.4: |
Comparative Studies of the Estimators / 9.7: |
Retrospect and Prospect / 10: |
Statistical Methods / A: |
Probability Concepts / A.1: |
Random Variable and Distribution Function / A.1.1: |
Conditional Distribution and Independence / A.1.2: |
Borel Measurable Functions / A.1.3: |
Inequalities Involving Expectations / A.1.4: |
Characteristic Function (c.f.) / A.1.5: |
Results on Convergence / A.2: |
Weak and Strong Convergence of Random Variables / A.2.1: |
Laws of Large Numbers / A.2.2: |
Convergence of Distribution Functions / A.2.3: |
Central Limit Theorems / A.2.4: |
Further Results on the Law of Large Numbers and Convergence in Moments and Distributions / A.2.5: |
Convergence in Moments / A.2.6: |
Some Probability Inequalities / A.3: |
Order of Magnitudes (Small o and Large O) / A.4: |
Asymptotic Theory for Dependent Observations / A.5: |
Ergodicity / A.5.1: |
Mixing Sequences / A.5.2: |
Near-Epoch Dependent Sequences / A.5.3: |
Martingale Differences and Mixingales / A.5.4: |
Rosenblatt's (1970) Measure of Dependence [beta][subscript n] / A.5.5: |
Stochastic Equicontinuity / A.5.6: |
References |
Index |