Showing papers in "Journal of the royal statistical society series b-methodological in 1975"
TL;DR: In this paper, the stability over time of regression relationships is investigated using recursive residuals, defined to be uncorrelated with zero means and constant variance, and tests based on the cusum and cusume of squares of recursive residual coefficients are developed.
Abstract: Methods for studying the stability over time of regression relationships are considered. Recursive residuals, defined to be uncorrelated with zero means and constant variance, are introduced and tests based on the cusum and cusum of squares of recursive residuals are developed. Further techniques based on moving regressions, in which the regression model is fitted from a segment of data which is moved along the series, and on regression models whose coefficients are polynomials in time are studied. The Quandt log-likelihood ratio statistic is considered. Emphasis is placed on the use of graphical methods. The techniques proposed have been embodied in a comprehensive computer program, TIMVAR. Use of the techniques is illustrated by applying them to three sets of data.
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TL;DR: In this article, the authors present computational results for some alternative methods of analysing multivariate data with missing values, and derive an approximate method of assigning standard errors to regression coefficients estimated from incomplete observations, and quote supporting evidence from simulation studies.
Abstract: SUMMARY This paper presents computational results for some alternative methods of analysing multivariate data with missing values. We recommend an algorithm due to Orchard and Woodbury (1972), which gives an estimator that is maximum likelihood when the data come from a multivariate normal population. We include a derivation of the estimator that does not assume a multivariate normal population, as an iterated form of Buck's (1960) method. We derive an approximate method of assigning standard errors to regression coefficients estimated from incomplete observations, and quote supporting evidence from simulation studies. A brief account is given of the application of these methods to some school examinations data.
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TL;DR: In this article, a generalized Dirichlet prior distribution for p = (Pl,...,Pk) having density function f(p) oc Hk 1p'-1 (1 -pl... p) is considered.
Abstract: Let F(x) be the c.d.f. for some population of life times. For real numbers tl O and F(tk))<1, let Pi = F(tl) and pi = F(ti) F(ti-1) for i = 2, 3, ..., k. A generalized Dirichlet prior distribution for p = (Pl, ...,Pk) having density function f(p) oc Hk 1p'-1 (1 -pl ... p) is considered. An intuitive justification for using this density is given and its properties are studied. Comparisons are made between this distribution and the Dirichlet distribution. The posterior distribution of F(ti) is also considered.
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TL;DR: In this article, the authors presented a simpler way of tackling the latter problem, using the invariance properties of Brownian motion, by reducing the problem to a curved boundary problem.
Abstract: Daniels successfully approximated the distribution of the maximum number of infectives during an epidemic in a closed population, by reducing the problem to a curved boundary problem for Brownian motion. The purpose of this note is to present a simpler way of tackling the latter problem, using the invariance properties of Brownian motion.