Search results for " Uncertainty"
showing 10 items of 777 documents
Sparse relative risk regression models
2020
Summary Clinical studies where patients are routinely screened for many genomic features are becoming more routine. In principle, this holds the promise of being able to find genomic signatures for a particular disease. In particular, cancer survival is thought to be closely linked to the genomic constitution of the tumor. Discovering such signatures will be useful in the diagnosis of the patient, may be used for treatment decisions and, perhaps, even the development of new treatments. However, genomic data are typically noisy and high-dimensional, not rarely outstripping the number of patients included in the study. Regularized survival models have been proposed to deal with such scenarios…
A Comment on the Coefficient of Determination for Binary Responses
1992
Abstract Linear logistic or probit regression can be closely approximated by an unweighted least squares analysis of the regression linear in the conditional probabilities provided that these probabilities for success and failure are not too extreme. It is shown how this restriction on the probabilities translates into a restriction on the range of the coefficient of determination R 2 so that, as a consequence, R 2 is not suitable to judge the effectiveness of linear regressions with binary responses even if an important relation is present.
The asymptotic covariance matrix of the Oja median
2003
The Oja median, based on a sample of multivariate data, is an affine equivariant estimate of the centre of the distribution. It reduces to the sample median in one dimension and has several nice robustness and efficiency properties. We develop different representations of its asymptotic variance and discuss ways to estimate this quantity. We consider symmetric multivariate models and also the more narrow elliptical models. A small simulation study is included to compare finite sample results to the asymptotic formulas.
Random Logistic Maps II. The Critical Case
2003
Let (X n )∞ 0 be a Markov chain with state space S=[0,1] generated by the iteration of i.i.d. random logistic maps, i.e., X n+1=C n+1 X n (1−X n ),n≥0, where (C n )∞ 1 are i.i.d. random variables with values in [0, 4] and independent of X 0. In the critical case, i.e., when E(log C 1)=0, Athreya and Dai(2) have shown that X n → P 0. In this paper it is shown that if P(C 1=1)<1 and E(log C 1)=0 then (i) X n does not go to zero with probability one (w.p.1) and in fact, there exists a 0<β<1 and a countable set ▵⊂(0,1) such that for all x∈A≔(0,1)∖▵, P x (X n ≥β for infinitely many n≥1)=1, where P x stands for the probability distribution of (X n )∞ 0 with X 0=x w.p.1. A is a closed set for (X n…
A Unified Approach to Likelihood Inference on Stochastic Orderings in a Nonparametric Context
1998
Abstract For data in a two-way contingency table with ordered margins, we consider various hypotheses of stochastic orders among the conditional distributions considered by rows and show that each is equivalent to requiring that an invertible transformation of the vectors of conditional row probabilities satisfies an appropriate set of linear inequalities. This leads to the construction of a general algorithm for maximum likelihood estimation under multinomial sampling and provides a simple framework for deriving the asymptotic distribution of log-likelihood ratio tests. The usual stochastic ordering and the so called uniform and likelihood ratio orderings are considered as special cases. I…
Relación entre conos de direcciones decrecientes y conos de direcciones de descenso
1984
Let f: N ? R a convex function and x I Ni, where N is a convex set in a real linear space. It is stated that, if Df<(x) is not empty, then Df<(x) is the algebraic interior of Df=(x).
Una solucion bayesiana a la Paradoja de Stein
1982
If we are interested in making inferences about the square norm of the mean in a multivariate normal model, the usual uniform prior for the mean is not sound, as revealed by Stein in his 1959 work. This paper studies in what sense this prior must be modified by using the maximization of missing information procedure (Bernardo, 1979)
Multiple testing of pairs of one-sided hypotheses
1986
Two-sided test procedures fork real parameters should point out in the case of rejection whether the left or the right alternative can be assumed. This sets up a multiple testing problem fork pairs of one-sided hypotheses. Holm's (1979, Scandinavian Journal of Statistics 6:65–70) sequentially rejective test provides a solution the critical levels of which are slightly improved. Considerable improvement is obtained when the hypotheses are redefined to be disjoint in pairs.
A generalized predictive criterion for model selection
2002
Given a random sample from some unknown model belonging to a finite class of parametric models, assume that the estimate of the density of a future observation is of interest San Martini & Spezzaferri (1984) proposed for this problem a predictive criterion based on the logarithmic utility function. The present authors investigate a generalization of this criterion that uses as a loss function an element of the class of α-divergences discussed by Ali & Silvey (1966) and Csiszar (1967). They also discuss briefly the case in which the class of models considered is not exhaustive. Un critere de prevision generalise pour la selection de modeles Supposons que l'on cherche a estimer la densite d'u…
Quasi Competition — a New Aspect
1978
The model of quasi competition put forward in 1967 is reinvestigated under the aspect that only large (N ∞) populations are considered. Under this new angle the conclusion that myomas develop from single cells seems better justified than the original discussion indicated.