We suggest two improved methods for conditional density estimation. The first is based on locally fitting a log-linear model, and is in the spirit of recent work on locally parametric techniques in...

http://eprints.lse.ac.uk/6092/1/Nonparametric_estimation_and_symmetry_tests_for_conditional_density_functions(LSERO).pdf

Nonparametric estimation and symmetry tests for conditional density functions

We suggest two new methods for conditional density estimation. The first is based on locally fitting a log-linear model, and is in the spirit of recent work on locally parametric techniques in density estimation. The second method is a constrained local polynomial estimator. Both methods always produce non-negative estimators. We propose an algorithm suitable for selecting the two bandwidths for either estimator. We also develop a new bootstrap test for the symmetry of conditional density functions. The proposed methods are illustrated by both simulation and application to a real data set.

Nonparametric Estimation and Symmetry Tests for Conditional Density Functions

I present a simple test, based on a runs statistic, for symmetry of a continuous distribution about a known median. The statistic has a binomial sampling distribution and desirable invariance properties. Monte Carlo studies demonstrate that, for a wide variety of alternative asymmetric distributions, the test is more powerful than tests proposed by Butler (1969), Rothman and Woodroofe (1972), or Hill and Rao (1977).

A Distribution-Free Test for Symmetry Based on a Runs Statistic

Omnibus tests for various nonparametric hypotheses are developed using the empirical likelihood method. These include tests for symmetry about zero, changes in distribution, independence and exponentiality. The approach is to localize the empirical likelihood using a suitable “time” variable implicit in the null hypothesis and then form an integral of the log-likelihood ratio statistic. The asymptotic null distributions of these statistics are established. In simulation studies, the proposed statistics are found to have greater power than corresponding Cram´‐von Mises type statistics.

/pdf/empirical-likelihood-based-hypothesis-testing-22vfm7inbw.pdf

Empirical likelihood based hypothesis testing

SUMMARY In the Koziol-Green (1976) model of random censorship the survival distribution of the censoring variables is some power, the censoring parameter, of the survival distribution of the lifetimes. Using a strong approximation result of Burke, Csorgo and Horvath, we construct empirical exact confidence bands for the life distribution of the censored variable, and a randomly Efron-transformed variant of the usual product-limit process is shown to converge weakly to the Brownian motion process on any interval [0, T] when the censoring parameter is also estimated from the sample. The technique automatically gives rates of convergence for a wide class of functionals including the Cramer-von Mises functional whose limit theory is worked out in detail. The latter goodness-of-fit statistic is applied to reexamine the hospital data of Koziol & Green (1976) to test whether oestrogen treatment for prostatic cancer was effective or not for the cancer itself while it caused censoring deaths of cardiovascular diseases.

On the Koziol-Green model for random censorship

A Cramer von-Mises type statistic is proposed for testing the symmetry of a continuous distribution function Its asymptotic null distribution is found explicitly, and its asymptotic distribution under a sequence of local alternatives is described A Monte Carlo study indicates that the asymptotic formulae are accurate for sample sizes as small as twenty

https://projecteuclid.org/download/pdf_1/euclid.aoms/1177690879

E. D. Rothman

Papers

A Cramer Von-Mises Type Statistic for Testing Symmetry