Parametric Nonlinear Regression with Endogenous Switching

Based on the insightful work of Olsen (1980 Olsen , R. J. ( 1980 ). A least squares correction for selectivity bias . Econometrica 48 : 1815 – 1820 .[Crossref], [Web of Science ®] , [Google Scholar]) for the linear context, a generic and unifying framework is developed that affords a simple extension of the classical method of Heckman (1974 Heckman , J. ( 1974 ). Shadow prices, market wages, and labor supply . Econometrica 42 : 679 – 694 .[Crossref], [Web of Science ®] , [Google Scholar], 1976 Heckman , J. ( 1976 ). The common structure of statistical models of truncation sample selection and limited dependent variables and a simple estimator for such models . Annals of Economic and Social Measurement 5 : 475 – 492 . [Google Scholar], 1978 Heckman , J. ( 1978 ). Dummy endogenous variables in a simultaneous equation system . Econometrica 46 : 931 – 959 .[Crossref], [Web of Science ®] , [Google Scholar], 1979 Heckman , J. ( 1979 ). Sample selection bias as a specification error . Econometrica 47 : 153 – 161 .[Crossref], [Web of Science ®] , [Google Scholar]) to a broad class of nonlinear regression models involving endogenous switching and its two most common incarnations, endogenous sample selection and endogenous treatment effects. The approach should be appealing to applied researchers for three reasons. First, econometric applications involving endogenous switching abound. Secondly, the approach requires neither linearity of the regression function nor full parametric specification of the model. It can, in fact, be applied under the minimal parametric assumptions—i.e., specification of only the conditional means of the outcome and switching variables. Finally, it is amenable to relatively straightforward estimation methods. Examples of applications of the method are discussed.     

Parsimonious Estimation of the Covariance Matrix in Multinomial Probit Models

This article presents a Bayesian analysis of a multinomial probit model by building on previous work that specified priors on identified parameters. The main contribution of our article is to propose a prior on the covariance matrix of the latent utilities that permits elements of the inverse of the covariance matrix to be identically zero. This allows a parsimonious representation of the covariance matrix when such parsimony exists. The methodology is applied to both simulated and real data, and its ability to obtain more efficient estimators of the covariance matrix and regression coefficients is assessed using simulated data.     

Bayesian Approaches to Nonparametric Estimation of Densities on the Unit Interval

This paper investigates nonparametric estimation of density on [0, 1]. The kernel estimator of density on [0, 1] has been found to be sensitive to both bandwidth and kernel. This paper proposes a unified Bayesian framework for choosing both the bandwidth and kernel function. In a simulation study, the Bayesian bandwidth estimator performed better than others, and kernel estimators were sensitive to the choice of the kernel and the shapes of the population densities on [0, 1]. The simulation and empirical results demonstrate that the methods proposed in this paper can improve the way the probability densities on [0, 1] are presently estimated.     

Lag Length Selection for Unit Root Tests in the Presence of Nonstationary Volatility

A number of recent papers have focused on the problem of testing for a unit root in the case where the driving shocks may be unconditionally heteroskedastic. These papers have, however, taken the lag length in the unit root test regression to be a deterministic function of the sample size, rather than data-determined, the latter being standard empirical practice. We investigate the finite sample impact of unconditional heteroskedasticity on conventional data-dependent lag selection methods in augmented Dickey–Fuller type regressions and propose new lag selection criteria which allow for unconditional heteroskedasticity. Standard lag selection methods are shown to have a tendency to over-fit the lag order under heteroskedasticity, resulting in significant power losses in the (wild bootstrap implementation of the) augmented Dickey–Fuller tests under the alternative. The proposed new lag selection criteria are shown to avoid this problem yet deliver unit root tests with almost identical finite sample properties as the corresponding tests based on conventional lag selection when the shocks are homoskedastic.     

MODELING THE LIFETIME OF LONGITUDINAL ELEMENTS

In the study of the stochastic behaviour of the lifetime of an element as a function of its length, it is often observed that the failure time (or lifetime) decreases as the length increases. In probabilistic terms, such an idea can be expressed as follows. Let T be the lifetime of a specimen of length x, so the survival function, which denotes the probability that an element of length x survives till time t, will be given by S_T (t, x) = P(T > t/α(x), where α(x) is a monotonically decreasing function. In particular, it is often assumed that T has a Weibull distribution. In this paper, we propose a generalization of this Weibull model by assuming that the distribution of T is Generalized gamma (GG). Since the GG model contains the Weibull, Gamma and Lognormal models as special and limiting cases, a GG regression model is an appropriate tool for describing the size effect on the lifetime and for selecting among the embedded models. Maximum likelihood estimates are obtained for the GG regression model with α(x) = cx^b . As a special case this provide an alternative to the usual approach to estimation for the GG distribution which involves reparametrization. Related parametric inference issues are addressed and illustrated using two experimental data sets. Some discussion of censored data is also provided.     

The Gaussian Mixture Dynamic Conditional Correlation Model: Parameter Estimation,Value at Risk Calculation,and Portfolio Selection

A multivariate generalized autoregressive conditional heteroscedasticity model with dynamic conditional correlations is proposed, in which the individual conditional volatilities follow exponential generalized autoregressive conditional heteroscedasticity models and the standardized innovations follow a mixture of Gaussian distributions. Inference on the model parameters and prediction of future volatilities are addressed by both maximum likelihood and Bayesian estimation methods. Estimation of the Value at Risk of a given portfolio and selection of optimal portfolios under the proposed specification are addressed. The good performance of the proposed methodology is illustrated via Monte Carlo experiments and the analysis of the daily closing prices of the Dow Jones and NASDAQ indexes.     

An alternative approach to variable selection for prediction

A procedure for selecting a subset of predictor variables in regression analysis is suggested. The procedure is so designed that it leads to the selection of a subset of variables having an adequate degree of informativeness with a directly specified confidence coefficient. Some examples are considered to illustrate the application of the procedure.     

A plug-in technique in nonparametric regression with dependence

The problem addressed is that of smoothing parameter selection in kernel nonparametric regression in the fixed design regression model with dependent noise. An asymptotic expression of the optimum bandwidth parameter has been obtained in recent studies, where this takes the form h = C ₀ n ^?1/5. This paper proposes to use a plug-in methodology, in order to obtain an optimum estimation of the bandwidth parameter, through preliminary estimation of the unknown value of C ₀.     

Extension of two-sided test to multiple treatment trials

In a two-treatment trial, a two-sided test is often used to reach a conclusion, Usually we are interested in doing a two-sided test because of no prior preference between the two treatments and we want a three-decision framework. When a standard control is just as good as the new experimental treatment (which has the same toxicity and cost), then we will accept both treatments. Only when the standard control is clearly worse or better than the new experimental treatment, then we choose only one treatment. In this paper, we extend the concept of a two-sided test to the multiple treatment trial where three or more treatments are involved. The procedure turns out to be a subset selection procedure; however, the theoretical framework and performance requirement are different from the existing subset selection procedures. Two procedures (exclusion or inclusion) are developed here for the case of normal data with equal known variance. If the sample size is large, they can be applied with unknown variance and with the binomial data or survival data with random censoring.     

Goodness of fit for thei ordered categories discrete uniform distribution

Goodness of fit for thei ordered categories discrete uniform distribution can be carried out using Pearson's X² _pstatistic and its components. Applications of this technique are considered and comparisons made with recently suggested empirical uniform distribution