Article

# On bootstrapping L2-type statistics in density testing

Sonderforschungsbereich 373, Humboldt-Universität zu Berlin, Spandauer Straße 1, D-10178 Berlin, Germany
(Impact Factor: 0.53). 11/2000; 50(2):137-147. DOI: 10.1016/S0167-7152(00)00091-2

ABSTRACT We consider non-parametric tests for checking parametric hypotheses about the stationary density of weakly dependent observations. The test statistic is based on the L2-distance between a non-parametric and a smoothed version of a parametric estimate of the stationary density. Since this statistic behaves asymptotically as in the case of independent observations an i.i.d.-type bootstrap to determine the critical value for the test is proposed.

### Full-text

Available from: Efstathios Paparoditis, Jul 08, 2014
0 Followers
·
59 Views
• Source
##### Article: Model Checks in Inverse Regression Models with Convolution-Type Operators
[Hide abstract]
ABSTRACT: We consider the problem of testing parametric assumptions in an inverse regression model with a convolution-type operator. An L^2-type goodness-of-fit test is proposed which compares the distance between a parametric and a nonparametric estimate of the regression function. Asymptotic normality of the corresponding test statistic is shown under the null hypothesis and under a general nonparametric alternative with different rates of convergence in both cases. The feasibility of the proposed test is demonstrated by means of a small simulation study. In particular, the power of the test against certain types of alternative is investigated.
Scandinavian Journal of Statistics 03/2013; 39(2). DOI:10.2307/41679796 · 1.06 Impact Factor
• Source
##### Article: Bickel–Rosenblatt Test for Weakly Dependent Data
[Hide abstract]
ABSTRACT: The aim of this paper is to analyze the Bickel–Rosenblatt test for simple hypothesis in case of weakly dependent data. Although the test has nice theoretical properties, it is not clear how to implement it in practice. Choosing different band-width sequences first we analyze percentage rejections of the test statistic under H0 by some empirical simulation analysis. This can serve as an approximate rule for choosing the bandwidth in case of simple hypothesis for practical implementation of the test. In the recent paper [12] a version of Neyman goodness-of-fit test was established for weakly dependent data in the case of simple hypotheses. In this paper we also aim to compare and discuss the applicability of these tests for both independent and dependent observations.
Mathematical Modelling and Analysis 06/2012; 17(3):383-395. DOI:10.3846/13926292.2012.685959 · 0.54 Impact Factor
• Source
##### Article: Characteristic function-based goodness-of-fit tests under weak dependence
[Hide abstract]
ABSTRACT: This article proposes two consistent hypothesis tests of L 2 -type for weakly dependent ob-servations based on the empirical characteristic function. We consider a symmetry test and a goodness-of-fit test for the marginal distribution of a time series. Since the asymptotic distributions of the test statistics depend on unknown parameters in a complicated way, we suggest to apply certain parametric bootstrap methods in order to determine critical values of the tests.