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We discuss an approach to construct explicitly calculable consistent estimators for parameters of some nonlinear regression models. The estimators of such a kind can be used as initial estimators in one-step estimation procedures for unknown parameters of these models. [ABSTRACT FROM AUTHOR]

Abstract: Two-step logit models are extensions of the ordinary logistic regression model, which are designed for complex ordinal outcomes commonly seen in practice. In this paper, we establish some asymptotic properties of the maximum likelihood estimator (MLE) of the regression parameter vector under some mild conditions, which include existence of the MLE, convergence rate and asymptotic normality of the MLE. We relax the boundedness condition of the regressors required in most existing theoretical results, and all conditions are easy to verify. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the independent component (IC) model, and the asymptotic properties of the complex valued unmixing matrix estimates that are based on simultaneous use of two scatter matrix functionals. [Copyright &y& Elsevier]

Abstract: In this paper, we investigate the estimation of conditional density function based on the single-index model for functional time series data. The asymptotic normality of the conditional density estimator and the conditional mode estimator for the mixing dependence functional time series data are obtained, respectively. Furthermore, as applications, the asymptotic confidence interval of the conditional density function and the conditional mode are also presented for . [Copyright &y& Elsevier]

Abstract: The estimation of a diffusion tensor imaging (DTI) model proposed by involves two steps. The second step requires solving an ordinary differential equation, which in practice is solved by using a numerical approximation. We investigate how to balance the additional numerical error introduced by this approximation with the statistical estimation error using empirical mean integrated squared error for Euler’s and the second order Runge–Kutta approximations. We give practical guideline on how fast should the numerical approximation step grow with respect to the sample size. However, the typical scales of the neural fibers estimated using DTI in brains are much smaller than the maximal allowed numerical approximation step for approximation of any order. It is further observed that a simple Euler’s approximation gives very similar results as obtained by using a more sophisticated numerical approximation of a higher order. In view of the increasing computational costs for numerical approximations of higher orders, the use of Euler’s approximation is well-justified for the DTI. [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: We study the large-sample properties of the penalized maximum likelihood estimator of a multivariate stochastic regression model with contemporaneously correlated data. The penalty is in terms of the square norm of some (vector) linear function of the regression coefficients. The model subsumes the so-called common transfer function model useful for extracting common signals in a panel of short time series. We show that, under mild regularity conditions, the penalized maximum likelihood estimator is consistent and asymptotically normal. The asymptotic bias of the regression coefficient estimator is also derived. [ABSTRACT FROM AUTHOR]

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]