This paper provides further contributions to the theory of linear sufficiency and linear completeness. The notion of linear sufficiency was introduced by [2], Ann. Statist. 9, 913-916) and Drygas (in press, Sankhya) with respect to the linear model Ey = X[beta], var y = V. In addition to...

Let (X, Y), (X1, Y1),..., (Xn, Yn) be i.i.d. (Rr - R)-valued random vectors with EY [infinity], and let mn(x) be a nearest neighbor estimate of the regression function m(x) = E(Ys[beta]X = x). We establish an exponential bound of the mean deviation between mn(x) and m(x) given the training...

Let [mu] be a [sigma]-finite measure, R = (rij) be a covariance matrix, and B1,..., Bn be dependent Gaussian measures satisfying EBi(A1) Bj(A2) = rij[mu](A1 [down curve] A2). Multiple integrals of the form In(f) = [integral operator]f(x1,..., xn) dB1(x1) ... dBn(xn), with f [set membership,...

Let Pn be a random probability measure on a metric space S. Let P^n be the empirical measure of kn iid random variables, each distributed according to Pn. Our main theorem asserts that if {Pn} converges in distribution, as random probability measures on S, then so does {P^n}. Applications of the...

The asymptotic distribution of the eigenvalues and eigenvectors of the robust scatter matrix proposed by R. Maronna in 1976 is given when the observations are from an ellipsoidal distribution. The elements of each characteristic vector are the coefficients of a robustified version of principal...

Analytical and numerical results are given for determining the location of the mode of a class of bivariate gamma densities as a function of the parameters. The model location for a class of bivariate gammas as considered by Kibble (1941, Sankhya A 5 137-150) is shown to satisfy a nonlinear...

In many practical problems, one needs to compare variabilities of several multidimensional populations. The concept of standardized generalized variance (SGV) is introduced as an extension of the concept of GV. Considering multivariate normal populations of possibly different dimensions and...

Let X1,..., Xn be i.i.d. random variables symmetric about zero. Let Ri(t) be the rank of Xi - tn-1/2 among X1 - tn-1/2,..., Xn - tn-1/2 and Tn(t) = [Sigma]i = 1n[phi]((n + 1)-1Ri(t))sign(Xi - tn-1/2). We show that there exists a sequence of random variables Vn such that sup0 <= t <= 1 Tn(t) - Tn(0) - tVn --> 0 in probability,...</=>

We propose a sequential procedure for detecting a possible changepoint in a random sequence of observations so that we can fix the probabilty of stopping at any level if there is no change, while otherwise we will stop with probabilty one in a specified length of time.

Consider a general linear model, Yi=x'i[beta]+Ri with R1, ..., Rn i.i.d., [beta][set membership, variant]Rp, and {x1, ..., xn} behaving like a random sample from a distribution in Rp. Let [beta] be a robust M-estimator of [beta]. To obtain an asymptotic normal approximation for the distribution...