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The testing of the null hypothesis of no treatment effect against the alternative of increasing treatment effect by means of rank statistics is extended from the classical Friedman random blocks model into an unbalanced design allowing treatments not to be applied simultaneously in each random block. The asymptotic normality of the constructed rank test statistic is proved both in the setting not allowing ties and also for models with presence of ties. As a by-product of the proofs a multiple comparisons...
The compound Poisson-gamma variable is the sum of a random sample from a gamma distribution with sample size an independent Poisson random variable. It has received wide ranging applications. In this note, we give an account of its mathematical properties including estimation procedures by the methods of moments and maximum likelihood. Most of the properties given are hitherto unknown.
The autocorrelation function has a very important role in several application areas involving stochastic processes. In fact, it assumes the theoretical base for Spectral analysis, ARMA (and generalizations) modeling, detection, etc. However and as it is well known, the results obtained with the more current estimates of the autocorrelation function (biased or not) are frequently bad, even when we have access to a large number of points. On the other hand, in some applications, we need to perform...
We study sample-based estimates of the expectation of the function
produced by the empirical minimization algorithm. We investigate the
extent to which one can estimate the rate of convergence of the
empirical minimizer in a data dependent manner. We establish three
main results. First, we provide an algorithm that upper bounds the
expectation of the empirical minimizer in a completely
data-dependent manner. This bound is based on a structural result
due to Bartlett and Mendelson, which relates...
2000 Mathematics Subject Classification: 62G07, 62L20.Tsybakov [31] introduced the method of stochastic approximation to construct a recursive estimator of the location q of the mode of a probability density. The aim of this paper is to provide a companion algorithm to Tsybakov's algorithm, which allows to simultaneously recursively approximate the size m of the mode. We provide a precise study of the joint weak convergence rate of both estimators. Moreover, we introduce the averaging principle...
"A high quantile is a quantile of order q with q close to one." A precise constructive definition of high quantiles is given and optimal estimates are presented.
In this paper we deepen the study of the nonlinear principal components introduced by Salinelli in 1998, referring to a real random variable. New insights on their probabilistic and statistical meaning are given with some properties. An estimation procedure based on spline functions, adapting to a statistical framework the classical Rayleigh–Ritz method, is introduced. Asymptotic properties of the estimator are proved, providing an upper bound for the rate of convergence under suitable mild conditions....
Non-linear mixed models defined by stochastic differential equations (SDEs) are considered: the parameters of the diffusion process are random variables and vary among the individuals. A maximum likelihood estimation method based on the Stochastic Approximation EM algorithm, is proposed.
This estimation method uses the Euler-Maruyama approximation of the diffusion, achieved using latent auxiliary data introduced to complete the diffusion process between each pair of measurement instants.
A tuned...
Approximations to the critical values for tests for multiple changes in location models are obtained through permutation tests principle. Theoretical results say that the approximations based on the limit distribution and the permutation distribution of the test statistics behave in the same way in the limit. However, the results of simulation study show that the permutation tests behave considerably better than the corresponding tests based on the asymptotic critical value.
Consider testing whether F = F0 for a continuous cdf on R = (-∞,∞)
and for a random sample X1,..., Xn from F.
We derive expansions of the associated asymptotic power based
on the Cramer-von Mises, Kolmogorov-Smirnov and Kuiper statistics. We provide numerical illustrations using a double-exponential example with a shifted alternative.
A method for estimation of probability distribution of transformed random variables is presented. The proposed approach admits an approximation of the transformation of the random variables. The approximate probability density function (pdf) is corrected to obtain a resulting pdf which incorporates a prior knowledge of approximation errors. The corrected pdf is not contaminated by any uncontrollable approximation. The method is applied to pattern recognition. It is shown that class conditional pdf...
In this paper we present a method for evaluating the importance of GO terms which compose multi-attribute rules. The rules are generated for the purpose of biological interpretation of gene groups. Each multi-attribute rule is a combination of GO terms and, based on relationships among them, one can obtain a functional description of gene groups. We present a method which allows evaluating the influence of a given GO term on the quality of a rule and the quality of a whole set of rules. For each...
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