Pollard showed for k-means clustering and a very broad class of sampling distributions that the optimal cluster means converge to the solution of the related population criterion as the size of the data set increases. We extend this consistency result to k-parameters clustering, a method derived...

Huang and Kotz (1999) [17] considered a modification of the Farlie–Gumbel–Morgenstern (FGM) distribution, introducing additional parameters, and paved the way for many research papers on modifications of FGM distributions allowing high correlation. The first part of the present paper is a...

Some robust sequential procedures for the detection of structural breaks in the Capital Asset Pricing Model (CAPM) are proposed and studied. Most of the existing procedures for this model are based on ordinary least squares (OLS) estimates. Here we propose a class of cumulative sum (CUSUM)-type...

In this paper we demonstrate that a higher-ranking principal component of the predictor tends to have a stronger correlation with the response in single index models and sufficient dimension reduction. This tendency holds even though the orientation of the predictor is not designed in any way to...

Given a reproducing kernel Hilbert space (H,〈.,.〉) of real-valued functions and a suitable measure μ over the source space D⊂R, we decompose H as the sum of a subspace of centered functions for μ and its orthogonal in H. This decomposition leads to a special case of ANOVA kernels, for...

Three graph theoretical statistics are considered for the problem of estimating the intrinsic dimension of a data set. The first is the “reach” statistic, r¯j,k, proposed in Brito et al. (2002) [4] for the problem of identification of Euclidean dimension. The second, Mn, is the sample...

In this paper, we study reliability properties in two classes of bivariate continuous distributions based on specification of conditional hazard functions. These classes were constructed by conditioning on two different kinds of events in Arnold and Kim [6]. Several reliability properties are...

We compare the hazard rate functions of the largest order statistic arising from independent heterogeneous gamma random variables and that arising from i.i.d. gamma random variables. Specifically, let X1,…,Xn be independent gamma random variables with Xi having shape parameter 0r≤1 and scale...

In this paper, we consider tests of correlation when the sample size is much lower than the dimension. We propose a new estimation methodology called the extended cross-data-matrix methodology. By applying the method, we give a new test statistic for high-dimensional correlations. We show that...

In this paper we propose a test for testing the equality of the mean vectors of two groups with unequal covariance matrices based on N1 and N2 independently distributed p-dimensional observation vectors. It will be assumed that N1 observation vectors from the first group are normally distributed...