Showing papers in "Statistics in 2010"
TL;DR: Scale mixtures of the skew normal (SMSN) distribution is a class of asymmetric thick-tailed distributions that includes the skew-normal (SN) distribution as a special case as discussed by the authors.
Abstract: Scale mixtures of the skew–normal (SMSN) distribution is a class of asymmetric thick–tailed distributions that includes the skew–normal (SN) distribution as a special case. The main advantage of these classes of distributions is that they are easy to simulate and have a nice hierarchical representation facilitating easy implementation of the expectation–maximization algorithm for the maximum-likelihood estimation. In this paper, we assume an SMSN distribution for the unobserved value of the covariates and a symmetric scale mixtures of the normal distribution for the error term of the model. This provides a robust alternative to parameter estimation in multivariate measurement error models. Specific distributions examined include univariate and multivariate versions of the SN, skew–t, skew–slash and skew–contaminated normal distributions. The results and methods are applied to a real data set.
40 citations
TL;DR: In this article, the authors discuss the problem of predicting future order statistics based on observed record values and similarly, the prediction of future records based on the observed order statistics and show that the coverage probabilities of these intervals are exact and are free of the parent distribution.
Abstract: In this paper, we discuss the problem of predicting future order statistics based on observed record values and similarly, the prediction of future records based on observed order statistics. The coverage probabilities of these intervals are exact and are free of the parent distribution F. Finally, two data sets are used to illustrate the proposed procedures.
39 citations
TL;DR: In this article, the dependence structure of the bivariate Burr type III distribution has been studied and the dependence measures such as the Kendall's tau, medial correlation and tail dependence have been studied.
Abstract: In this paper, we extend some results related to the dependence structure of the bivariate Burr type III distribution, proposed by Rodriguez [Multivariate Burr III distributions, Part I. Theoretical Properties, Research Publication GMR-3232, General Motors Research Laboratories, Warren, Michigan, 1980; Frequency surfaces, system of, in Encyclopedia of Statistical Sciences, Vol. 3, 1983, Wiley, New York, pp. 232–247]. Using copula representations of bivariate distributions, in the first part of the work, we study some dependence properties and ordering, and we prove that this model can also describe situations of negative dependence. In the second part, we study some dependence measures such as the Kendall's tau, medial correlation and tail dependence. Finally, we show that the correlation coefficient exists and can also be negative.
31 citations
TL;DR: The Pinsker inequality for finite measures and the generalized Ornstein distance of stationary random processes are among the illustrations of applicability in the information theory as mentioned in this paper, where basic properties of the modified φ-divergences are investigated, such as the range of values, symmetry and a decomposition into local and global components.
Abstract: Modifications of the classical φ-divergences D φ(μ, ν)=∈t q φ (p/q) dλ of finite measures μ, ν on a σ-finite measure space (𝒳, 𝒜, λ) with Radon–Nikodym densities p=dμ/dλ, q=dν/dλ are introduced by the formula 𝔇φ(μ, ν)=∈t q φ˜ (p/q) dλ using the nonnegative convex functions . Basic properties of the modified φ-divergences are investigated, such as the range of values, symmetry and a decomposition into local and global components. A general φ-divergence formula for right-censored observations illustrates the statistical applicability. The Pinsker inequality for finite measures and the generalized Ornstein distance of stationary random processes are among the illustrations of applicability in the information theory.
28 citations
TL;DR: In this paper, the estimation of a two-parameter Burr-XII distribution under Type II progressive censoring was considered and several pivotal quantities were proposed to construct the confidence interval for the shape parameter and the confidence region for two parameters.
Abstract: This study considers the estimation of a two-parameter Burr-XII distribution under Type II progressive censoring. Several pivotal quantities are proposed to construct the confidence interval for the shape parameter and the confidence region for two parameters. A biometrical example is given to illustrate the proposed confidence intervals or confidence regions. The criteria of minimum confidence length and minimum confidence area are used to obtain the optimal estimation. At last, a simulation study is done to compare the performances of all proposed pivotal quantities.
18 citations
TL;DR: In this article, the least square estimators for the outbreak regression without assumption of a parametric regression function are given, and it is shown that the least squares estimators are also the maximum likelihood estimators of distributions in the regular exponential family such as the Gaussian or Poisson distribution.
Abstract: A regression may be constant for small values of the independent variable (for example time), but then a monotonic increase starts. Such an ‘outbreak’ regression is of interest for example in the study of the outbreak of an epidemic disease. We give the least square estimators for this outbreak regression without assumption of a parametric regression function. It is shown that the least squares estimators are also the maximum likelihood estimators for distributions in the regular exponential family such as the Gaussian or Poisson distribution. The approach is thus semiparametric. The method is applied to Swedish data on influenza, and the properties are demonstrated by a simulation study. The consistency of the estimator is proved.
14 citations
TL;DR: In this article, a quadratic statistic Σˆ(Y), distributed as a Wishart distribution, is proposed and proved to be a uniformly minimum variance unbiased invariant estimator of the second-order parameter matrix Σ.
Abstract: Let be the extended growth curve model with error matrix ℰ distributed as a normal distribution with mean 0 and covariance I⊗ Σ, subject to some specified conditions. A quadratic statistic Σˆ(Y), distributed as a Wishart distribution, is proposed and proved to be a uniformly minimum variance unbiased invariant estimator of the second-order parameter matrix Σ. In addition, unbiased and explicit estimators Θˆ i (Y) of the first-order parameter matrices Θ i are given. And explicit formulae to compute the traces of the covariance matrices of Θˆ i (Y) are derived.
13 citations
TL;DR: In this paper, the asymptotic distributions of sample parameters of the efficient frontier and sample characteristics of optimal portfolios are derived under the assumption that the asset returns follow a k-dimensional VARMA-GARCH process.
Abstract: In this paper, the asymptotic distributions of sample parameters of the efficient frontier and sample characteristics of optimal portfolios are derived. This is done assuming the asset returns to follow a k-dimensional VARMA–GARCH process. Moreover, estimators of the mean vector and the covariance matrix of the asset returns are suggested, which are asymptotic independent normally distributed within the considered class of stochastic processes.
13 citations
TL;DR: In this paper, a parallel system consisting of a finite number of identical components with independent lifetimes having a common distribution function is considered, when the failure time of the system is restricted to a finite interval (double regularly checking).
Abstract: In this paper, a parallel system consisting of a finite number of identical components with independent lifetimes having a common distribution function is considered, when the failure time of the system is restricted to a finite interval (double regularly checking). Under these conditions, the mean past lifetime (MPL) of the system is presented and some of its properties are derived. It is shown that the underlying distribution function can be recovered from the proposed MPL. Then, a consistent estimator for MPL is presented and some of its properties are studied. This estimator also could be used for the single monitoring case or ordinary MPL. Finally, some properties of the MPL of a parallel system with nonidentical components are discussed.
12 citations
TL;DR: In this paper, the authors considered the number of observations in two-sided neighbourhoods of the kth and (n−r)th order statistics from a sample of size n and showed that they are asymptotically independent as n→∞.
Abstract: In this paper, we consider the numbers of observations in two-sided neighbourhoods of the kth and (n−r)th order statistics from a sample of size n and show that they are asymptotically independent as n→∞. We also establish a result that generalizes all the existing results regarding the asymptotic independence of numbers of observations in the left and right neighbourhoods of order statistics. Finally, we consider the limiting joint behaviour of numbers of observations in the neighbourhoods of s central order statistics and establish that they are asymptotically independent.
11 citations
TL;DR: This article developed an extension of categorical analysis of variance for one response and two factors, based on a partitioning of a measure of predictability for three-way contingency tables, known as Gray and Williams's index.
Abstract: In this article we develop an extension of categorical analysis of variance for one response and two factors, based on a partitioning of a measure of predictability for three-way contingency tables, known as Gray and Williams's index. At the first instance moment the decomposition of this multiple measure of association in partial association measures is shown. Finally, for ordinal-scale variables, we propose an extension of this decomposition using a particular set of orthogonal polynomials.
TL;DR: In this article, the authors developed influence diagnostics for generalized Poisson regression (GPR) models based on global and local influence analysis, where the case-deletion model is equivalent to the mean shift outlier model (MSOM) in GPR models and an outlier test is presented based on the MSOM.
Abstract: This work develops influence diagnostics for generalized Poisson regression (GPR) models based on global and local influence analysis. The one-step approximations of the estimates in the case-deletion model are given and case-deletion measures and local influence measures are obtained. At the same time, it is shown that the case-deletion model is equivalent to the mean shift outlier model (MSOM) in GPR models and an outlier test is presented based on the MSOM. Furthermore, we discuss score tests for significance and homogeneity of the dispersion parameter in GPR models, respectively. Finally, two count data sets are given to illustrate our methodology and the properties of score test statistics are investigated through Monte Carlo simulations.
TL;DR: In this paper, the problem of estimating the width of a symmetric uniform distribution on the line together with the error variance, when data are measured with normal additive error, is considered.
Abstract: The problem of estimating the width of a symmetric uniform distribution on the line together with the error variance, when data are measured with normal additive error, is considered. The main purpose is to analyse the maximum-likelihood (ML) estimator and to compare it with the moment-method estimator. It is shown that this two-parameter model is regular so that the ML estimator is asymptotically efficient. Necessary and sufficient conditions are given for the existence of the ML estimator. As numerical problems are known to frequently occur while computing the ML estimator in this model, useful suggestions for computing the ML estimator are also given.
TL;DR: In this article, the asymptotic properties of smoothed nonparametric kernel spectral density estimators for the spatial spectral density were studied for continuous stationary spatial processes under a shrinking asymPTotic framework.
Abstract: In this work, we study the asymptotic properties of smoothed nonparametric kernel spectral density estimators for the spatial spectral density. We consider the case of continuous stationary spatial processes under a shrinking asymptotic framework. Expressions for the bias and the covariance structure are obtained and the implications for the edge effect bias of the choice of the kernel, bandwidth and spacing parameter in the design are also discussed, both for tapered and untapered estimates. Results are illustrated with a simulation study.
TL;DR: In this paper, the problem of obtaining uniformly minimum variance unbiased estimators of ξ = P(Y>X) and ξ k (where k is a positive integer) when X and Y follow two-parameter exponential distributions was revisited.
Abstract: The problems of obtaining uniformly minimum variance unbiased estimators of ξ=P(Y>X) and ξ k (where k is a positive integer) when X and Y follow two-parameter exponential distributions considered by Pal et al. [M. Pal, M. Ali Masoom, and J. Woo, Estimation and testing of P(Y>X) in two parameter exponential distributions, Statistics 39 (2005), pp. 415–428] are revisited. Much simpler techniques of obtaining these estimators are provided.
TL;DR: In this paper, the likelihood ratio test (LRT) for testing a mean change after an unknown point in a sequence of n uncorrelated p-dimensional elliptically contoured distributed observations is established.
Abstract: The likelihood ratio test (LRT) for testing a mean change after an unknown point in a sequence of n uncorrelated p-dimensional elliptically contoured distributed observations is established. It is shown that the LRT has the same form as well as null distribution as in the multivariate normal case.
TL;DR: In this article, the notion of the mean residual waiting time of records was introduced and some monotonic and aging properties were investigated for mean residual life function or life expectancy, which plays an important role in studying the conditional tail measure of lifetime data.
Abstract: Often, in reliability theory, risk analysis, renewal processes and actuarial studies, mean residual life function or life expectancy plays an important role in studying the conditional tail measure of lifetime data. In this paper, we introduce the notion of the mean residual waiting time of records and present some monotonic and aging properties. Sharp bounds for the mean residual waiting time of records are also investigated.
TL;DR: Golosnoy and Schmid as mentioned in this paper introduced exponentially weighted moving average type control charts for this task based on the processes of the estimated weights as well as of their first differences and proposed new approximations to these processes exhibiting better stochastic properties for sequential monitoring purposes.
Abstract: This paper elaborates the tools for the surveillance of the global minimum variance portfolio weights Golosnoy and Schmid [V Golosnoy and W Schmid, EWMA control charts for optimal portfolio weights, Sequential Anal 26 (2007), pp 195–224] introduced exponentially weighted moving average-type control charts for this task based on the processes of the estimated weights as well as of their first differences This paper proposes the new approximations to these processes exhibiting better stochastic properties for sequential monitoring purposes The control schemes for the new processes are compared for different types of economically relevant changes using Monte Carlo simulations The suggested procedures appear to be superior for the considered performance measures
TL;DR: In this article, the authors established additive and block decompositions of weighted least squares estimators under a multiple partitioned linear model and its k small models based on orthogonality of regressors with respect to a given weight matrix.
Abstract: While considering the mechanism of weighted least-squares estimators (WLSEs) of regression coefficients in a partitioned linear model, Tian and Takane [On sum decompositions of weighted least-squares estimators under the partitioned linear model, Comm Statist Theory Methods 37 (2008), pp 55–69] gave some identifying conditions for the WLSEs to be the sum of WLSEs under its two small models based on orthogonality of regressors with respect to the given weight matrix The purpose of this paper is to show how to establish additive and block decompositions of WLSEs under a multiple partitioned linear model and its k small models based on orthogonality of regressors with respect to a given weight matrix
TL;DR: This work discusses locally optimal designs, where the experimenter is only interested in the slope at a particular point, and standardized minimax optimal Designs, which could be used if precise estimation of the slope over a given region is required.
Abstract: In the common linear model with quantitative predictors we consider the problem of designing experiments for estimating the slope of the expected response in a regression We discuss locally optimal designs, where the experimenter is only interested in the slope at a particular point, and standardized minimax optimal designs, which could be used if precise estimation of the slope over a given region is required General results on the number of support points of locally optimal designs are derived if the regression functions form a Chebyshev system For polynomial regression and Fourier regression models of arbitrary degree the optimal designs for estimating the slope of the regression are determined explicitly for many cases of practical interest
TL;DR: In this paper, the authors proposed bandwidth selectors for nonparametric regression with dependent errors, which are based on criteria that approximate the average squared error, and they show that these approximations are uniform over the bandwidth sequence.
Abstract: In this paper, we propose bandwidth selectors for nonparametric regression with dependent errors. The methods are based on criteria that approximate the average squared error. We show that these approximations are uniform over the bandwidth sequence. The criteria involve some constants that depend on the unknown error correlations. We propose a novel way of estimating these constants. Our numerical study shows that the method is quite efficient in a variety of error models.
TL;DR: In this paper, the authors study a limiting distribution induced by Bartlett's formulation of the Luria-Delbruck mutation model and devise an algorithm for computing the probability mass function.
Abstract: In this paper, we study a limiting distribution induced by Bartlett's formulation of the Luria–Delbruck mutation model. We establish the validity of the probability generating function and devise an algorithm for computing the probability mass function. Maximum-likelihood estimation and asymptotic behaviour of the distribution are considered.
TL;DR: In this article, a novel estimator of Mahalanobis distance D 2 between two non-normal populations is presented, which is enormously more efficient and robust than the traditional estimator based on least squares estimators.
Abstract: We give a novel estimator of Mahalanobis distance D 2 between two non-normal populations. We show that it is enormously more efficient and robust than the traditional estimator based on least squares estimators. We give a test statistic for testing that D 2=0 and study its power and robustness properties.
TL;DR: This work considers second-order probability matching priors that ensure frequentist validity of posterior quantiles with margin of error o(n −1, where n is the sample size) and explores how this problem can be resolved via consideration of data-dependent priors.
Abstract: We consider second-order probability matching priors that ensure frequentist validity of posterior quantiles with margin of error o(n −1), where n is the sample size. It is well known that there are many models of interest where data-free second-order probability matching priors do not exist. We explore how this problem can be resolved via consideration of data-dependent priors. This is done both in the absence and presence of nuisance parameters.
TL;DR: In this article, the asymptotic properties of the nonparametric estimation of K-function in stationary spatial point processes have been studied, and the authors investigated the non-stationary K-functions for a class of nonstationary processes, where stationary is often not a reasonable assumption.
Abstract: The K-function is one of the most commonly used summary statistics. It plays the role for spatial point processes that the covariance function or the variogram plays for continuous observation. The asymptotic properties of the nonparametric estimation of K-function in stationary spatial point processes have been studied. However, in practice, stationary is often not a reasonable assumption. In this article, we investigate the asymptotic behaviour of the nonparametric estimation of K-function for a class of nonstationary processes.
TL;DR: In this article, a new nonparametric testing method for increasing mean inactivity time class is proposed; and a comparison between the proposed test and two other related ones in the literature is conducted through evaluating the asymptotic Pitman efficiency.
Abstract: In this paper, a new nonparametric testing method for increasing mean inactivity time class is proposed; and a comparison between the proposed test and two other related ones in the literature is conducted through evaluating the asymptotic Pitman efficiency. Furthermore, Edgeworth expansion is employed to improve the accuracy of the convergence rate of the test statistic. Some numerical results are also presented to demonstrate the performance of the testing method.
TL;DR: The aim of this paper is to cast the method into a more rigorous statistical framework and to propose some developments, and to give evidence that the IFA model represents a special case of mixture of factor analysers.
Abstract: Independent factor analysis (IFA) has recently been proposed in the signal processing literature as a way to model a set of observed variables through linear combinations of latent independent variables and a noise term. A peculiarity of the method is that it defines a probability density function for the latent variables by mixtures of Gaussians. The aim of this paper is to cast the method into a more rigorous statistical framework and to propose some developments. In the first part, we present the IFA model in its population version, address identifiability issues and draw some parallels between the IFA model and the ordinary factor analysis (FA) one. Then we show that the IFA model may be reinterpreted as an independent component analysis-based rotation of an ordinary FA solution. We also give evidence that the IFA model represents a special case of mixture of factor analysers. In the second part, we address inferential issues, also deriving the standard errors for the model parameter estimates and pro...
TL;DR: In this paper, lower bounds for sup-norm losses of estimators of the distribution function of a sample maximum and its density were derived, and it was shown that their consistent estimation in a general situation is impossible.
Abstract: We derive lower bounds for sup-norm losses of estimators of the distribution function of a sample maximum and its density and show that their consistent estimation in a general situation is impossible.
TL;DR: In this article, it was proved that weak convergence on a compact interval to a continuous, strictly increasing limit function of the distribution function of a record value implies weak convergence throughout ℝ.
Abstract: In this paper it is proved that the weak convergence on a compact interval to a continuous, strictly increasing limit function, of the distribution function of a record value, implies weak convergence throughout ℝ.