Nonparametric Simple Regression: Smoothing Scatterplots

by John Fox
Sage Publications, 2000



 

Table of Contents


1. What is Nonparametric Regression?

    1.1 Preliminary Examples
        1.1.1 Infant Mortality
        1.1.2 Married Women's Labor-Force Participation
        1.1.3 Prestige of Canadian Occupations
    1.2 Plan of This Monograph
    1.3 Notes on Background, Approach, and Computing

2. Binning and Local Averaging

    2.1 Binning
        2.1.1 Statistical Considerations*
    2.2 Local Averaging
        2.2.1 Moving Averages for Time-Series Data

3. Kernel Estimation

4. Local Polynomial Regression
    4.1 Selecting the Span
    4.2 Statistical Issues in Local Regression*
    4.3 Bandwidth Revisited*
        4.3.1 Selecting the Span by Cross-Validation
    4.4 Making Local Regression Resistant to Outliers
        4.4.1 Normal Quantile-Comparison Plots of Residuals
    4.5 Displaying Spread and Asymmetry*
    4.6 Smoothing Time-Series Data*

5. Statistical Inference for Local-Polynomial Regression
    5.1 Confidence Envelopes
    5.2 Hypothesis Tests
    5.3 Some Statistical Details and Alternative Inference Procedures*
        5.3.1 The Smoother Matrix and the Variance of the Fitted Values
        5.3.2 Degrees of Freedom
        5.3.3 A Caveat
        5.3.4 Bootstrap Confidence Bands
        5.3.5 Randomization Tests

6.    Splines*
    6.1 Regression Splines
    6.2 Smoothing Splines
    6.3 Equivalent Kernels

7.    Nonparametric Regression and Data Analysis
    7.1 The "Bulging Rule"
    7.2 Partial-Residual Plots
    7.3 Concluding Remarks



* Material marked by asterisks is relatively difficult.


Last modified: 29 May 2000 by John Fox jfox@mcmaster.ca