1 Introduction 1
2 Density and Probability Function Estimation 5
2.1 Parametric Density Estimators 6
2.2 Histograms and Kernel Density Estimators 6
2.3 Bandwidth Selection 12
2.4 Frequency and Kernel Probability Estimators 16
2.5 Kernel Density Estimation with Discrete
and Continuous Data 18
2.6 Constructing Error Bounds 20
2.7 Curse-of-Dimensionality 21
3 Conditional Density Estimation 25
3.1 Kernel Estimation of a Conditional PDF 25
3.2 Kernel Estimation of a Conditional CDF 28
3.3 Kernel Estimation of a Conditional Quantile 29
3.4 Binary Choice and Count Data Models 31
4 Regression 33
4.1 Local Constant Kernel Regression 33
4.2 Local Polynomial Kernel Regression 38
ix
4.3 Assessing Goodness-of-Fit 46
4.4 A Resistant Local Constant Method 48
5 Semiparametric Regression 51
5.1 Partially Linear Models 52
5.2 Index Models 54
5.3 Smooth Coefficient (Varying Coefficient) Models 57
6 Panel Data Models 59
6.1 Nonparametric Estimation of Fixed Effects
Panel Data Models 60
7 Consistent Hypothesis Testing 63
7.1 Testing Parametric Model Specification 64
7.2 A Significance Test for Nonparametric Regression Models 66
8 Computational Considerations 71
8.1 Use Binning Methods 72
8.2 Use Transforms 72
8.3 Exploit Parallelism 72
8.4 Use Multipole and Tree-Based Methods 72
9 Software 75
Conclusions 77
Acknowledgments 79
Background Material 81
Notations and Acronyms 83
References 85