四阶Laguerre型微分方程的左定空间和左定算子

本文讨论了某四阶Laguerre型微分方程的下有界性，并构造了相关的左定空间和左定算子．     

EXCHANGEABLE PAIRS OF BERNOULLI RANDOM VARIABLES,KRAWTCHOUCK POLYNOMIALS,AND EHRENFEST URNS

This paper derives characterizations of bivariate binomial distributions of the Lancaster form with Krawtchouk polynomial eigenfunctions. These have been characterized by Eagleson, and we give two further characterizations with a more probabilistic flavour: the first as sums of correlated Bernoulli variables; and the second as the joint distribution of the number of balls of one colour at consecutive time points in a generalized Ehrenfest urn. We give a self‐contained development of Krawtchouck polynomials and Eagleson’s theorem.     

Adaptive Deconvolution on the Non‐negative Real Line

In this paper, we consider the problem of adaptive density or survival function estimation in an additive model defined by Z=X+Y with X independent of Y, when both random variables are non‐negative. This model is relevant, for instance, in reliability fields where we are interested in the failure time of a certain material that cannot be isolated from the system it belongs. Our goal is to recover the distribution of X (density or survival function) through n observations of Z, assuming that the distribution of Y is known. This issue can be seen as the classical statistical problem of deconvolution that has been tackled in many cases using Fourier‐type approaches. Nonetheless, in the present case, the random variables have the particularity to be supported. Knowing that, we propose a new angle of attack by building a projection estimator with an appropriate Laguerre basis. We present upper bounds on the mean squared integrated risk of our density and survival function estimators. We then describe a non‐parametric data‐driven strategy for selecting a relevant projection space. The procedures are illustrated with simulated data and compared with the performances of a more classical deconvolution setting using a Fourier approach. Our procedure achieves faster convergence rates than Fourier methods for estimating these functions.     

q－Hermite多项式与Askey－Wilson积分

应用ｑ－微分算子研究了ｑ－Ｈｅｒｍｉｔｅ多项式，得到了若干结论．应用这些结论简洁地计算了Ａｓｋｅｙ－Ｗｉｌｓｏｎ积分．     

Psychotropic drug classification based on sleep–wake behaviour of rats

Summary.  The aim of the paper is to present methodology for the classification of potential psychotropic drugs on the basis of their activity. We first sketch the background of this class of drugs and then zoom in on so-called pharmacoelectroencephalogram studies. These data pose some statistical challenges. For classification purposes, we propose a flexible hierarchical discriminant analysis tool, allowing us to take the specific nature of the drug class into account, as well as the features of the mixed models, in combination with fractional polynomials, fitted to the electroencephalogram data. The method is evaluated against the background of existing methods. The method's performance is studied by using a comprehensive analysis of a large electroencephalogram data set.     

On some formulas for weighted sum of invariant polynomials of two matrix arguments

Some properties of the generalized binomial coefficients and new coefficients related to symmetric functions are discussed. Several formulas of the weighted sum of invariant polynomials of two matrix arguments which are useful in multivariate distribution theory are presented.     

Equally spaced design points in polynomial regression: A comparison of systematic sampling methods with the optimal design of experiments

In some situations an experimenter may desire to have equally spaced design points. Three methods of obtaining such points on the interval [—1,1]—namely systematic random sampling, centrally located systematic sampling, and a purposive systematic sampling method which includes the endpoints - 1 and 1 as two of the design points-are evaluated under the D-optimal and G-optimal criteria. These methods are also compared to the optimal designs in polynomial regression and to the limiting designs of Kiefer and Studden (1976).     

Forecasting of some; transformed series

The delta method is proposed as a. retransformation approach for coramputing forecasts for a nonstationary process (Z$inf:t$einf t, = 1, 2, ...), A derived variance stabilizing transformation technique is also used to compute forecasts, The performance of the two methods is compared to other techniques. Numerical results show that forecasts based on the variance stabilizing transformation method (VSTM) can lead to forecasts with a lower mean square error (MSE) as compared to other transformation techniqnes.     

Polynomial trends in time series

The J^* test which was previously proposed by the present author for the detection of a trend in a time series does not depend on any quantitative assumptions, but in the case of a polynomial trend it depends on its degree; if this degree is too high, the test cannot be applied. The author finds a bound of the significance level at which the test can be applied when the sample size, as well as a bound of the degree of the trend, are given. Asymptotic results are used only when we trust the asymptotic distribution of J^* under the null hypothesis.     

Estimating herd-specific force of infection by using random-effects models for clustered binary data and monotone fractional polynomials

Summary.  In veterinary epidemiology, we are often confronted with hierarchical or clustered data. Typically animals are grouped within herds, and consequently we cannot ignore the possibility of animals within herds being more alike than between herds. Based on a serological survey of bovine herpes virus type 1 in cattle, we describe a method for the estimation of herd-specific rates at which susceptible animals acquire the infection at different ages. In contrast with the population-averaged force of infection, this method allows us to model the herd-specific force of infection, allowing investigation of the variability between herds. A random-effects approach is used to account for the correlation in the data, allowing us to study both population-averaged and herd-specific force of infection. In contrast, generalized estimating equations can be used when interest is only in the population-averaged force of infection. Further, a flexible predictor model is needed to describe the dependence of covariates appropriately. Fractional polynomials as proposed by Royston and Altman offer such flexibility. However, the flexibility of this model should be restricted, since only positive forces of infection have a meaningful interpretation.