On the optimization of the weighted Bickel-Rosenblatt test
نویسنده
چکیده
We consider Bickel-Rosenblatt tests of fit for a density f . Their asymptotic properties are studied under local Pitman’s alternatives ; we investigate their power functions. Our goal is to look for the best test in this class, by optimizing the power as done by Mason (1983) in the context of minimax comparisons. This approach leads to a continuous versions of a χ type test. Finally a simulation study is presented. AMS Subject Classifications: primary 60F05, 60F17; secondary 62G07, 62G10.
منابع مشابه
A note on the Bickel - Rosenblatt test in autoregressive time series
In a recent paper Lee and Na (2001) introduced a test for a parametric form of the distribution of the innovations in autoregressive models, which is based on the integrated squared error of the nonparametric density estimate from the residuals and a smoothed version of the parametric fit of the density. They derived the asymptotic distribution under the null-hypothesis, which is the same as fo...
متن کاملOn the Asymptotic Behaviour of Location-scale Invariant Bickel-rosenblatt Tests
Location-scale invariant Bickel-Rosenblatt goodness-of-fit tests (IBR tests) are considered in this paper to test the hypothesis that f , the common density function of the observed independent d-dimensional random vectors, belongs to a null location-scale family of density functions. The asymptotic behaviour of the test procedures for fixed and non-fixed bandwidths is studied by using an unify...
متن کاملA Goodness-of-fit test for GARCH innovation density
We prove asymptotic normality of a suitably standardized integrated square difference between a kernel type error density estimator based on residuals and the expected value of the error density estimator based on innovations in GARCH models. This result is similar to that of Bickel-Rosenblatt under i.i.d. set up. Consequently the goodness-of-fit test for the innovation density of the GARCH pro...
متن کاملOn the Finite Sample Behavior of Fixed Bandwidth Bickel-Rosenblatt Test for Univariate and Multivariate Uniformity
The Bickel-Rosenblatt (BR) goodness-of-fit test with fixed bandwidth was introduced by Fan in 1998 [Econometric Theory 14, 604–621, 1998]. Although its asymptotic properties have being studied by several authors, little is known about its finite sample performance. Restricting our attention to the test of uniformity in the d-unit cube for d ≥ 1, we present in this paper a description of the fin...
متن کاملKernel Density Estimators: Convergence in Distribution for Weighted Sup-norms
Let fn denote a kernel density estimator of a bounded continuous density f in the real line. Let Ψ(t) be a positive continuous function such that ‖Ψf‖∞<∞. Under natural smoothness conditions, necessary and sufficient conditions for the sequence √ nhn 2 log h−1 n supt∈R ∣∣Ψ(t)(fn(t)−Efn(t))∣∣ (properly centered and normalized) to converge in distribution to the double exponential law are obtaine...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2003