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We study the existence, strong consistency and asymptotic normality of estimators obtained from estimating functions, that are p -dimensional martingale transforms. The problem is motivated by the analysis of evolutionary clustered data, with distributions belonging to the exponential family, and which may also vary in terms of other component series. Within a quasi-likelihood approach, we construct estimating equations, which accommodate different forms of dependency among the components of the response vector and establish multivariate extensions of results on linear and generalized linear models, with stochastic covariates. Furthermore, we characterize estimating functions which are asymptotically optimal, in that they lead to confidence regions for the regression parameters which are of minimum size, asymptotically. Results from a simulation study and an application to a real dataset are included. [ABSTRACT FROM AUTHOR]

We present a framework for estimating average and conditional effects of a discrete treatment variable on a continuous outcome variable, conditioning on categorical and continuous covariates. Using the new approach, termed theEffectLiteRapproach, researchers can consider conditional treatment effects given values of all covariates in the analysis and various aggregates of these conditional treatment effects such as average effects, effects on the treated, or aggregated conditional effects given values of a subset of covariates. Building on structural equation modeling, key advantages of the new approach are (1) It allows for latent covariates and outcome variables; (2) it permits (higher order) interactions between the treatment variable and categorical and (latent) continuous covariates; and (3) covariates can be treated as stochastic or fixed. The approach is illustrated by an example, and open source software EffectLiteR is provided, which makes a detailed analysis of effects conveniently accessible for applied researchers. [ABSTRACT FROM PUBLISHER]

In this paper we consider a Linear Regression Model with a design matrix that fits the periodic structure of a time series. As a consequence, the residuals are very often autocorrelated. The main problem is that residual autocorrelation does not necessarily entail error autocorrelation. To analyse the effects of selecting different formulations to accommodate the autocorrelation in the residuals, we consider two seemingly different ways to deal with this problem: the Linear Regression Model with the error terms following an Autoregressive Stationary Process and the Partial Adjustment Model. We study the equivalence between the two formulations. We go over the problem of estimating the parameters and, especially, of making inferences in this framework. After parameter estimation, we analyse the adequacy of the models. We demonstrate that the issue of selecting the most appropriate model to capture the autocorrelation in the residuals is, in this context, a kind of an artefact since the main results concerning the fitted values and forecasting features are the same. These modelling procedures are applied to the Portuguese coastal upwelling data and we compare the estimated models. [ABSTRACT FROM AUTHOR]

Abstract: Our main interest is on-line parameter estimation of infinite AR models with exponentially decaying coefficients. The practical importance of the problem follows from the fact that the class of such models includes (but not limited to) all causal invertible ARMA() models. On-line parameter estimation means that the length of the observed data sample is not known a priori and may indefinitely increase. Hence, the parameter estimates should be refined upon arrival of every new observation. So use of the maximum likelihood (ML) method is not feasible due to the high computational burden, and recursive estimation procedures are preferable. We usually assume that the true underlying model of the observed process is a finite AR, MA or a mixed ARMA equation. However, this assumption can be rarely justified in practice. A common approach is to approximate the true model by finite AR models whose orders are chosen by information criterions such as AIC, BIC, PLS and whose parameters may be estimated by the ordinary least-squares method, the Yule–Walker method and others. In this paper we investigate a limiting case for approximating by finite AR models, i.e. an AR model of infinite order. We focus on the strong consistency properties of the regularized least-squares estimates. The regularizer may be interpreted as the smoothing operator applied to the number of the AR coefficients being estimated, and constitutes a link to the model selection criterions. The rate of a.s. convergence of the infinite LS estimates is established. In addition, a complimentary result on the convergence of almost semi-martingales, which is also of independent interest, is presented. The proposed identification procedure is evaluated by numerical examples. [Copyright &y& Elsevier]