Showing papers in "Journal of Multivariate Analysis in 1986"

TL;DR: In this paper, the authors propose procedures for detection of the number of signals in presence of Gaussian white noise under an additive model, which is related to the problem of finding the multiplicity of the smallest eigenvalue of the covariance matrix of the observation vector.

TL;DR: In this paper, the spectral distribution of A p = (1 n ) X p X p p T p ⊆ T p, where Xp = [Xij:i, j = 1, 2,…,n] tends to a non-random limit distribution as p → ∞, n → ǫ, but p n → y > 0, under the mild conditions that Xy's are i.i.d.s.

TL;DR: In this paper, it was shown that when the random vector X in R n has a mean and when the conditional expectation E ( u ∈ R n | v ∈ X ) = 0, then the distribution of X is orthogonally invariant.

TL;DR: The authors proposed model selection methods for determination of the number of signals in presence of noise with arbitrary covariance matrix and the methods used in these procedures are based upon certain information theoretic criteria.

TL;DR: In this article, the class of fractional delta sequence estimators is defined and treated, including the familiar kernel, orthogonal series, and histogram methods, and it is shown that both the average square error and integrated square error provide reasonable (random) approximations to the Mean Integral Square Error.

TL;DR: In this paper, it is shown that if m diverges at a slower rate than n 1 2 then the commonly used sum-function will detect alternatives distant (mn) −1 4 from the uniform.

TL;DR: In this article, the central limit (or fluctuation) phenomena in the interacting diffusion system are discussed and the tightness in the Kolmogorov-Prokhorov sense is proved for a sequence of distribution valued processes arising from finite particle systems.

TL;DR: In this paper, a complete comparison is made between the value V (X 1,…, X n ) = sup{ EX t : t is a stop rule for X 1,..., X n } and E (max j ≤ n X j ) for all uniformly bounded sequences of i.i.d.

TL;DR: In this article, the authors define definitions de base and resultats concernant les splines univariables and multivariables, and decrit leurs applications a l'interpolation polynomiale.

TL;DR: In this article, the path properties of a symmetric a-stable process X(r) = Is h(t, s) d&f(s), to T, are studied in terms of the kernel h. The existence of an appropriate modification of kernel h enables one to use results from stable measures on Banach spaces in studying X.

TL;DR: In this paper, the authors investigate various third-order asymptotic properties of maximum likelihood estimators for Gaussian ARMA processes by the thirdorder Edgeworth expansions of the sampling distributions.

TL;DR: In this paper, the problem of predicting wide sense stationary processes on Z2 with respect to the column-by-column or row-byrow lexicographic order is studied and a theorem giving an explicit realization of the corresponding canonical factorization of the spectral density is proved and conditions are given for a process to have a quarterplane representation in terms of its innovations.

TL;DR: In this article, the authors draw attention to the danger of leakage from omitted frequencies and show that the consequent bias can be reduced by means of tapering, which is a common technique in the errors-in-variables problem.

TL;DR: In this article, second order asymptotically efficient tests, confidence regions, and estimators for the nonlinear regression model which are based on the least-squares estimator and the residual sum of squares.

TL;DR: In this paper, the authors proved that the limit of the spectral distribution of STn exists where S = XX′, where S is the second moments of the norm |xi| (i = 1,2,n) and X is a sample from an isotropic population.

TL;DR: In this paper, a class of procedures for choosing the bandwidth, or smoothing parameter, for linear nonparametric estimates of the rth derivative of a smooth function observed with error on a discrete set of points is proposed.

TL;DR: In this paper, the authors give explicit bounds of Δ(X) = supi|p(|X|≤t)−P(|T| ≥ 0) in terms of truncated moments of the variables X = Σi≤nXi.

TL;DR: On obtient une classe d'estimateurs minimax, par la methode de Stein qui inclut l',estimateur d'Efron Morris comme cas particulier as discussed by the authors.

TL;DR: Cambanis, S., Keener, R., and Simons, G. as discussed by the authors used the Radon transform to obtain integral representations for the density functions of certain absolutely continuous α-symmetric distributions.

TL;DR: In this paper, sufficient conditions are given for the central limit theorem to hold for the target statistic Fn(Un), where {Un} is a sequence of U-statistics, and a kernel type density estimator based on a random sample of size n from a smooth distribution function F is presented.

TL;DR: In this paper, it was shown that there is a numerical constant U lim n → x sup g ∈ G n |H −1 (n/V) 1/2 S n (g)| ⩽ U as P ∗, where P ≔ ⊗i = 1xP(i) and H ≔ H(n) is the square root of the entropy of the class G n.

TL;DR: In this article, large deviation local limit theorems for arbitrary multidimensional random variables based solely on conditions imposed on their moment generating functions are presented. But these results generalize the results of W. Richter ( Theory Probab. Appl. 3 (1958), 100−106) for sums of independent and identically distributed random vectors.

TL;DR: In this paper, the generalized least squares estimators are shown to be consistent and asymptotically multivariate normal for the functional MLEM model and the structural model.

TL;DR: In this article, strong approximation results for the empirical Q-Q process were obtained and some Glivenko-Cantelli-type results were also obtained, and these results are applicable to construct confidence bands for Q -Q plots.

TL;DR: In this article, the set of ordered triples of a martingale Y0, Y1, Y2, Yn−1 for each p ≥ 1 is compared to the set for all martingales Y 0, Y 1, Y 2, Y n−1, where ψ n,p ∗ is the concave conjugate function of ψn,p.

TL;DR: In this paper, the distribution theory for a generalized least squares estimator of the growth curve model is developed for a special case of the estimator is the maximum likelihood estimator which is weighted by the sample covariance matrix.

TL;DR: In this paper, a functional form for the central limit theorem obtained by Bradley for strong mxing sequences of random variables, under a certain assumption about the size of the maximal coefficients of correlations, is given.

TL;DR: In this article, diverses notions de compacite racine and des exemples connus are rappelle and donne de nouveaux resultats sur les semi-groupes de convolution localement tendres.

TL;DR: In this paper, the decomposability properties of operator-stable and operator-semistable limit distributions were investigated and the infinitely differentiable Lebesgue density of an OLS was shown to be even analytic in some cases.

TL;DR: In this paper, a general theorem covering the case of Cauchy random variables is given, and an affirmative answer to the above question for general bivariate normal random variables with non-zero correlations is given.