A general approach for developing distribution free tests for general linear models based on simplicial depth is presented. In most relevant cases, the test statistic is a degenerated U-statistic so that the spectral decomposition of the conditional expectation of the kernel function is needed to derive the asymptotic distribution. A general formula for this conditional expectation is derived. ...

A new method for detecting significant p-values is described in this paper. This method, based on the distribution of the m-th order statistic of a U(0, 1) distribution, is shown to be suitable in applications where m → ∞ independent hypothesis are tested and it is of interest for a fixed type I error probability to determine those being significant while controlling the false positives. Equiva...

In this paper we describe a novel approach to the study of U -statistics in the markovian setup, based on the (pseudo-) regenerative properties of Harris Markov chains. Exploiting the fact that any sample path X1, . . . , Xn of a general Harris chain X may be divided into asymptotically i.i.d. data blocks B1, . . . , BN of random length corresponding to successive (pseudo-) regeneration times, ...

We analyze the fluctuations of incomplete U-statistics over a triangular array independent random variables. give criteria for Central Limit Theorem (CLT, short) to hold in sense that we prove an appropriately scaled and centered version U-statistic converges normal variable. Our method proof relies on martingale CLT. An application, CLT hitting time walks graphs, will be presented Löwe Terveer...

Given n independent, identically distributed random vectors in R, drawn from a common density f , one wishes to find out whether the support of f is convex or not. In this paper we describe a decision rule which decides correctly for sufficiently large n, with probability 1, whenever f is bounded away from zero in its compact support. We also show that the assumption of boundedness is necessary...

We consider the standard linear regression model with all standard assumptions, except that the disturbances are not white noise, but distributed N(0,p2X(h)) where X(0)"I n . Our interest lies in testing linear restrictions using the usual F-statistic based on OLS residuals. We are not interested in "nding out whether h"0 or not. Instead we want to "nd out what the e!ect is of possibly nonzero ...

Given n independent, identically distributed random vectors in Rd, drawn from a common density f , one wishes to find out whether the support of f is convex or not. In this paper we describe a test which decides correctly for sufficiently large n, with probability 1, whenever f is bounded away from zero in its compact support. We also show that the assumption of boundedness is necessary. The pr...

This study was designed to elucidate the effect of ascorbic acid on salivary total antioxidant capacity in smokers. In this single blind crossover clinical trial, the whole unstimulated saliva of 30 smokers, who were randomly divided into two groups, was collected. In the first phase after the saliva collection, one group of patients took 500 mg of vitamin C powder, for 3 weeks. Then, saliva of...

We discuss a graph-based approach for testing spatial point patterns. This approach falls under the category of data-random graphs, which have been introduced and used for statistical pattern recognition in recent years. Our goal is to test complete spatial randomness against segregation and association between two or more classes of points. To attain this goal, we use a particular type of para...