B0901
Title: A goodness-of-fit test for marginal distribution of linear random fields with long memory
Authors: Nao Mimoto - University of Akron (United States) [presenting]
Hira Koul - Michigan State University (United States)
Donatas Surgailis - Vilnius university - Institute of mathematics and informatics (Lithuania)
Abstract: The problem considered is the goodness-of-fit test of fitting a specified distribution function to the marginal distribution of a stationary long-memory moving average random field observed on increasing $v$-dimensional cubic domains when its mean and scale parameters are known or unknown. This set up includes the time series case as $v=1$. In the case of unknown mean, if the mean is estimated by the sample mean, the first order difference between the residual empirical process and null distribution functions is known to be asymptotically degenerate at zero, and hence can not be used to fit a distribution up to an unknown mean. We show that by choosing suitable class of estimators of the mean, this first order degeneracy does not occur. Further, using a sample standard deviation as a estimate of scale, a modified Kolmogorov-Smirnov statistic based on the residual empirical process has Cauchy-type limit distribution, independent of mean and scale parameter, as well as the long-memory parameter $d$. Based on this result, a simple goodness-of-fit test for the marginal distribution is constructed, which does not require the estimation of d or any other underlying nuisance parameters. A simulation study investigating the finite sample behavior of size and power is presented.
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