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The purpose of this paper is, in the first step, to consider a class of GMM estimators with interesting asymptotic properties and a reasonable number of computations for two dimensionally indexed Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model. In the second step, we use the central limit theorem of Huang (1992) for spatial martingale differences to establish the LAN property for general two-dimensional discrete models on a regular grid with Gaussian errors. We then apply this result to the spatial GARCH model and derive the limit distribution of the maximum likelihood estimators of the parameters. Results of numerical simulations are presented. [ABSTRACT FROM AUTHOR]

Abstract: Necessary and sufficient conditions for the existence of order statistics moments of -stable random variables are introduced. Using the obtained results, all parameters of -stable distribution are estimated. [Copyright &y& Elsevier]

Abstract: A class of absolutely continuous bivariate exponential distributions is constructed using the product form of a first order autoregressive model. Inference methods are proposed for parameter estimation and diagnosis. Data analysis is carried out to illustrate the applications. [Copyright &y& Elsevier]

Abstract: Given measurements of the number of customers in a queueing system over a finite time interval, it is natural to try to fit a stationary birth-and-death process model, because it is remarkably tractable, even when the birth and death rates depend on the state in an arbitrary way. Natural estimators of the birth (death) rate in each state are the observed number of transitions up (down) from that state divided by the total time spent in that state. It is tempting to validate the model by comparing the steady-state distribution of the model based on those estimated rates to the empirical steady-state distribution recording the proportion of time spent in each state. However, it is inappropriate to draw strong conclusions from a close fit to the same data, because these two distributions are necessarily intimately related, even if the model assumptions are not nearly satisfied. We elaborate by (i) establishing stochastic comparisons between these two fitted distributions using likelihood-ratio stochastic ordering and (ii) quantifying their difference. [Copyright &y& Elsevier]

Abstract: With sparse structures and conditional independence, one could estimate the precision matrix of Gaussian graphical models more efficiently. studied objective priors for star-shape graphical models. We consider a generative star-shape model. Objective priors such as invariance priors, the Jeffreys prior and reference priors are derived for the proposed model. Closed form expressions of posterior distributions are derived based on a family of priors including the studied objective priors. [Copyright &y& Elsevier]

Abstract: The Laplace distribution is one of the earliest distributions in probability theory. For the first time, based on this distribution, we propose the so-called beta Laplace distribution, which extends the Laplace distribution. Various structural properties of the new distribution are derived, including expansions for its moments, moment generating function, moments of the order statistics, and so forth. We discuss maximum likelihood estimation of the model parameters and derive the observed information matrix. The usefulness of the new model is illustrated by means of a real data set. [Copyright &y& Elsevier]

Abstract: One major goal in clinical applications of multi-state models is the estimation of transition probabilities. In a recent paper, introduce a substitute for the Aalen–Johansen estimator in the case of a non-Markov illness–death model. The idea behind their estimator is to weight the data by the Kaplan–Meier weights pertaining to the distribution of the total survival time of the process. In this paper we propose a modification of estimator based on presmoothing. Consistency is established. We investigate the finite sample performance of the new estimator through simulations. Data from a study on colon cancer are used for illustration purposes. [Copyright &y& Elsevier]

Abstract: Backward recurrence times in stationary renewal processes and current durations in dynamic populations observed at a cross-section may yield estimates of underlying interarrival times or survival distributions under suitable stationarity assumptions. Regression models have been proposed for these situations, but accelerated failure time models have the particularly attractive feature that they are preserved when going from the backward recurrence times to the underlying survival distribution of interest. This simple fact has recently been noticed in a sociological context and is here illustrated by a study of current duration of time to pregnancy. [Copyright &y& Elsevier]

Abstract: The modeling and analysis of lifetime data is an important aspect of statistical work in a wide variety of scientific and technological fields. introduced a probability distribution which is commonly used in the analysis of lifetime data. For the first time, based on this distribution, we propose the so-called exponentiated generalized inverse Gaussian distribution, which extends the exponentiated standard gamma distribution (). Various structural properties of the new distribution are derived, including expansions for its moments, moment generating function, moments of the order statistics, and so forth. We discuss maximum likelihood estimation of the model parameters. The usefulness of the new model is illustrated by means of a real data set. [Copyright &y& Elsevier]

Abstract: An adjusted -squared type measure for exponential dispersion models, based on Kullback–Leibler divergences, is described and it is proved that the corrected measure is an asymptotically unbiased estimator of the population value, under the null hypotheses of no covariates. [Copyright &y& Elsevier]

Abstract: We consider semiparametric models whose infinite-dimensional parameter corresponds to a probability distribution. The NPMLE based on the profile empirical likelihood for this kind of semiparametric model has attracted considerable interest. We propose the use of a modified profile empirical likelihood to improve the accuracy of this estimation. We consider applications to the exponential-tilt model and show that the accuracy of the proposed estimator is better than that of the conventional NPMLE by numerical study. [Copyright &y& Elsevier]

Abstract: It is well known that the Kaplan–Meier estimate of QAL data leads to a biased estimate due to the induced dependence between the QAL and censoring time in the QAL scale. However, the issue of induced dependent censoring in the QAL scale remains less understood. We present a formal study of this induced dependence in the context of a simple illness–death model. The bias of the Kaplan–Meier estimate of the QAL distribution has been investigated. [Copyright &y& Elsevier]

Abstract: Multi-casting autoregression (MCAR, for short) is suggested as a natural extension of the bifurcating autoregressive (BAR) model (cf. [Cowan, R., Staudte, R.G., 1986. The bifurcating autoregression model in cell lineage studies. Biometrics 42, 769–783]) in order to analyze multi-splitting tree-structured data. Pathwise stationarity of the MCAR model is discussed. Least squares estimation for the autoregressive parameter is considered and relevant limiting distribution is derived, in particular, for the pathwise explosive case. These results can be regarded as generalizations of those for standard stationary and explosive AR(1) time series. A simulation study is conducted to illustrate our results. [Copyright &y& Elsevier]

Abstract: Modeling and estimating a tail copula play an important role in forecasting rare events. Due to their easy simulation, elliptical copulas have been employed in risk management. Recently, Klüppelberg, [Klüppelber, C., Kuhn, G., Peng, L., 2007. Estimating the tail dependence function of an elliptical distribution. Bernoulli 13 (1), 229–251; Klüppelberg, C., Kuhn, G., Peng, L., 2008. Semi-parametric models for the multivariate tail dependence function—the asymptotically dependent case. Scandinavian Journal of Statistics 35, 701–718] proposed to model a tail copula by an elliptical copula, which results in an explicit parametric model for the tail copula. In this paper, we propose a goodness-of-fit test for such a parametric model and some real data analyses show that this fitting cannot be rejected. Therefore we demonstrate the practical applicability of this model. [Copyright &y& Elsevier]

Abstract: In this note, we investigate the asymptotic behavior of two special functions that satisfy defective renewal equations and have a key role in risk theory. Heavy-tailed distributions are important in our analysis. Furthermore, applying our results to the renewal and classical models of risk theory yields a generalisation of a well-known asymptotic formula of [Embrechts, P., Veraverbeke, N., 1982. Estimates for the probability of ruin with special emphasis on the possibility of large claims. Insurance Math. Econom. 1, 55–72]. [Copyright &y& Elsevier]

Abstract: Let be gap times corresponding to two consecutive events, which are observed subject to random right-censoring. In this paper a simple estimator of the bivariate distribution function of is proposed. We investigate the conditions under which the introduced estimator is consistent. Applications to the estimation of the marginal distributions of the gap times and to correlation analysis are included. We explore the behaviour of the proposed methods through simulations. [Copyright &y& Elsevier]

Abstract: A proof load design is useful for estimation of the dependence between two strength properties of a unit when either property can only be measured by loading to failure. Here we extend the application of the proof load design to estimate the parameters of a bivariate Weibull distribution. An example concerning the bending and tensile strengths lumber is presented. [Copyright &y& Elsevier]

Abstract: proposed covariance reducing models as a method for modeling the differences among covariance matrices. The model was developed via a property of a conditional distribution for the sample covariance matrices and this conditional distribution was used to obtain maximum likelihood estimators. In this work, we show that the same maximum likelihood estimators can be obtained using the unconditional distribution of the sample covariance matrices along with a condition on the population covariance matrices that holds if and only if the covariance reducing model holds. In addition, it is shown that when , specialized numerical methods are not needed to compute the maximum likelihood estimators. [Copyright &y& Elsevier]