Showing papers in "Statistics & Probability Letters in 1992"

TL;DR: In this article, the authors studied the almost sure convergence of sums of negatively dependent random variables, in particular, the classical strong law of large numbers for independent distributed random variables is generalized to the case of pairwise negative quadrant dependent Random variables.

TL;DR: In this paper, a wavelets characterization of Besov spaces is used to reduce the question of density estimation with Besov constraints to a problem in a sequences space, leading to very natural proofs.

TL;DR: In this paper, the authors define a multivariate Linnik distribution based upon closure under geometric compounding, where the characteristic function is 1/(1 + (∑mi = 1s'Ωis)α/2, where 0 < α ⩽ 2, the Ωi's are r × r positive semi definite matrices and no two of ΩI's are proportional.

TL;DR: In this paper, some recurrence relations between the moments of record values from the Gumbel distribution are established and all the single and product moments of all record values can be obtained in a very simple recursive process.

TL;DR: In this article, the authors proved the complete convergence of ∑nk=1∑∞i=−∞ai+kYi/n1/t;n⩾1, assuming EY1=0 and E|E|Y1|2t∞.

TL;DR: In this paper, the asymptotic behavior of a class of M-estimators in linear models when errors are Gaussian, or a function of Gaussian random variables, that are long range dependent is discussed.

TL;DR: In this article, a criterion of stability for PCA scatterplots is defined based on a classical distance between projectors, which is constructed as a risk function and can be estimated by bootstrap or jackknife methods.

TL;DR: In this article, a modified version of Easton and Ronchetti's saddlepoint approximations for the bootstrap distribution in the AR(1) model is proposed and shown to be useful in the case of small sample sizes.

TL;DR: In this article, it was shown that the convergence rate of a stationary α-mixing sequence of real-valued r.v.'s with distribution function (d.f.) f, probability density function (p.d.) f and mixing coefficient α(n) is O((log log n/n) 1 2 ).

TL;DR: The classic asymptotic properties of the maximum likelihood estimator and generalized likelihood ratio statistic do not hold when the true parameter is on the boundary of the parameter space.

TL;DR: In this article, the efficiency of an S-estimator in the linear model is maximized under a constraint on the breakdown point and the form of the optimal score function is derived.

TL;DR: In this paper, the goodness of fit test for the composite hypothesis that the distribution of a random sample X, is a Poisson distribution was proposed. But the test was not consistent against alternative distributions with finite expectation.

TL;DR: The laws of large numbers for sums of i.i.d. random variables can be generalized in various ways as discussed by the authors, and the purpose of this note is to collect some domination conditions and to provide a fairly general weak law for arrays.

TL;DR: In this article, the authors considered the problem of finding the cu-quantile of an IW%alued (k > 1) random variable X is a point 0 E iWk minimizing the expectation E( II X - 0 II p.a - II XII p,,), where I/. II p,a is defined in terms of the!P-norm, 1 Q p Q m, and (Y E (0, 1).

TL;DR: In this paper, a functional CLT is derived and applied to an L-statistic, which estimates the center of a smooth symmetric distribution on d-dimensional Euclidean space.

TL;DR: Upper and lower bounds are given for FXr:n, the distribution function of the rth order statistic from n possibly dependent random variables, and it is shown that these bounds may be reached when the random variables have a common distribution function.

TL;DR: In this paper, two point processes where the intervals between successive events form a sequence of correlated and identically distributed gamma variables are presented, where the interval between consecutive events is represented by a Gaussian distribution.

TL;DR: This article showed that Spearman's rho is a measure of average positive (and negative) quadrant dependence, and that Kendall's tau measures average total positivity (and reverse regularity) of order two.

TL;DR: For any known λk, the natural estimator for aλk(τ) and the kernel estimators for its spectral density gλkγ are consistent in quadratic mean as discussed by the authors.

TL;DR: In this paper, a local influence approach to the linear regression model with first-order autoregressive errors is developed and discussed, which avoids the inappropriate case-deletion diagnostic in the autoregression model and allows simultaneous perturbations on all responses.

TL;DR: In this paper, the existence of stochastically extremal sequences and subsequences of order statistics is studied for samples of possibly dependent identically distributed random variables, and the smallest and largest distributions of each order statistic are constructed.

TL;DR: In this article, the authors derived asymptotic normality for a nonparametric measure of independence of the components of random two-vectors without the restrictive assumptions previuosly made on rate of convergence of the bandwidth sequence of the density estimates used.

TL;DR: In this paper, the authors find two fundamental statistics in discriminant analysis on which many influence measures depend and discuss several other measures also proposed and discussed, such as approximate contours of the measure can be plotted to reveal influence information.

TL;DR: In this article, the authors considered the estimation problem of unknown variance of a multivariate normal vector under quadratic loss and entropy loss, and the behavior of risk functions of the Brewster-Zidek estimator and the original Stein estimator was examined.

TL;DR: Using the concept of r-extremal dependence, which generalizes Lai and Robbins (1976) maximal dependence, alternative proofs and some new results concerning expectations of order statistics with any rank, from possibly dependent variates are proposed.

TL;DR: In this paper, direct and recursive formulae for the general moments E(XN) in the parametric family of Cantor(θ) distributions are derived and the first 25 moments of the Cantor( 1 3 ) distribution are printed.

TL;DR: The most commonly used method of setting confidence intervals for the correlation coefficient is based on the normal approximation to the Fisher Z -transformation as discussed by the authors, which has been shown to be conservative and numerically confirmed to be tight in the sense that the actual coverage probability is close to a preset value.

TL;DR: In this article, the authors derived the probability distribution and extinction probabilities for a birth-death process with piecewise constant rates and applied them to multistage models of carcinogenesis incorporating clonal expansion.

TL;DR: In this paper, strong and strong laws of large numbers for bootstrap sample means under minimal moment conditions were proved for both weak and strong deterministic deterministic laws for large numbers.

TL;DR: In this article, it was shown that for any integrable function, ∫ √ gf dFn → ∫ ǫ gf √ dF w.p. 1.