Rank test for heteroscedastic functional data

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

In this paper, we consider (mid-)rank based inferences for testing hypotheses in a fully nonparametric marginal model for heteroscedastic functional data that contain a large number of within subject measurements from possibly only a limited number of subjects. The effects of several crossed factors and their interactions with time are considered. The results are obtained by establishing asymptotic equivalence between the rank statistics and their asymptotic rank transforms. The inference holds under the assumption of α-mixing without moment assumptions. As a result, the proposed tests are applicable to data from heavy-tailed or skewed distributions, including both continuous and ordered categorical responses. Simulation results and a real application confirm that the (mid-)rank procedures provide both robustness and increased power over the methods based on original observations for non-normally distributed data.

Original languageEnglish (US)
Pages (from-to)1791-1805
Number of pages15
JournalJournal of Multivariate Analysis
Volume101
Issue number8
DOIs
StatePublished - Sep 1 2010

Fingerprint

Rank Test
Functional Data
Statistics
Testing
Rank Statistics
Asymptotic Equivalence
Marginal Model
Skewed Distribution
Testing Hypotheses
Heavy-tailed Distribution
Nonparametric Model
Categorical
Transform
Robustness
Moment
Interaction
Rank test
Simulation
Inference

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

Cite this

@article{aa74a52a0416418f8b6c3fb92572f2b2,
title = "Rank test for heteroscedastic functional data",
abstract = "In this paper, we consider (mid-)rank based inferences for testing hypotheses in a fully nonparametric marginal model for heteroscedastic functional data that contain a large number of within subject measurements from possibly only a limited number of subjects. The effects of several crossed factors and their interactions with time are considered. The results are obtained by establishing asymptotic equivalence between the rank statistics and their asymptotic rank transforms. The inference holds under the assumption of α-mixing without moment assumptions. As a result, the proposed tests are applicable to data from heavy-tailed or skewed distributions, including both continuous and ordered categorical responses. Simulation results and a real application confirm that the (mid-)rank procedures provide both robustness and increased power over the methods based on original observations for non-normally distributed data.",
author = "Haiyan Wang and {Akritas Michael G.}, {M. G.}",
year = "2010",
month = "9",
day = "1",
doi = "10.1016/j.jmva.2010.03.012",
language = "English (US)",
volume = "101",
pages = "1791--1805",
journal = "Journal of Multivariate Analysis",
issn = "0047-259X",
publisher = "Academic Press Inc.",
number = "8",

}

Rank test for heteroscedastic functional data. / Wang, Haiyan; Akritas Michael G., M. G.

In: Journal of Multivariate Analysis, Vol. 101, No. 8, 01.09.2010, p. 1791-1805.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Rank test for heteroscedastic functional data

AU - Wang, Haiyan

AU - Akritas Michael G., M. G.

PY - 2010/9/1

Y1 - 2010/9/1

N2 - In this paper, we consider (mid-)rank based inferences for testing hypotheses in a fully nonparametric marginal model for heteroscedastic functional data that contain a large number of within subject measurements from possibly only a limited number of subjects. The effects of several crossed factors and their interactions with time are considered. The results are obtained by establishing asymptotic equivalence between the rank statistics and their asymptotic rank transforms. The inference holds under the assumption of α-mixing without moment assumptions. As a result, the proposed tests are applicable to data from heavy-tailed or skewed distributions, including both continuous and ordered categorical responses. Simulation results and a real application confirm that the (mid-)rank procedures provide both robustness and increased power over the methods based on original observations for non-normally distributed data.

AB - In this paper, we consider (mid-)rank based inferences for testing hypotheses in a fully nonparametric marginal model for heteroscedastic functional data that contain a large number of within subject measurements from possibly only a limited number of subjects. The effects of several crossed factors and their interactions with time are considered. The results are obtained by establishing asymptotic equivalence between the rank statistics and their asymptotic rank transforms. The inference holds under the assumption of α-mixing without moment assumptions. As a result, the proposed tests are applicable to data from heavy-tailed or skewed distributions, including both continuous and ordered categorical responses. Simulation results and a real application confirm that the (mid-)rank procedures provide both robustness and increased power over the methods based on original observations for non-normally distributed data.

UR - http://www.scopus.com/inward/record.url?scp=77953082404&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77953082404&partnerID=8YFLogxK

U2 - 10.1016/j.jmva.2010.03.012

DO - 10.1016/j.jmva.2010.03.012

M3 - Article

AN - SCOPUS:77953082404

VL - 101

SP - 1791

EP - 1805

JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

SN - 0047-259X

IS - 8

ER -