The limit of the partial sums process of spatial least squares residuals
type: Item
instance of: scholarly article
title: The limit of the partial sums process of spatial least squares residuals
zbMATH Open document ID: 1183.60008
author: Wolfgang Bischoff
author: Wayan Somayasa
published in: Journal of Multivariate Analysis
publication date: 2009-11-13T00:00:00Z
review text: From the abstract: We establish a functional central limit theorem for a sequence of least squares residuals of spatial data from a linear regression model. Under mild assumptions on the model we explicitly determine the limit process in the case where the assumed linear model is true. We recognize the structure of the limit process: it is a projection of the Brownian sheet onto a certain subspace of the reproducing kernel Hilbert space of the Brownian sheet. Several examples are discussed.
reviewed by: Wiesław Dziubdziela
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 62G10
Mathematics Subject Classification ID: 62G20
Mathematics Subject Classification ID: 62J05
Mathematics Subject Classification ID: 62M30
zbMATH DE Number: 5632781
zbMATH Keywords: spatial least squares residuals
zbMATH Keywords: partial sums process
zbMATH Keywords: set indexed partial sums
zbMATH Keywords: Brownian sheet
zbMATH Keywords: Brownian pillow
zbMATH Keywords: bounded variation
zbMATH Keywords: Riemann-Stieltjes integral
MaRDI profile type: Publication
full work available at URL: j.jmva.2009.04.005
OpenAlex ID: W1968415419
cites work: Properties of sequences of partial sums of polynomial regression residuals with applications to tests for change of regression at unknown times
cites work: Limit processes for sequences of partial sums of regression residuals
cites work: Q4850608
cites work: Q3533323
cites work: Q4431554
cites work: Exact asymptotics for boundary crossings of the Brownian bridge with trend with application to the Kolmogorov test
cites work: Analysis of a change-point regression problem in quality control by partial sums processes and Kolmogorov type tests
cites work: Wiener Measure in a Space of Functions of Two Variables
cites work: The Invariance Principle for a Lattice of Random Variables
cites work: Q5560061
cites work: Q3962244
cites work: Functional law of the iterated logarithm and uniform central limit theorem for partial-sum processes indexed by sets
cites work: A uniform central limit theorem for set-indexed partial-sum processes with finite variance
cites work: Q4308169
cites work: On Definitions of Bounded Variation for Functions of Two Variables
cites work: On double Riemann-Stieltjes integrals
cites work: Q3269253
cites work: Pointwise behavior of double Fourier series of functions of bounded variation
cites work: Q4340096
cites work: Characterisation of weak convergence of signed measures on $[0,1]$.
cites work: An Elementary Characterization of Weak Convergence of Measures
cites work: A Multi-Parameter Gaussian Process
cites work: Q5633320
DOI: 10.1016/J.JMVA.2009.04.005
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description: scientific article; zbMATH DE number 5632781