Cramér-von Mises regression
نویسندگان
چکیده
Consider a linear regression model with unknown regression parameters 0 and independent errors of unknown distribution. Block the observations into q groups whose independent variables have a common value and measure the homogeneity of the blocks of residuals by a Cramér-von Mises q-sample statistic Tq( ). This statistic is designed so that its expected value as a function of the chosen regression parameter has a minimum value of zero precisely at the true value 0. The minimizer ̂ of Tq( ) over all is shown to be a consistent estimate of 0. It is also shown that the bootstrap distribution of Tq( 0) can be used to do a lack of fit test of the regression model and to construct a confidence region for 0.
منابع مشابه
Cramér-Von Mises Statistic for Repeated Measures El estadístico de Cramér-Von Mises para medidas repetidas
The Cramér-von Mises criterion is employed to compare whether the marginal distribution functions of a k-dimensional random variable are equal or not. The well-known Donsker invariance principle and the KarhunenLoéve expansion is used in order to derive its asymptotic distribution. Two different resampling plans (one based on permutations and the other one based on the general bootstrap algorit...
متن کاملAsymptotic local efficiency of Cramér--von Mises tests for multivariate independence
Deheuvels [J. Multivariate Anal. 11 (1981) 102–113] and Genest and Rémillard [Test 13 (2004) 335–369] have shown that powerful rank tests of multivariate independence can be based on combinations of asymptotically independent Cramér–von Mises statistics derived from a Möbius decomposition of the empirical copula process. A result on the large-sample behavior of this process under contiguous seq...
متن کاملfastGCVM: A Fast Algorithm for the Computation of the Discrete Generalized Cramér-von Mises Distance
Comparing two random vectors by calculating a distance measure between the underlying probability density functions is a key ingredient in many applications, especially in the domain of image processing. For this purpose, the recently introduced generalized Cramér-von Mises distance is an interesting choice, since it is well defined even for the multivariate and discrete case. Unfortunately, th...
متن کاملCombining Standardized Time Series Area and Cramér–von Mises Variance Estimators
We propose three related estimators for the variance parameter arising from a steady-state simulation process. All are based on combinations of standardized-time-series area and Cramér–von Mises (CvM) estimators. The first is a straightforward linear combination of the area and CvM estimators; the second resembles a Durbin–Watson statistic; and the third is related to a jackknifed version of th...
متن کاملEstimators based on ω-dependent generalized weighted Cramér-von Mises distances under censoring - with applications to mixture models
Estimators based on ω-dependent generalized weighted Cramér-von Mises distances are defined for data that are subject to a possible right censorship. The distance between the data, summarized by the Kaplan-Meier estimator, and the target model is allowed to depend on the sample size and, for example, on the number of censored items. It is shown that the estimators are consistent and asymptotica...
متن کامل