Bernoulli

  • Bernoulli
  • Volume 11, Number 6 (2005), 1093-1113.

Spectral decomposition of score functions in linkage analysis

Ola Hössjer

Full-text: Open access

Abstract

We consider stochastic processes occurring in nonparametric linkage analysis for mapping disease susceptibility genes in the human genome. Under the null hypothesis that no disease gene is located in the chromosomal region of interest, we prove that the linkage process Z converges weakly to a mixture of Ornstein-Uhlenbeck processes as the number of families N tends to infinity. Under a sequence of contiguous alternatives, we prove weak convergence towards the same Gaussian process with a deterministic non-zero mean function added to it. The results are applied to power calculations for chromosome- and genome-wide scans, and are valid for arbitrary family structures. Our main tool is the inheritance vector process v, which is a stationary and continuous-time Markov process with state space the set of binary vectors w of given length. Certain score functions are expanded as a linear combination of an orthonormal system of basis functions which are eigenvectors of the intensity matrix of v.

Article information

Source
Bernoulli, Volume 11, Number 6 (2005), 1093-1113.

Dates
First available in Project Euclid: 16 January 2006

Permanent link to this document
https://projecteuclid.org/euclid.bj/1137421641

Digital Object Identifier
doi:10.3150/bj/1137421641

Mathematical Reviews number (MathSciNet)
MR2189082

Zentralblatt MATH identifier
1098.62146

Keywords
continuous-time Markov process inheritance vectors invariance principle linkage analysis Ornstein-Uhlenbeck process spectral decomposition

Citation

Hössjer, Ola. Spectral decomposition of score functions in linkage analysis. Bernoulli 11 (2005), no. 6, 1093--1113. doi:10.3150/bj/1137421641. https://projecteuclid.org/euclid.bj/1137421641


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