Random coe cient regression models have been applied in di erent elds and they constitute a unifying setup for many statistical problems. The nonparametric study of this model started with Beran and Hall (1992) and it has become a fruitful framework. In this paper we propose and study statistics for testing a basic hypothesis concerning this model: the constancy of coe cients. The asymptotic be...

As part of his recent research into Cubical Spheres, G. Hetyei gave an inductive proof that a certain sequence of polynomials have nonnegative coe cients. In a poster session at the FPSAC'96 conference he asked for a combinatorial interpretation of these coe cients. In this short note we show that known results in rook theory imply that the coe cients count permutations subject to certain const...

In the common trigonometric regression model we investigate the optimal design problem for the estimation of the individual coe cients where the explanatory vari able varies in the interval a a a It is demonstrated that the structure of the optimal design depends sensitively on the size of the design space For many cases optimal designs can be found explicitly where the complexity of the soluti...

We present two algorithms for inducing structural equation models from data. Assuming no latent variables, these models have a causal interpretation and their parameters may be estimated by linear multiple regression. Our algorithms are comparable with PC [15] and IC [12, 11], which rely on conditional independence. We present the algorithms and empirical comparisons with PC and IC. This resear...

We consider an elliptic partial di erential operator P (x; @) with analytic coe cients and discuss the unique continuation along an analytic curve. That is, let P (x; @)u = 0 in a simply connected domain R, be an analytic curve and let fxgj2N have an accumulation point. Our main result asserts that if u(x) = 0, j 2 N , then u(x) = 0 for any x 2 . Furthermore we apply such uniqueness to an isotr...

This article proposes some non-linear, thresholded wavelet density estimators, and investigates the practical problems involved in their implementation. Our proposed thresholding method exploits the non-stationary variance structure of the wavelet coe cients. One proposed method of estimating the variances of the raw coe cients uses the scaling function coe cients. Since these are available as ...

The multiplicities in the decomposition (Equation 0.1) are equivalent to the famousLittlewood-Richardson coe cients, 1 and in this appendix, we describe a result known as the Littlewood-Richardson (LR) rule which will allow us to compute the Littlewood-Richardson coe cients tractably (at least for low-order terms). There are several methods for computing these numbers (see [Knutson and Tao, 199...

A Maximum Entropy statistical treatment of an inverse problem concerning frame theory is presented. The problem arises from the fact that a frame is an overcomplete set of vectors that de nes a mapping with no unique inverse. Although any vector in the concomitant space can be expressed as linear combination of frame elements, the coe cients of the expansion are not unique. Frame theory guarant...

In this paper we examine the ̄nite-sample properties of the approximate maximum likelihood estimate (MLE) of the fractional di®erencing parameter d in an ARFIMA(p, d, q) model based on the wavelet coe±cients. Ignoring wavelet coe±cients of higher order of resolution, the remaining wavelet coe±cients approximate a sample of independently and identically distributed normal variates with homogeneo...

The Article deals with the controlled influence of adhesive force in contact road vehicle’s wheel road. first section shows how is reduced. next step familiarization experimental vehicle Alternative SkidCar, where measurements were carried out, assessment advantages and disadvantages SkidCar drive on sliding surface following test methods. objective article to determine great difference b...