Search

Abstract: Finding optimal designs for experiments for non-linear models and dependent data is a challenging task. We show how the problem simplifies when the search is restricted to designs that are minimally supported; that is, the number of distinct runs (treatments) is equal to the number of unknown parameters, p, in the model. Under this restriction, the problem of finding a locally or pseudo-Bayesian D-optimal design decomposes into two simpler problems that are more widely studied. The first is that of finding a minimum-support D-optimal design d 1 with p runs for the corresponding model for the mean but assuming independent observations. The second problem is finding a D-optimal block design for assigning the treatments in d 1 to the experimental units. We find and assess optimal minimum-support designs for three examples, each assuming a mean model from a different member of the exponential family: binomial, Poisson and normal. In each case, the efficiencies of the designs are compared to the optimal design where the restriction on the number of distinct support points is relaxed. The optimal minimum-support designs are found to often perform satisfactorily under both local and Bayesian D-optimality for concentrated prior distributions. The results are also relatively insensitive to the assumed degree of dependence in the data. [Copyright &y& Elsevier]

Abstract: An extension of some standard likelihood based procedures to heteroscedastic nonlinear regression models under scale mixtures of skew-normal (SMSN) distributions is developed. This novel class of models provides a useful generalization of the heteroscedastic symmetrical nonlinear regression models (), since the random term distributions cover both symmetric as well as asymmetric and heavy-tailed distributions such as skew-t, skew-slash, skew-contaminated normal, among others. A simple EM-type algorithm for iteratively computing maximum likelihood estimates of the parameters is presented and the observed information matrix is derived analytically. In order to examine the performance of the proposed methods, some simulation studies are presented to show the robust aspect of this flexible class against outlying and influential observations and that the maximum likelihood estimates based on the EM-type algorithm do provide good asymptotic properties. Furthermore, local influence measures and the one-step approximations of the estimates in the case-deletion model are obtained. Finally, an illustration of the methodology is given considering a data set previously analyzed under the homoscedastic skew-t nonlinear regression model. [Copyright &y& Elsevier]

Abstract: In this paper we discuss bias-corrected estimators for the regression and the dispersion parameters in an extended class of dispersion models (). This class extends the regular dispersion models by letting the dispersion parameter vary throughout the observations, and contains the dispersion models as particular case. General formulae for the bias are obtained explicitly in dispersion models with dispersion covariates, which generalize previous results obtained by , , , and . The practical use of the formulae is that we can derive closed-form expressions for the biases of the maximum likelihood estimators of the regression and dispersion parameters when the information matrix has a closed-form. Various expressions for the biases are given for special models. The formulae have advantages for numerical purposes because they require only a supplementary weighted linear regression. We also compare these bias-corrected estimators with two different estimators which are also bias-free to order that are based on bootstrap methods. These estimators are compared by simulation. [Copyright &y& Elsevier]

Abstract: A partially time-varying coefficient time series model is introduced to characterize the nonlinearity and trending phenomenon. To estimate the regression parameter and the nonlinear coefficient function, the profile least squares approach is applied with the help of local linear approximation. The asymptotic distributions of the proposed estimators are established under mild conditions. Meanwhile, the generalized likelihood ratio test is studied and the test statistics are demonstrated to follow asymptotic under the null hypothesis. Furthermore, some extensions of the proposed model are discussed and several numerical examples are provided to illustrate the finite sample behavior of the proposed methods. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we consider the problem of estimation of semi-linear regression models. Using invariance arguments, Bhowmik and King [2007. Maximal invariant likelihood based testing of semi-linear models. Statist. Papers 48, 357–383] derived the probability density function of the maximal invariant statistic for the non-linear component of these models. Using this density function as a likelihood function allows us to estimate these models in a two-step process. First the non-linear component parameters are estimated by maximising the maximal invariant likelihood function. Then the non-linear component, with the parameter values replaced by estimates, is treated as a regressor and ordinary least squares is used to estimate the remaining parameters. We report the results of a simulation study conducted to compare the accuracy of this approach with full maximum likelihood and maximum profile-marginal likelihood estimation. We find maximising the maximal invariant likelihood function typically results in less biased and lower variance estimates than those from full maximum likelihood. [Copyright &y& Elsevier]

The paper introduces DT-optimum designs that provide a specified balance between model discrimination and parameter estimation. An equivalence theorem is presented for the case of two models and extended to an arbitrary number of models and of combinations of parameters. A numerical example shows the properties of the procedure. The relationship with other design procedures for parameter estimation and model discrimination is discussed. [Copyright &y& Elsevier]