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

Hira Koul (), Nao Mimoto and Donatas Surgailis

Metrika: International Journal for Theoretical and Applied Statistics, 2016, vol. 79, issue 2, 165-193

Abstract: 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 $$\nu $$ ν -dimensional “cubic” domains when its mean $$\mu $$ μ and scale $$\sigma $$ σ are known or unknown. Using two suitable estimators of $$\mu $$ μ and a classical estimate of $$\sigma $$ σ , a modification of the Kolmogorov–Smirnov statistic is defined based on the residual empirical process and having a Cauchy-type limit distribution, independent of $$\mu ,\sigma $$ μ , σ 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 $$\nu =1$$ ν = 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. Copyright Springer-Verlag Berlin Heidelberg 2016

Keywords: Degenerate residual empirical process; Cauchy distribution; Primary 62G07; Secondary 62M10 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:spr:metrik:v:79:y:2016:i:2:p:165-193

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DOI: 10.1007/s00184-015-0550-z

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