TY - JOUR

T1 - Two samples tests for functional data

AU - Zhang, Chongqi

AU - PENG, Heng

AU - Zhang, Jin Ting

N1 - Funding Information:
Chongqi Zhang’s research is supported by NNSF of China 10871054, and Heng Peng’s research is supported by the CERG grant of Hong Research Grant Council, HKBU 201707 and the FRG grant of Hong Kong Baptist University, FRG/06-07/II-14.

PY - 2010/1

Y1 - 2010/1

N2 - Data in many experiments arises as curves and therefore it is natural to use a curve as a basic unit in the analysis, which is in terms of functional data analysis (FDA). Functional curves are encountered when units are observed over time. Although the whole function curve itself is not observed, a sufficiently large number of evaluations, as is common with modern recording equipment, is assumed to be available. In this article, we consider the statistical inference for the mean functions in the two samples problem drawn from functional data sets, in which we assume that functional curves are observed, that is, we consider the test if these two groups of curves have the same mean functional curve when the two groups of curves without noise are observed. The L2-norm based and bootstrap-based test statistics are proposed. It is shown that the proposed methodology is flexible. Simulation study and real-data examples are used to illustrate our techniques.

AB - Data in many experiments arises as curves and therefore it is natural to use a curve as a basic unit in the analysis, which is in terms of functional data analysis (FDA). Functional curves are encountered when units are observed over time. Although the whole function curve itself is not observed, a sufficiently large number of evaluations, as is common with modern recording equipment, is assumed to be available. In this article, we consider the statistical inference for the mean functions in the two samples problem drawn from functional data sets, in which we assume that functional curves are observed, that is, we consider the test if these two groups of curves have the same mean functional curve when the two groups of curves without noise are observed. The L2-norm based and bootstrap-based test statistics are proposed. It is shown that the proposed methodology is flexible. Simulation study and real-data examples are used to illustrate our techniques.

KW - Bootstrap-based test statistic

KW - Functional data

KW - Hypothesis test

KW - L2-norm-based test statistic

UR - http://www.scopus.com/inward/record.url?scp=76949107468&partnerID=8YFLogxK

U2 - 10.1080/03610920902755839

DO - 10.1080/03610920902755839

M3 - Journal article

AN - SCOPUS:76949107468

SN - 0361-0926

VL - 39

SP - 559

EP - 578

JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

IS - 4

ER -