Topics: DTIC Archive, Marsaglia, George, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS,...

Topics: DTIC Archive, MARSAGLIA, GEORGE, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS,...

The aim of this article is to apply some results of L. Schwartz's theory of radonifying maps to prove existence theorems for infinite dimensional valued random variables. As a consequence, we deduce some known results in this direction due to K. Ito, M. Perez-Abreu C., and T. Bojdecki and L.G. Gorostiza.

Topics: DTIC Archive, Ramaswamy,S, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS, *RANDOM VARIABLES

Topics: DTIC Archive, HOTELLING, HAROLD, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS, *SAMPLING,...

Topics: DTIC Archive, ROY, S. N., NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS, *STATISTICAL TESTS

The problem considered in this paper is whether the capacity of a discrete time Gaussian channel is increased by feedback or not. It is well known that the capacity of a white Gaussian channel under the average power constraint is not changed by feedback. We give some conditions under which the capacity of a discrete time Gaussian channel is increased by feedback. It is also shown that there exists a non-white Gaussian channel whose capacity is not increased by feedback. Keywords: Gaussian...

Topics: DTIC Archive, Ihara, Shunsuke, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS, *INFORMATION...

The author extends three well-known facts of Fourier series on the disc to Fourier series on the torus, a theorem of Riesz, a theorem of Szego, and the fact that any function in H sub 1 can be factored as the product of two functions in H sub 2. Here the role of negative integers is played by the lattice points in the third quadrant. In earlier extensions of these theorems this role was played by half-planes. Additional keywords: stochastic processes; stationary fields; measures on torus;...

Topics: DTIC Archive, Miamee,A, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS, *FOURIER SERIES,...

Topics: DTIC Archive, Gould,Jerren, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS, *MATHEMATICAL...

Topics: DTIC Archive, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS, *STATISTICAL ANALYSIS,...

We consider sampling methods for multidimensional random fields. We study the convergence of a sampler process generated by the methods stated in Introduction. We can apply convergence theorem to the restoration of degraded images in image processing. (Author)

Topics: DTIC Archive, Yanagi,Kenjiro, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS, *IMAGE...

Topics: DTIC Archive, CHU, J. T., NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS, *SAMPLING,...

Topics: DTIC Archive, SMITH, WALTER L, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS, *PROBABILITY,...

This document examines the paths of the stable fields that are the analogs of index-beta Gaussian fields. The author finds Holder conditions on their paths and finds the Hausdorff dimension of the image, graph, and level sets when we have local nondeterminism, generalizing the Gaussian results. Keywords: inversion; random variables.

Topics: DTIC Archive, Nolan, John P, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS, *STOCHASTIC...

Certain aspects of extremal theory for stationary sequences and continuous parameter stationary processes, are discussed in this paper. A slightly modified form of a previously used dependence condition, leads to simple proofs of some key results in extremal theory of stationary sequences. Dependence conditions of a 'weak mixing' type are introduced for continuous parameter stationary processes and results of classical extreme value theory extended to that context. (Author)

Topics: DTIC Archive, Leadbetter,M R, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS, *STOCHASTIC...

Topics: DTIC Archive, ROY, S. N., NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS, *STATISTICAL...

Contents: Introduction; properties of hypercontractive random variables; hypercontractivity on the real line; hypercontractivity in normal spaces. Keywords: Stochastic processes; Inequalities.

Topics: DTIC Archive, Szulga, Jerzy, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS, *RANDOM...

Several sequential analogs of Stein's two-stage test procedure are presented for testing hypotheses about the mean of a normal population with unknown variance and with specified error probabilities. When sequential experimentation is feasible, they provide alternatives to the sequential normal test (variance known) or the sequential t-test. If the variance is assumed known, the procedures may still be recommended since the added cost may be only a very few additional observations on the...

Topics: DTIC Archive, HALL, WILLIAM JACKSON, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS,...

Topics: DTIC Archive, Pachares, James, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS, *POLYNOMIALS,...

The viewpoint is taken that every probabilistic automation is situated within a sequence of environments which affects the initial state distribution and the transition function. There exists a probabilistic automaton within a deterministic environment sequence (ADE) which defines an event which is not a PCE, yet in certain nontrivial cases the behavior of an ADE can be simulated by a probabilistic automaton. For probabilistic automata within random environment sequences there is a mean...

Topics: DTIC Archive, Gould,Jerren, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS, *AUTOMATA,...

Sequential Feynman integrals are defined for classes of functions on a Hilbert space and on an abstract Weiner space. A Cameron-Martin formula is proved for analytic and sequential Feynman integrals for two classes.

Topics: DTIC Archive, Kallianpur,G, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS, *STOCHASTIC...

The emphasis is on development of likelihood ratios and detection algorithms for problems involving nonGaussian data. The first problem considered is that of detecting a nonGaussian signal in Gaussian noise. This frequently arises in active sonar; it could also be important for passive sonar. General results are presented on nonsingular detection and likelihood ratio. A recursive discrete-time detection algorithm is obtained and is shown to be a likelihood ratio detector when the...

Topics: DTIC Archive, Baker,C R, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS, *DETECTION,...

A necessary requirement for existence of the Frechet derivative is that the defining psi function is uniformly bounded, and this naturally excludes those nonrobust estimators such as the maximum likelihood estimator in normal parametric models. In this paper the methods of nonsmooth analysis, described in the book by F.H. Clarke (1983), are introduced to the theory of statistical expansions, and are used here in the proofs of weak continuity and Frechet differentiability of M-functionals....

Topics: DTIC Archive, Clarke,B R, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS, *DISTRIBUTION...

It is shown, under conditions which include invariant sequential probability ratio tests, that the stopping time is always exponentially bounded when the null or alternative hypothesis holds, except in a trivial instance. (Author)

Topics: DTIC Archive, Rootzen,Holger, Simons,Gordon, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS,...

Several Topics in Stochastic Analysis are studied. A partial list is as follows: (i) Asymptotic Results for Near Critical Branching Processes, (ii) Large Deviation Properties of Weakly Interacting Processes, (iii) Multiscale Diffusion Approximations for Stochastic Networks in Heavy Traffic, (iv) Adaptive Ergodic Control of Markov Chains, (v) Controlled Stochastic Networks in Heavy Traffic, (vi) Exit Time and Invariant Measure Asymptotics for Small Noise Constrained Diffusions, (vi) Tug of War...

Topics: DTIC Archive, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS, *STOCHASTIC CONTROL,...

A modified simplex method has been developed for attacking large linear programs with inexact data in the right hand sides. Results from performing a limited series of computational experiments are reported. These results indicate reductions in computer time of 30 to 70 per cent over the ordinary simplex method.

Topics: DTIC Archive, Gould, Floyd J, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS, *LINEAR...

In most practical situations, the data one has do not follow the normal distribution; if the data were normal, one could use all of the procedures of multivariate analysis which apply to normally distributed data. In this paper, a routine method for making the data follow the normal distribution more closely is discussed; this method is to transform the data. (Author)

Topics: DTIC Archive, Fondren,Robert A, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS,...

A model for shot noise generated by a semi-Markov process is developed. The moments of the shot noise process are found and some applications of this model are briefly indicated.

Topics: DTIC Archive, Smith, Woollcott, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS, *STOCHASTIC...

It is well known that in linear programming the knowledge of optimal dual variables can be used to simplify the finding of an optimal solution to the primal problem. In this paper, the analogous notion is considered for nonlinear and particularly nonconcave programming problems. A new theoretic result on Lagrange multipliers is presented which enables one to make a statement for nonlinear problems similar to the above assertion for linear programs.

Topics: DTIC Archive, Gould, F J, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS, *NONLINEAR...

It is shown that some recent results of Wong (1983) concerning his version of the modified likelihood criterion for smoothing parameter selection in kernel density estimation can be very misleading, because the wrong mode of convergence is established. An example is given to demonstrate that the results are false when a more reasonable mode of convergence is used. Slightly stronger conditions are added and valid proofs for the correct version of these results are indicated.

Topics: DTIC Archive, Marron,J S, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS, *DENSITY,...

Recent results on detection of random nonGaussian signals in additive Gaussian noise are discussed. A discrete-time approximation to a likelihood ratio detection algorithm is discussed, and preliminary results are presented for a computational evaluation of the performance for this approximation.

Topics: DTIC Archive, Baker, C R, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS, *DETECTION,...

This document surveys some recent results on the admissible translates of stable processes and we contrast them with the analogs for Gaussian processes. Whereas Gaussian moving averages and Fourier transforms of independent increment increments processes have rich classes of admissible translates, their stable counterparts frequently have all translates singular. By removing the requirement of independence of the increments, we introduce stable processes that are generalized moving averages and...

Topics: DTIC Archive, Cambanis, Stamatis, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS,...

Indirect censoring is defined as the effect on observed variables of censoring on unobserved variables. Methods of testing for indirect censoring are discussed, and exemplified, using a bivariate Farlie-Gumbel-Morgenstern distribution. (Author)

Topics: DTIC Archive, Johnson,N L, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS, *MULTIVARIATE...

A generalized shot noise in Banach spaces is defined as the a.s. limit of certain centered sums of dependent random vectors; and, a necessary and sufficient condition for its existence is given. As an immediate application, the LePage-type series representations of infinitely divisible random vectors are obtained. Keywords: Stochastic processes; Convergence; Hilbert space.

Topics: DTIC Archive, Rosinski, Jan, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS, *POISSON...

Smoothed estimations are developed for the intensity function (i.e., density for the expectation intensity measure) of a point process. The main results concern mean square and almost sure pointwise consistency and asymptotic distributional properties of the estimator, emphasizing the features which differ from those in other forms of function estimation. The results are illustrated in the particular case of renewal processes. (Author)

Topics: DTIC Archive, Leadbetter,M R, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS, *STOCHASTIC...

Statistical aspects of the Williams-Watts relaxation model are derived explicity from the limit theorem in probability theory. It is shown that the relaxation rate distribution is governed by completely asymmetric Levy alpha-stable distributions, 0 alpha 1. This gives a rigorous approach to the stretched exponential form of relaxation function and also relates the effective relaxation time to the primitive relaxation time. It is demonstrated how useful is the technique of Levy alpha-stable...

Topics: DTIC Archive, Weron,K, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS, *PROBABILITY, *GLASS,...

Let (Xi,Yi) be in independent rv's from some bivariate distribution. Let X(r:n) denote the rth ordered X-variate, and Y(r:n) the Y-variate paired with X(r:n). The distribution of R(r,n), the rank of Y(r:n), is applied to a matching problem. Also, it is shown that pi(1n) pi(1, n-1) ... pi(11) when sampling from Gumbel's bivariate exponential distribution, where pi(rs) = P(R(r,n) = s). (Author)

Topics: DTIC Archive, Lucas,Donna, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS, *ORDER...

In this note two characterizations of the exponential distribution are discussed, based on a generalization of the lack of memory property. These results were motivated by the notion of 'relevation of distributions' introduced by Krakowski (1973). (Author)

Topics: DTIC Archive, Grosswald,E, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS, *EXPONENTIAL...

A communications channel model with additive, independent increment, stochastically continuous noise is presented. The information capacity of this channel is obtained for a mean-square constraint imposed on the generalized intensity of the channel encoder. The capacity is derived by exploiting the Levy decomposition of the noise to decompose the channel into a white Gaussian noise channel in parallel with a marked Poisson channel. The information capacity is then obtained using results for...

Topics: DTIC Archive, Frey, Michael R, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS, *WHITE NOISE,...

The main purpose of this paper is to derive de Finetti-type representations of arbitrary separately or jointly exchangeable random measures. By this is meant representations of the distributions of xi as unique mixtures (convex combinations) of so called extreme exchangeable distributions. The existence of such integral representations is essentially a consequence of general theory so the author's main point is to describe the extreme measures explicitly. Through suitable Borel isomorphisms...

Topics: DTIC Archive, Kallenberg, Olav, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS,...

Durbin has presented a compact formula for the first passage density of a Gaussian process, which is locally like Brownian motion, to a smooth barrier. In previous works, we have extended the formula to the case of processes which are smooth functions of a continuously differentiable Gaussian vector process and to more general kinds of first passage time problems, so called marked crossings. In the present paper we obtain similar results for the first passage density in presence of a second...

Topics: DTIC Archive, Rychlik, Igor, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS, *PROBLEM...

This result is proved. If sub n is a separable metric space for nor = infinity, phi sub n: S sub n approaches limit of S sub infinity is measurable for sub infinity, X sub n is an S sub n valued random variable for nor = infinity and phi sub n (X sub n) approaches limit of sub x sub infinity in S sub infinity, then there exists S sub n valued random variables X sub n such that X sub n = d sub x sub n for nor = infinity and phi sub n (X sub n) approaches limit of X sub infinity wpl. Conditions...

Topics: DTIC Archive, Bai, Z D, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS, *WEAK CONVERGENCE,...

Research was conducted and directed in the area of stochastic processes by three of the Principal Investigators, Cambanis, Kallianpur and Leadbetter,and their associates, and in statistical inference by Carroll. A summary of the main areas of research activity follows for each Principal Investigator and co-workers. More detailed descriptions of the work of all participants is given in the main body of the report. Keywords: Statistical influence, Signal processing, White noise, Weighted least...

Topics: DTIC Archive, Cambanis, Stamatis, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS,...

Algorithms are presented for detection of signals in Gaussian noise. The signals can be Gaussian or nonGaussian. The algorithms are derived from a general solution to the continuous-time problem, and are approximations to the continuous-time likelihood ratio. They do not require knowledge of the probability distributions for the signal-plus-noise process, but instead require knowledge (or estimation) of a function. Independent sampling is not assumed. One algorithm is fully adaptive to the...

Topics: DTIC Archive, Baker, C R, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS, *SIGNAL...

A data-driven method of choosing the bandwidth, h, of a kernel density estimator is proposed. It is seen that this means of selecting h is asymptotically equivalent to taken the h that minimizes a certain weighted version of the mean integrated square error. Thus, for a given kernel function, the bandwidth can be chosen optimally without making precise smoothness assumptions on the underlying density. The proposed technique is a modification of cross-validation.

Topics: DTIC Archive, Marron,J S, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS, *ESTIMATES,...

We prove a law of the iterated logarithm for nonparametric regression function estimators using strong approximations to the two dimensional empirical process. We consider the case of Nadaraya-Watson kernel estimators and of estimators based on orthogonal polynomials when the marginal density of the design variable X is unknown or known. (Author)

Topics: DTIC Archive, Hardle,Wolfgang, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS,...

We consider here general (i.e. possibly skewed or asymmetric) stable distribution and processes. A decomposition result and a moment equality are given for these distributions. More importantly, we determine the form of all stable independent increments processes, construct a Wiener-type stochastic integral with respect to these processes, and prove a representation theorem for general stable processes analogous to (and in some sense including) the spectral representation theorem for symmetric...

Topics: DTIC Archive, Hardin,C D , Jr, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS, *STATISTICAL...

In earlier papers various aspects of analysis of possibly incomplete random samples have been discussed. These analyses all apply to data from a single random sample only. The present paper describes some extensions of these methods when sets of samples are available. When more than one sample is available, the field of hypotheses, alternate to that of having complete samples, becomes much richer. Some of the more interesting possible situations are discussed, though no exhaustive general...

Topics: DTIC Archive, Johnson, N L, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS, *SAMPLING,...

Necessary and sufficient conditions are given for the almost sure convergence of a quadratic form where (M sub j) is a sequence of i.i.d. p-stable random variables. A connection is established between the convergence of the quadratic form and a radonifying property of the infinite matrix operator (f sub kj). (Author)

Topics: DTIC Archive, Cambanis,S, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS, *Numerical...

Two general forms of multiple stage hierachal replacement are described: one proceeds from replacements over larger subsets to smaller subsets (ultimately individuals), and other is an inverse system. Replacements are from simultaneously aging populations. Some detailed calculations are given for Weibull survival time distributions. (Author)

Topics: DTIC Archive, Johnson,N L, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS, *CLASSIFICATION,...

The angle between past and future for stationary random fields on the lattice points of the plane is defined and it is shown that in contrast with other problems related to the past of random fields the positivity of the angle between past and future is independent of different pasts which have been considered. Most of the known facts concerning the angle for stochastic processes have been extended to the case of random fields. Additional keywords: random variables; Hilbert space;...

Topics: DTIC Archive, Miamee,A G, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS, *HILBERT SPACE,...