JSM 2004 - Toronto

Abstract #301420

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Activity Number: 341
Type: Contributed
Date/Time: Wednesday, August 11, 2004 : 10:30 AM to 12:20 PM
Sponsor: Section on Nonparametric Statistics
Abstract - #301420
Title: A Unified Nonparametric Approach for Unbalanced Factorial Designs
Author(s): Xin Gao*+ and Mayer Alvo
Companies: York University and University of Ottawa
Address: Dept. of Maths & Stats, North York, ON, M3J 1P3, Canada
Keywords: linear rank statistics ; main effect ; interaction effect ; nested effect ; Pitman alternative ; quantitative trait
Abstract:

Motivated by questions arising from the field of statistical genetics, we consider the problem of testing main, nested, and interaction effects in unbalanced factorial designs. Based on the concept of composite linear rank statistics, a new notion of weighted rank is proposed. Asymptotic normality of weighted linear rank statistics is established under mild conditions and consistent estimators are developed for the corresponding limiting covariance structure. A unified framework to employ weighted rank to construct test statistics for main, nested, and interaction effects in unbalanced factorial designs is established. The proposed test statistics are applicable to unbalanced designs with arbitrary cell replicates that are greater than one per cell. The limiting distributions under both the null hypotheses and Pitman alternatives are derived. Monte Carlo simulations are conducted to confirm the validity and power of the proposed tests. Genetic datasets from a simulated backcross study are analyzed to demonstrate the application of the proposed tests in quantitative trait loci mapping.

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