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SEMI‐PARAMETRIC ANALYSIS OF COVARIANCE UNDER DEPENDENCE CONDITIONS WITHIN EACH GROUP
Author(s) -
AneirosPérez Germán
Publication year - 2008
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/j.1467-842x.2008.00510.x
Subject(s) - mathematics , mahalanobis distance , parametric statistics , test statistic , statistics , analysis of covariance , covariance , statistic , nonparametric statistics , statistical hypothesis testing
Summary Consider the problem of covariance analysis based on regression models whose regression function is the sum of a linear and a non‐parametric component. We propose a parametric and a non‐parametric statistical test to compare the effects of the linear and non‐parametric components, respectively, on the response variable in L ≥ 2 groups. Serially correlated errors within each group are allowed. The first (second) test compares the differences between the estimates of the parametric (non‐parametric) components of each group by means of a Mahalanobis ( L 2 ) distance. The asymptotic distribution of each statistic under the null hypothesis is obtained. A modest simulation study and an application to a real data set illustrate our methodology.