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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: For distributed as normal or lognormal, the interval estimation of the mean and variance of the corresponding limited or truncated random variable is addressed using the concept of a generalized confidence interval, based on a sample from the distribution of . Numerical results and practical examples are used to illustrate the results. [Copyright &y& Elsevier]

Abstract: In this paper I return to the issue of estimating linear state space models with constrained state vectors. My endeavor is towards the following tasks: (i) to give a new elementary derivation for restricted Kalman filtering under augmentation of the measurement equation, (ii) to prove the statistical efficiency due to the imposition of restrictions using a geometrical framework, and (iii) to propose an alternative approach for imposing time-invariant restrictions to the estimation of random walk state vectors. [Copyright &y& Elsevier]

Abstract: In this note we show that the locally stationary wavelet process can be decomposed into a sum of signals, each of which follows a moving average process with time-varying parameters. We then show that such moving average processes are equivalent to state space models with stochastic design components. Using a simple simulation step, we propose a heuristic method of estimating the above state space models and then we apply the methodology to foreign exchange rates data. [Copyright &y& Elsevier]

Abstract: Omelka [Omelka, M., 2007. Second-order linearity of Wilcoxon rank statistics. Ann. Inst. Statist. Math. 59, 385–402] proposed an alternative way of constructing a confidence interval based on -estimators for single parameters in linear models. We will compare this confidence interval with a traditional (Wald type) confidence interval theoretically as well as by means of a Monte Carlo experiment. As a by-product we will show the asymptotic normality of the estimator of proposed in [Koul, H.L., Sievers, G.L., McKean, J., 1987. An estimator of the scale parameter for the rank analysis of linear models under general score functions. Scand. J. Statist. 14, 131–141] under somewhat different assumptions from those in [Thewarepperuma, P.S., 1987. On estimation of some density functionals under regression and one sample models. Ph.D. Thesis. Michigan State University, Department of Statistics and Probability]. [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: The purpose of this paper is to study the change point estimation problem in multi-phase regression models. This is a non-regular statistical estimation; thus the asymptotic distribution of the maximum likelihood estimator is verified by means of the weak convergence of the likelihood ratio process. These weak convergence results differ depending on the jump size of the regression function. [Copyright &y& Elsevier]

Abstract: This paper examines the size performance of Breitung''s [2002. Nonparametric tests for unit roots and cointegration. J. Econometrics 108, 343–363.] nonparametric unit root test in the presence of a variance shift. We show that the limiting distribution of the test statistic in the presence of a variance shift depends on the break point of the variance and the ratio of the prebreak to the postbreak variance, as in the case of the standard Dickey–Fuller test. However, our Monte Carlo simulations provide clear evidence that Breitung''s nonparametric unit root test achieves a far superior size performance as compared with the Dickey–Fuller test. [Copyright &y& Elsevier]

Abstract: In a mixture experiment the measured response is assumed to depend only on the relative proportion of ingredients or components present in the mixture. Scheffe [1958. Experiments with mixtures. Journal of Royal Statistical Society B 20, pp. 344–360; 1963. Simplex-centroid design for experiments with mixtures. Journal of Royal Statistical Society B 25, 235–263] first systematically considered this problem and introduced different models and designs suitable in such situations. Optimum designs for the estimation of parameters of different mixture models are available in the literature. The problem of estimating the optimum proportion of mixture components is of great practical importance. Pal and Mandal [2006. Optimum designs for optimum mixtures. Statistics and Probability Letters 76, 1369–1379] first attempted to find a solution to this problem using the trace criterion, assuming prior knowledge about the optimum mixing proportions. In this paper the minimax criterion has been employed to find a solution to the above problem. [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: The method of least squares provides the most widely used algorithm for fitting a linear model. A variety of nonparametric procedures have been developed that are designed to be robust against model violations and resistant against aberrant points. One such method introduced by Theil [1950. A rank-invariant method of linear and polynomial regression analysis. I, II, III. Proc. Ned. Akad. Wet. 53, 386–392, 521–525, 1397–1412] is based on pairwise estimates. There are many examples in which the data are nonlinear, and in particular, where a quadratic fit may be more appropriate. We here propose a nonparametric method for fitting a quadratic regression. [Copyright &y& Elsevier]

Abstract: Reproductive dispersion linear models (RDLMs) include generalized linear model [Nelder and Wedderburn (1972). Generalized linear models. J. Roy. Statist. Soc. Ser. A 135, 370–384] as a special case. Some mild regularity conditions analogous to those given by Fahrmeir and Kaufmann [1985. Consistency and asymptotic normality of the maximum likelihood estimator in generalized linear models. Ann. Statist. 13, 342–368] are proposed. On the basis of the proposed mild conditions, the existence, weak consistency, strong consistency, and asymptotic normality of the maximum likelihood estimate (MLE) are provided in RDLMs. The asymptotic results of Fahrmeir and Kaufmann [1985. Consistency and asymptotic normality of the maximum likelihood estimator in generalized linear models. Ann. Statist. 13, 342–368] are generalized to RDLMs. [Copyright &y& Elsevier]

Abstract: This paper considers a wavelet method for the estimation of the density and hazard rate functions from randomly censored data. We establish the weak uniform consistency of the density and hazard rate estimators. [Copyright &y& Elsevier]

Abstract: In this paper, an empirical Bayes (EB) estimator is derived for the estimable functions of the parameters in normal linear model. The superiority of the EB estimator over ordinary least-squares (LS) estimator is investigated under mean square error matrix (MSEM) criterion. [Copyright &y& Elsevier]

Abstract: Motivated by a statistical model for the structural line segment relationship developed for computer vision applications we derive an estimator for the slope of a regression line in univariate measurement error models. We show that under the typical side conditions, this estimator coincides, in most cases, with the maximum likelihood estimator for the normal structural model. Its large sample properties are derived. [Copyright &y& Elsevier]

This article explores alternative state space representations for ARMA models. We advocate representations that have minimal state order and appealing Kalman filter steady state properties. We derive expressions for smoother output and describe concrete connections to classical infinite sample representations. [Copyright &y& Elsevier]

The paper proves that the maximum likelihood estimates of item and person parameters of the Rasch model preserve the order of item and person total scores. The result is valid for conditional and unconditional maximum likelihood estimation. [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]

Abstract: This note studies the () spurious regression model for the special case where the weight matrix is normalized and has equal elements, and where the nonstationarity is caused by near unit roots. It shows that spurious spatial regression will not occur in a spatially autoregressive (SAR) model when the spatial weight matrix is row-normalized and has equal weights. In fact, the asymptotic distribution of the OLS estimate will always converge to its true value zero. The only condition required is that the spatial coefficients of the dependent and independent variables be both less than 1, which is a requirement for the SAR model to be an equilibrium model. [ABSTRACT FROM AUTHOR]

Abstract: An alternative criterion is presented for a linear function of the unknown parameters, in a linear model, to be estimable. If there is a linear relationship between members of a subset of the columns of the design matrix , then the parameters associated with all the columns in that subset are not estimable. Also any part of their linear relationship is non-estimable. [Copyright &y& Elsevier]

Abstract: In [Przystalski M., Krajewski P., 2007. Constrained estimators of treatment parameters in semiparametric models. Statist. Probab. Lett. 77, 914–919] we presented a method of estimation of treatment effects in a semiparametric model with one smoothing term under additional conditions on their linear functions and its application to hypothesis testing. In this note we will present the corrected version of the proof of Theorem 3.1. [Copyright &y& Elsevier]