Nonparametric conditional estimation
Many nonparametric regression techniques (such as kernels, nearest neighbors, and smoothing splines) estimate the conditional mean of Y given X = chi by a weighted sum of observed Y values, where observations with X values near chi tend to have larger weights. In this report the weights are taken to represent a finite signed measure on the space of Y values. This measure is studied as an estimate of the conditional distribution of Y given X = chi. From estimates of the conditional distribution, estimates of conditional means, standard deviations, quantiles and other statistical functionals may be computed. Chapter 1 illustrates the computation of conditional quantiles and conditional survival probabilities on the Stanford Heart Transplant data. Chapter 2 contains a survey of nonparametric regression methods and introduces statistical metrics and von Mises' method for later use. Chapter 3 proves some consistency results. Chapter 4 provides conditions under which the suitably normalized errors in estimating the conditional distribution of Y have a Brownian limit. Using von Mises' method, asymptotic normality is obtained for nonparametric conditional estimates of compactly differentiable statistical functionals.
- Research Organization:
- Stanford Linear Accelerator Center, Menlo Park, CA (USA)
- DOE Contract Number:
- AC03-76SF00515
- OSTI ID:
- 6536801
- Report Number(s):
- SLAC-309; ON: DE87010324
- Country of Publication:
- United States
- Language:
- English
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