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| Preface | |
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| Introduction | |
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| Methods of Density Estimation | |
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| Introduction | |
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| Nonparametric Density Estimation | |
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| A "Local" Histogram Approach | |
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| A Formal Derivation of andfirac;[subscript 1] (x) | |
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| Rosenblatt-Parzen Kernel Estimator | |
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| The Nearest Neighborhood Estimator | |
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| Variable Window-Width Estimators | |
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| Series Estimators | |
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| Penalized Likelihood Estimators | |
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| The Local Log-Likelihood Estimators | |
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| Summary | |
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| Estimation of Derivatives of a Density | |
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| Finite-Sample Properties of the Kernel Estimator | |
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| The Exact Bias and Variance of the Estimator andfirac; | |
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| Approximations to the Bias and Variance and Choices of h and K | |
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| Reduction of Bias | |
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| Asymptotic Properties of the Kernel Density Estimator andfirac; with Independent Observations | |
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| Asymptotic Unbiasedness | |
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| Consistency | |
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| Asymptotic Normality | |
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| Small-Sample Confidence Intervals | |
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| Sampling Properties of the Kernel Density Estimator with Dependent Observations | |
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| Unbiasedness | |
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| Consistency | |
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| Asymptotic Normality | |
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| Bibliographical Summary (Approximate and Asymptotic Results) | |
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| Choices of Window Width and Kernel: Further Discussion | |
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| Choice of h | |
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| Choice of Higher Order Kernels | |
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| Choice of h for Density Derivatives | |
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| Multivariate Density Estimation | |
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| Testing Hypotheses about Densities | |
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| Comparison with a Known Density Function | |
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| Testing for Symmetry | |
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| Comparison of Unknown Densities | |
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| Testing for Independence | |
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| Examples | |
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| Density of Stock Market Returns | |
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| Estimating the Dickey-Fuller Density | |
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| Conditional Moment Estimation | |
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| Introduction | |
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| Estimating Conditional Moments by Kernel Methods | |
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| Parametric Estimation | |
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| Nonparametric Estimation: A "Local" Regression Approach | |
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| Kernel-Based Estimation: A Formal Derivation | |
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| A General Nonparametric Estimator of m(x) | |
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| Unifying Nonparametric Estimators | |
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| Estimation of Higher Order Conditional Moments | |
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| Finite-Sample Properties | |
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| Approximate Results: Stochastic x | |
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| The Local Linear Regression Estimator | |
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| Combining Parametric and Nonparametric Estimators | |
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| Asymptotic Properties | |
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| Asymptotic Properties of the Kernel Estimator with Independent Observations | |
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| Asymptotic Properties of the Kernel Estimator with Dependent Observations | |
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| Bibliographical Summary (Asymptotic Results) | |
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| Implementing the Kernel Estimator | |
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| Choice of Window Width | |
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| Robust Nonparametric Estimation of Moments | |
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| Estimating Conditional Moments by Series Methods | |
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| Asymptotic Properties of Series Estimators with Independent Observations | |
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| Asymptotic Properties of Series Estimators with Dependent Observations | |
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| Implementing the Estimator | |
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| Imposing Structure on the Conditional Moments | |
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| Generalized Additive Models | |
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| Projection Pursuit Regression | |
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| Neural Networks | |
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| Measuring the Affinity of Parametric and Nonparametric Models | |
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| Examples | |
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| A Model of Strike Duration | |
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| Earnings-Age Profiles | |
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| Review of Applied Work on Nonparametric Regression | |
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| Nonparametric Estimation of Derivatives | |
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| Introduction | |
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| The Model and Partial Derivative Formulae | |
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| Estimation | |
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| Estimation of Partial Derivatives by Kernel Methods | |
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| Estimation of Partial Derivatives by Series Methods | |
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| Estimation of Average Derivatives | |
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| Local Linear Derivative Estimators | |
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| Pointwise Versus Average Derivatives | |
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| Restricted Estimation and Hypothesis Testing | |
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| Imposing Linear Equality Restriction on Partial Derivatives | |
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| Imposing Linear Inequality Restrictions | |
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| Hypothesis Testing | |
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| Asymptotic Properties of Partial Derivative Estimators | |
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| Asymptotic Properties of Kernel-Based Estimators | |
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| Series-Based Estimators | |
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| Higher Order Derivatives | |
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| Local Linear Estimators | |
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| Asymptotic Properties of Kernel-Based Average Derivative Estimators | |
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| Implementing the Derivative Estimators | |
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| Illustrative Examples | |
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| A Monte Carlo Experiment with a Production Function | |
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| Earnings-Age Relationship | |
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| Review of Applied Work | |
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| Semiparametric Estimation of Single-Equation Models | |
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| Introduction | |
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| Semiparametric Estimation of the Linear Part of a Regression Model | |
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| General Results | |
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| Diagnostic Tests after Nonparametric Regression | |
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| Semiparametric Estimation of Some Macro Models | |
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| The Asymptotic Covariance Matrix of SP Estimators without Asymptotic Independence | |
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| Efficient Estimation of Semiparametric Models in the Presence of Heteroskedasticity of Unknown Form | |
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| Conditions for Adaptive Estimation | |
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| Efficient Estimation of Regression Parameters with Unknown Error Density | |
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| Efficient Estimation by Likelihood Approximation | |
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| Efficient Estimation by Kernel-Based Score Approximation | |
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| Efficient Estimation by Moment-Based Score Approximation | |
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| Estimation of Scale Parameters | |
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| Optimal Diagnostic Tests in Linear Models | |
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| Adaptive Estimation with Dependent Observations | |
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| M-Estimators | |
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| Estimation | |
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| Diagnostic Tests with M-Estimators | |
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| Sequential M-Estimators | |
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| The Semiparametric Efficiency Bound for Moment-Based Estimators | |
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| Approximating the SP Efficiency Bound by a Conditional Moment Estimator | |
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| Applications | |
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| Semiparametric Estimation of a Heteroskedastic Model | |
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| Adaptive Estimation of a Model of House Prices | |
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| Review of Other Applications | |
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| Semiparametric and Nonparametric Estimation of Simultaneous Equation Models | |
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| Introduction | |
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| Single-Equation Estimators | |
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| Parametric Estimation | |
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| Rilstone's Semiparametric Two-Stage Least Squares Estimator | |
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| Systems Estimation | |
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| A Parametric Estimator | |
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| The SP3SLS Estimator | |
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| Newey's Estimator | |
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| Newey's Efficient Distribution-Free Estimators | |
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| Finite-Sample Properties | |
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| Nonparametric Estimation | |
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| Identification | |
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| Nonparametric Two-Stage Least Squares (2SLS) Estimation | |
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| Semiparametric Estimation of Discrete Choice Models | |
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| Introduction | |
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| Parametric Estimation of Binary Discrete Choice Models | |
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| Semiparametric Efficiency Bounds for Binary Discrete Choice Models | |
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| Semiparametric Estimation of Binary Discrete Choice Models | |
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| Ichimura's Estimator | |
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| Klein and Spady's Estimator | |
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| The SNP Maximum Likelihood Estimator | |
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| Local Maximum Likelihood Estimation | |
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| Alternative Consistent SP Estimators | |
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| Manski's Maximum Score Estimator | |
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| Horowitz's Smoothed Maximum Score Estimator | |
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| Han's Maximum Rank Correlation Estimator | |
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| Cosslett's Approximate MLE | |
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| An Iterative Least Squares Estimator | |
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| Derivative-Based Estimators | |
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| Models with Discrete Explanatory Variables | |
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| Multinomial Discrete Choice Models | |
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| Some Specification Tests for Discrete Choice Models | |
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| Applications | |
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| Semiparametric Estimation of Selectivity Models | |
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| Introduction | |
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| Some Parametric Estimators | |
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| Some Sequential Semiparametric Estimators | |
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| Cosslett's Dummy Variable Method | |
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| Powell's Kernel Estimator | |
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| Newey's Series Estimator | |
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| Newey's GMM Estimator | |
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| Maximum Likelihood-Type Estimators | |
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| Gallant and Nychka's Estimator | |
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| Newey's Estimator | |
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| Estimation of the Intercept in Selection Models | |
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| Applications of the Estimators | |
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| Conclusions | |
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| Semiparametric Estimation of Censored Regression Models | |
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| Introduction | |
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| Some Parametric Estimators | |
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| Semiparametric Efficiency Bounds for the Censored Regression Model | |
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| The Kaplan-Meier Estimator of the Distribution Function of a Censored Random Variable | |
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| Semiparametric Density-Based Estimators | |
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| The Semiparametric Generalized Least Squares Estimator (SGLS) | |
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| Estimators Replacing Part of the Sample | |
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| Maximum Likelihood Type Estimators | |
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| Semiparametric Nondensity-Based Estimators | |
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| Powell's Censored Least Absolute Deviation (CLAD) Estimator | |
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| Powell's (1986a) Censored Quantile Estimators | |
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| Powell's Symmetrically Censored Least Squares Estimators | |
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| Newey's Efficient Estimator under Conditional Symmetry | |
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| Comparative Studies of the Estimators | |
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| Retrospect and Prospect | |
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| Statistical Methods | |
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| Probability Concepts | |
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| Random Variable and Distribution Function | |
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| Conditional Distribution and Independence | |
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| Borel Measurable Functions | |
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| Inequalities Involving Expectations | |
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| Characteristic Function (c.f.) | |
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| Results on Convergence | |
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| Weak and Strong Convergence of Random Variables | |
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| Laws of Large Numbers | |
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| Convergence of Distribution Functions | |
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| Central Limit Theorems | |
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| Further Results on the Law of Large Numbers and Convergence in Moments and Distributions | |
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| Convergence in Moments | |
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| Some Probability Inequalities | |
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| Order of Magnitudes (Small o and Large O) | |
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| Asymptotic Theory for Dependent Observations | |
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| Ergodicity | |
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| Mixing Sequences | |
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| Near-Epoch Dependent Sequences | |
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| Martingale Differences and Mixingales | |
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| Rosenblatt's (1970) Measure of Dependence [beta][subscript n] | |
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| Stochastic Equicontinuity | |
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| References | |
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| Index | |