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Abstract: We propose a new efficient root- consistent estimate for the direction of the index parameter vector in a class of models with single-index structure. To select the important predictors, we suggest using the adaptive LASSO and establish the oracle property. Simulation results also confirm the theoretical findings. [Copyright &y& Elsevier]

Abstract: In this paper, we study -estimation for the partially linear model under monotonic constraints. We use monotone -splines to approximate the monotone nonparametric function. We show the large sample properties of the resulting estimators. The proposed estimator of parameter part is root- consistent, and asymptotically normal and the estimator for the nonparametric component achieves the optimal convergence rate. A simulation study is conducted to evaluate the finite sample performance of the method. The proposed procedure is illustrated by an air pollution study. [Copyright &y& Elsevier]

Abstract: This paper proposes two estimation methods based on a weighted least squares criterion for non-(strictly) stationary power ARCH models. The weights are the squared volatilities evaluated at a known value in the parameter space. The first method is adapted for fixed sample size data while the second one allows for online data available in real time. It will be shown that these methods provide consistent and asymptotically Gaussian estimates having asymptotic variance equal to that of the quasi-maximum likelihood estimate (QMLE) regardless of the value of the weighting parameter. Finite-sample performances of the proposed WLS estimates are shown via a simulation study for various sub-classes of power ARCH models. [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: 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: 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]

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]

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]