Journal ArticleDOI
Algorithm AS 155 : The distribution of a linear combination of χ^2 random variables
Reads0
Chats0
TLDR
In this paper, the numerical inversion of the characteristic function is used to find the distribution of the ratio of two quadratic forms in independent normal variables, and the accuracy is set by the user, a maximum error of 0-0001 being an appropriate value.Abstract:
pr(Q<c). (2) The algorithm is based on the method of Davis (1973) involving the numerical inversion of the characteristic function. It will yield results for most linear combinations that are likely to be encountered in practice but is more satisfactory if the sum (1) is not dominated by terms involving a total of less than four degrees of freedom. The accuracy is set by the user, a maximum error of 0-0001 being an appropriate value. Any quadratic form in independent normal variables can be reduced to the form (1) and so this algorithm can be used to calculate the distribution of such a quadratic form. Since the Ai need not all be positive the quadratic form need not be positive definite. In particular, the algorithm can be used to find the distribution of the ratio of two quadratic forms.read more
Citations
More filters
Journal ArticleDOI
Optimal unified approach for rare-variant association testing with application to small-sample case-control whole-exome sequencing studies.
Seunggeun Lee,Mary J. Emond,Michael J. Bamshad,Kathleen C. Barnes,Mark J. Rieder,Deborah A. Nickerson,David C. Christiani,Mark M. Wurfel,Xihong Lin +8 more
TL;DR: A unified approach for testing the association between rare variants and phenotypes in sequencing association studies is proposed and it is shown that the unified test corresponds to the optimal test in an extended family of SKAT tests, which is referred to as SKAT-O.
Journal ArticleDOI
Rare-variant association analysis: study designs and statistical tests.
TL;DR: An overview of statistical issues in rare-variant association studies with a focus on study designs and statistical tests is provided and various gene- or region-based association tests are compared in terms of their assumptions and performance.
Journal ArticleDOI
The Fourier-series method for inverting transforms of probability distributions
Joseph Abate,Ward Whitt +1 more
TL;DR: This paper reviews the Fourier-series method for calculating cumulative distribution functions (cdf's) and probability mass functions (pmf's) by numerically inverting characteristic functions, Laplace transforms and generating functions and describes two methods for inverting Laplace transform based on the Post-Widder inversion formula.
Journal ArticleDOI
Optimal tests for rare variant effects in sequencing association studies.
TL;DR: This paper proposes a class of tests that include burden tests and SKAT as special cases, and derives an optimal test within this class that maximizes power, and shows that this optimal test outperforms burden testsand SKAT in a wide range of scenarios.
Journal ArticleDOI
Flexible Methods for Analyzing Survival Data Using Splines, with Applications to Breast Cancer Prognosis
TL;DR: In an analysis of a large data set taken from clinical trials conducted by the Eastern Cooperative Oncology Group, these methods are seen to give useful insight into how prognosis varies as a function of continuous covariates, and also into how covariate effects change with follow-up time.
References
More filters
Journal ArticleDOI
Numerical inversion of a characteristic function
TL;DR: In this paper, a method is described for finding a bound on the error when a version of the usual characteristic function inversion formula is evaluated by numerical integration, which is applied to the calculation of the distribution function of a quadratic form in normal random variables.