A Cramer Von-Mises Type Statistic for Testing Symmetry
01 Dec 1972-Annals of Mathematical Statistics (Institute of Mathematical Statistics)-Vol. 43, Iss: 6, pp 2035-2038
TL;DR: In this article, a Cramer von-Mises type statistic is proposed for testing the symmetry of a continuous distribution function and its asymptotic null distribution is found explicitly.
Abstract: 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
Citations
More filters
TL;DR: In this article, two improved methods for conditional density estimation were proposed based on locally fitting a log-linear model, and is in the spirit of recent work on locally parametric techniques in estimation.
Abstract: 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...
135 citations
Posted Content•
TL;DR: This work suggests two improved methods for conditional density estimation based on locally fitting a log-linear model and a constrained local polynomial estimator, both of which always produce non-negative estimators.
Abstract: 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.
133 citations
Cites background from "A Cramer Von-Mises Type Statistic f..."
...…testing the symmetry of unconditional density functions, which include, among others, Butler (1969), Hollander (1971), Rothman and Woodroofe (1972), Srinivasan and Godio (1974), Doksum et al. (1977), Hill and Rao (1977), Lockhart and McLaren (1985), Csörgö and Heathcote (1987), Zhu (1998) and…...
[...]
TL;DR: In this paper, the authors present a simple test based on a runs statistic for symmetry of a continuous distribution about a known median, which has a binomial sampling distribution and desirable invariance properties.
Abstract: 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).
99 citations
Cites methods from "A Cramer Von-Mises Type Statistic f..."
...A Cramer-von Mises type of statistic proposed by Rothman and Woodroofe (1972):...
[...]
01 Jan 2000
TL;DR: In this article, the empirical likelihood is used to localize the empirical probability using a suitable time variable implicit in the null hypothesis and then form an integral of the log-likelihood ratio statistic.
Abstract: 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.
87 citations
TL;DR: In this paper, a strong approximation result of Burke, Csorgo and Horvath is used to 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.
Abstract: 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.
84 citations