There is only one fully supported ergodic invariant probability measure for the adic transformation on the space of infinite paths in the graph that underlies the eulerian numbers. This result may partially justify a frequent assumption about the equidistribution of random permutations.
A method is introduced to select the significant or non null mean terms among a collection of independent random variables. As an application we consider the problem of recovering the significant coefficients in non ordered model selection. The method is based on a convenient random centering of the partial sums of the ordered observations. Based on L-statistics methods we show consistency of the proposed estimator. An extension to unknown parametric distributions is considered. Simulated examples...
Bayesian networks are a popular model for reasoning under uncertainty. We study the problem of efficient probabilistic inference with these models when some of the conditional probability tables represent deterministic or noisy -out-of- functions. These tables appear naturally in real-world applications when we observe a state of a variable that depends on its parents via an addition or noisy addition relation. We provide a lower bound of the rank and an upper bound for the symmetric border rank...
This paper deals with the hypotheses of symmetry of distributions with respect to a location parameter when the response variables are subject to measurement errors. Rank tests of hypotheses about the location parameter and the related R-estimators are studied in an asymptotic set up. It is shown, when and under what conditions, these rank tests and R-estimators can be used effectively, and the effect of measurement errors on the power of the test and on the efficiency of the R-estimators is indicated....
In this paper properties of some ranking and selection procedures based on robust -estimates of location parameter are studied. The least favorable configuration of parameters and the asymptotic efficiency relative to procedures based on sample means are found.
This work deals with Random Coefficient Autoregressive models where the error process is a martingale difference sequence. A class of estimators of unknown parameter is employed. This class was originally proposed by Schick and it covers both least squares estimator and maximum likelihood estimator for instance. Asymptotic behavior of such estimators is explored, especially the rate of convergence to normal distribution is established.
The paper studies polynomial approximation models with a new type of constraints that enable to get estimates with significant properties. Recently we enhanced a representation of polynomials based on three reference points. Here we propose a two-part cubic smoothing scheme that leverages this representation. The presence of these points in the model has several consequences. The most important one is the fact that by appropriate location of the reference points the resulting approximant of two...
Interpolating and approximating polynomials have been living separately more than two centuries. Our aim is to propose a general parametric regression model that incorporates both interpolation and approximation. The paper introduces first a new -point transformation that yields a function with a simpler geometrical structure than the original function. It uses reference points and decreases the polynomial degree by . Then a general representation of polynomials is proposed based on reference...