A goodness-of-fit test for marginal distribution of linear random fields with long memory

作者：Koul Hira L^*; Mimoto Nao; Surgailis Donatas

来源：Metrika, 2016, 79(2): 165-193.

DOI：10.1007/s00184-015-0550-z

• Degenerate residual empirical process
• Cauchy distribution

This paper addresses the problem of fitting a known distribution function to the marginal distribution of a stationary long memory moving average random field observed on increasing nu-dimensional "cubic" domains when its mean mu and scale sigma are known or unknown. Using two suitable estimators of mu and a classical estimate of sigma, a modification of theKolmogorov-Smirnov statistic is defined based on the residual empirical process and having a Cauchy-type limit distribution, independent of mu, sigma and 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. The result is new even for the case of time series, i.e., when nu = 1. Findings of a simulation study investigating the finite sample behavior of size and power of the proposed test is also included in this paper.

• 出版日期2016-2