Showing papers in "Statistics in 1989"
TL;DR: In this article, approximate discrete-time schemes for statistics of diffusion processes are presented, which are based on approximated discrete time schemes for diffusion processes with a fixed number of nodes.
Abstract: (1989). Approximate discrete-time schemes for statistics of diffusion processes. Statistics: Vol. 20, No. 4, pp. 547-557.
314 citations
TL;DR: In this paper, it was shown that for all neN and all xeR where c1 < 31.935, the analytical structure of C1=C1 is given without numerical calculation.
Abstract: Let X1,X2 be a sequence of independent random variable such that . It is shown that for all neN and all xeR where c1<31.935 In the general case only tha analytical structure of C1=C1 is given without numerical calculation
45 citations
35 citations
TL;DR: In this paper, two different approaches to the design of optimal observations networks are compared, one based on the traditional experimental design theory, the other essentially uses the covariance analysis methodology of observed fields.
Abstract: Two different approaches to the design of optimal observations networks are compared. One approach is based on the traditional experimental design theory, the other essentially uses the covariance analysis methodology of observed fields, It is found that for random fields generated by regression models with random parameters both approaches lead to similar solutions
31 citations
TL;DR: The exact power of two-sample location tests based on exceedance statistics against shifts in exponential-, logistic- and rectangular distributions is derived in this paper, where the exact power functions for the MANN-WHITNEY-WILCOXON, the MOOD-WESTENBERG and the MATHISEN test are compared.
Abstract: The exact power of two-sample location tests based on exceedance statistics against shifts in exponential-, logistic- and rectangular distributions is derived. As an example; the exact power functions for the MANN-WHITNEY-WILCOXON, the MOOD-WESTENBERG and the MATHISEN test for shifts in exponential distributions is compared
15 citations
TL;DR: In this paper, a generalization of the GLIVENKO-CANTELLI theorem under a φ-mixing,condition on the sequence (Xn) was derived.
Abstract: Let X be a multivariate random variable and (Xn)N a sequence of realisations of X which are not necessarily assumed to be independent. We derive a generalization of GLIVENKO-CANTELLI theorem under a φ-mixing,condition on the sequence (Xn). This result together with an improvement of the uniform rate of convergence on a compact set of density kernel estimate leads to uniform rate of convergence of hazard kernel estimate. This last result is illustrated by means of Monte Carlo experiments
14 citations
TL;DR: In this paper, deviations from this optimistic approach are investigated by comparing E-optimal x-charts (using the assumption of an exponentially distributed lifetime) and M-optimalityxcharts which are obtained by the pessimistic muumax principle applied to all possible lifetime distributions with the same mean value.
Abstract: In process control the simple x-charts are widely used. In determining an optimum economic design for such a control procedure the time of satisfactory production is usually assumed to be exponentially distributed. In this paper deviations from this optimistic approach are investigated by comparing E-optimal x-charts (using the assumption of an exponentially distributed lifetime) and M-optimal x-charts which are obtained by tfie pessimistic muumax principle applied to all possible lifetime distributions with the same mean value. The comparison shows that the differences between E- and M-optimal x-charts are only minor with respect to a suitable loss function and therefore, the model under consideration is verv robust against deviations from the assumption about the distribution of the time of satisfactory production.
13 citations
TL;DR: In this paper, the optimum and robustness properties of usual F test for balanced random and mixed effects nested models are derived, for nested models with the underlying distribution assumed to be elliptically symmetric.
Abstract: In this note certain optimum and robustness properties of usual F test are derived, for balanced random and mixed effects nested models The underlying distribution assumed is elliptically symmetric WIJSMAN'S Representation theorem is applied as a tool Attention is confined to the testing of random effects only
13 citations
TL;DR: In this paper, the problem of consistently estimating the mean and covariance operator of a quite arbitrary GAUSSian random vector with values in a separable BANACH space is considered, and two methods are given.
Abstract: The problem of consistently estimating the mean and the covariance operator of a quite arbitrary GAUSSian random vector with values in a separable BANACH space is considered. Two methods are given. One, the method of sieves, requires some prior in¬formation about the covariance operator. The other, which has no restriction, is the analog of the usual method of multivariate analysis
12 citations
TL;DR: In this article, it was proved that an nxn symmetric random matrix has m large in absolute value eigenvalues of order √ n while the remaining eigen values are of order fn as n tends to infinity.
Abstract: Let m be a fixed integer It is proved that an nxn symmetric random matrix: consisting of mxm blocks has m large in absolute value eigenvalues of order√ n while the remaining eigenvalues are of order fn as n tends to infinity We assume the associations between observations to be independent random variables ie the sample is in some sense infinite dimensional This random matrix cluster structure-can be obtained by means of the eigenvectors corresponding to the extremal eigenvalues of the association matrix
11 citations
TL;DR: In this article, a sequence of suitably defined multivariate gamma distributions with decreasing skewness is proved to converge to the respective multivariate normal distribution, and the generation of pseudorandom numbers is presented.
Abstract: A sequence of suitably defined multivariate gamma distributions with decreasing skewness is proved to converge to the respective multivariate normal distribution. Other properties of multivariate gamma distributions are given, and the generation of pseudorandom numbers is presented. Parameter estimation is shown to reduce to the evaluation of shape parameter ? in the univariate case. A new estimator of ?, based on the mode of the smallest sample observation, is proposed. A simulation study suggests that the estimator performs better than several other estimators being in use
TL;DR: In this article, a test statistics where is the KAPLAN-MIEER Product limit estimator of F is proposed, and the efficiency loss due to ocensoring is studied compared to DESHPANDE'S (1983) test uncensored case.
Abstract: A life distribution F is an increasing failure rate average (IFRA) if For testing H0: F is exponential, versus H1 F is IFRA, but not exponential based on randomly censored data, we propose a test statistics where is the KAPLAN–MIEER Product limit estimator of F. The asymptotic normality of Jn c(b) is established and an asymptotically distribution – free test is obtained. /The efficiency loss due to ocensoring is studied compared to DESHPANDE'S (1983) test uncensored case. The asymptotic relati ve efficiency with respect to CHEN,HOLLANDER AND LANGBERG'S (1983) test is shoen to be reasonably high
TL;DR: In this article, the Infinitesimal Jackknife method is used to give stability index of the results of a PCA on a variance or a correlation matrix and the exact variance of a bootstrapped variance matrix is given.
Abstract: General results are given about the asymptotic convergence of the Infinitesimal Jackknife estimation method. The development until the order four are given. The Infinitesimal Jackknife method is used to give stability index of the results of a PCA. The exact variance of a bootstrapped variance matrix is given. Infinitesimal Jackknife estimates are obtained for the bias and variances of eigenvalues, eigenvectors and stability index for a PCA on a variance or a correlation matrix. The Infinitesimal Jackknife method is compared with the bootstrap on real data
TL;DR: In this paper, the authors consider the problem of choosing between two density estimates, a non-parametric estimate with the standard properties of nonparametric estimates (universal consistency, robustness, but not extremely good rate of convergence) and a special estimate designed to perform well on a given set T of densities.
Abstract: We consider the problem of choosing between two density estimates, a non-parametric estimate with the the standard properties of nonparametric estimates (universal consistency, robustness, but not extremely good rate of convergence) and a special estimate designed to perform well on a given set T of densities. The special estimate can often be thought of as a parametric estimate. The selection we propose is based upon the L1 distance oetween both estimates. Among otner things, we show how one should proceed to insure that the selected estimate matches the special estimate's rate on T, and that it matches the nonparametric estimate's rate off T
TL;DR: In this article, the authors consider a nonlinear regression model under standard assumptions on the error distribution, and prove an almost sure convergence of weighted sums with an interesting uniformity, and under very general conditions on the parameter space and the regression function they prove the a.s, boundedness and the strong consistency of the least squares estimator.
Abstract: We consider a nonlinear regression model under standard assumptions on the error distribution, We prove an almost sure convergence of weighted sums with an interesting uniformity, and under very general conditions on the parameter space and the regression function we prove the a.s, boundedness and the strong consistency of the least squares estimator, Here we generalize results of Jennrich (1969) to unbounded parameter spaces
TL;DR: In this paper, a stochastic urn model was discussed in which there are two urns A and B and a player selects integers n>O and b>O. The player stops after drawing n+bx balls and is declared to be a win-near if urn B has x black balls.
Abstract: We discuss a stochastic urn model in which there are two urns A and B. B is originally empty and A contains some fixed number of white and black balls. A player selects integers n>O and b>O. Balls are drawn with replacement in A and balls of the same color are put in B as long as the number of white balls in B exceeds (b-1) times the number of black balls in B. Under this condition, the player stops after drawing n+bx balls and is declared to be a winnear if urn B has x black balls. This number of black balls, x, is shown to have the generalized negative binomial distribution
TL;DR: For the model of simple linear regression through the origin and unconditional neighborhoods (errors-in-variables) as well as conditional neighborhoods (error free variables) of the L1-type, an estimator of the slope of the regression line is derived which, among all estimators, is minimax at finite sample size and extends Huber's (1964) robust interval estimator as discussed by the authors.
Abstract: For the model of simple linear regression through the origin and unconditional neighborhoods (errors–in–variables) as well as conditional neighborhoods (error–free–variables) of the L1 –type, an estimator of the slope of the regression line is derived which, among all estimators, is minimax at finite sample size and extends Huber's (1964) robust interval estimator of location
TL;DR: This paper is a review of nonlinear processes used in time series analysis and presents some new original results about stationary distribution of a nonlinear autoregres-sive process of the first order.
Abstract: The paper is a review of nonlinear processes used in time series analysis and presents some new original results about stationary distribution of a nonlinear autoregres-sive process of the first order. The following models are considered: nonlinear autoregessive processes, threshold AR processes, threshold MA processes, bilinear models, auto-regressive models with random parameters including double stochastic models, exponential AR models, generalized threshold models and smooth transition autoregressive models, Some tests for linearity of processes are also presented.
TL;DR: In this paper, a condition for invertibility of a special bilinear model is derived, where the M-estimators of the parameters of the model are considered.
Abstract: In the paper a condition for invertibility of a special bilinear model is derived. We also consider M-estimators of the parameters and prove teir consistence.
TL;DR: In this article, the problem of interval estimation for the class of modified power series distribution (MPSD) is considered and the critical region for the uniformly most powerful test is used to obtain a uniformly most accurate one-sided confidence bound.
Abstract: The problem of interval estimation for the class of modified power series distribution (MPSD) is considered in this paper. Both the cases of small and large samples are investigated in setting 100 (1 -α) %() confidence bounds for the parameter. By using the critical region for the uniformly most powerful test, we obtain a uniformly most accurate one-sided confidence bound. The general results are then applied to the generalized POTSSOX, generalized negative binomial and generalized logarithmic series distributions and particular results are derived for them
TL;DR: In this article, the objective function is seen to be separable and this is helpful in the derivation of D-optimai measures for fourth-order rotatable designs, where the objective functions are derived from the D-optimal objective function.
Abstract: This paper derives D-optimai measures for fourth-order rotatable designs. The objective function is seen to be separable and this is helpful in the derivation
TL;DR: In this article, the essential completeness of the decision rules based on sufficient information in decision models with continuous observations is established, as defined by IRLE-SCHMITZ [7].
Abstract: The aim of this paper is to establish the essential completeness of the decision rules based on sufficient information in decision models with continuous observations, as defined by IRLE-SCHMITZ [7] In this way, a generalization of similar results for sequen-tial decision processes, given by BAHADUR [1] and FERGUSON [5], is obtained In this sense, our results may be compared with those of [5] (section 73) We use essentially the tech-nique of martingales as developed in [4]
TL;DR: In this article, the variance of the iidrv's ηi, under conditions on the (fixed) covariates xi which are little stronger than known necessary and sufficient conditions for those properties in the case ρ = 0.
Abstract: For the linear regression model yi=α+βxi+ei with autoregressive errors ei=ρei-1+ηi, asymptotic existence, uniqueness, consistency and normality of the maximum likelihood estimators of α, β, ρ and σ2, the variance of the iidrv's ηi, are proved under conditions on the (fixed) covariates xi which are little stronger than known necessary and sufficient conditions for those properties in the case ρ = 0. Under the same conditions, the asymptotic distributions of the likelihhor ratio tests for β = 0. i.e., no trend in the presence of autocorrelation, and ρ = 0, no antocorrelation in alinear regression, are shown to be chi-square with one degree of freedom.
TL;DR: In this article, the authors consider the case where the sequence is the indicator function of the interval and show that for any x ∞,x, arithmetic means does not converge with probability one, but if subsequences are considered then arithmetic means converge almost surely.
Abstract: Let Sn be the sum of n i.i.d.r.v.'s with vanishing expectation and variance one, We consider the sequence is the indicator function of the interval (-∞,x), This sequence does not converge for any x and likewise arithmetic means diverge with probability one, But if subsequences are considered then arithmetic means converge almost surely, The speed of this convergence is shown to bo nearly of order k-α2
TL;DR: In this paper, the score-generating functions of locally most powerful rank tests (l.m.p.r.i.d.t) are estimated for bivariate random variables with a nondegene-rated continuous distribution function.
Abstract: Let (1, 1), …, (n, n) be i.i.d. bivariate random variables with a nondegene-rated continuous distribution function. In the testing problem H: (1, 1) are independent versus K: (1, 1) are positively dependent we estimate the score-generating functions of locally most powerful rank tests (l.m.p.r.t.). Thereby a convergence theorem of BEHNEN NEUHAUS (1982) is used
TL;DR: In this paper, the authors combine the outlier-behaviour of certain distribution families and the ability of a most powerful level α-test to separate hypotheses in these families for small α.
Abstract: The aim of this paper is to combine the outlier–behaviour of certain distribution families and the ability of a most powerful level–α–test to separate hypotheses in these families for small α. It turns out that certain location families are well separable in this sense if and only if the underlying distribution is outlier–resistant. Analogous results hold for certain scale families
TL;DR: In this article, the authors consider a class of shrinkage estimators of the mean whose shrinkage functions are not necessarily differentiate and establish a sufficient condition for uniform domination of the maximum likelihood estimator, with respect to an arbitrary quadratic loss.
Abstract: A random normal vector is observed in a finite dimensional real vector space E. Its mean is unknown but belongs to a known subspace of E of dimension >3. Its co variance operator is known up to a multiplicative factor. We consider a class of shrinkage estimators of the mean whose shrinkage functions are not necessarily differentiate. We establish a sufficient condition for uniform domination of the maximum likelihood estimator, with respect to an arbitrary quadratic loss.
TL;DR: In this paper, a family of optimality eriteria (distances) is introduced, of which well-known criteria such as maximum likelihood, Pearson- and Neyman chi-square, the Kullback-Liebler distance turn out to be special cases.
Abstract: The present paper investigates estimation under the hypothesis of homogeneity or independence for a two-way contingency table. A family of optimality eriteria(distances, is introduced, of which well-known criteria such as maximum likelihood, Pearson- and Neyman chi-square, the Kullback-Liebler distance turn out to be special cases. We investigate the statistical properties of this family via a Monte Carlo study