Semiparametric quantile regression estimation in dynamic models with partially varying coefficients

We study quantile regression estimation for dynamic models with partially varying coefficients so that the values of some coefficients may be functions of informative covariates. Estimation of both parametric and nonparametric functional coefficients are proposed. In particular, we propose a three stage semiparametric procedure. Both consistency and asymptotic normality of the proposed estimators are derived. We demonstrate that the parametric estimators are root-n$n$ consistent and the estimation of the functional coefficients is oracle. In addition, efficiency of parameter estimation is discussed and a simple efficient estimator is proposed. A simple and easily implemented test for the hypothesis of a varying-coefficient is proposed. A Monte Carlo experiment is conducted to evaluate the performance of the proposed estimators.     

Reparameterized inverse gamma regression models with varying precision

In this article, we propose a mean linear regression model where the response variable is inverse gamma distributed using a new parameterization of this distribution that is indexed by mean and precision parameters. The main advantage of our new parametrization is the straightforward interpretation of the regression coefficients in terms of the expectation of the positive response variable, as usual in the context of generalized linear models. The variance function of the proposed model has a quadratic form. The inverse gamma distribution is a member of the exponential family of distributions and has some distributions commonly used for parametric models in survival analysis as special cases. We compare the proposed model to several alternatives and illustrate its advantages and usefulness. With a generalized linear model approach that takes advantage of exponential family properties, we discuss model estimation (by maximum likelihood), black further inferential quantities and diagnostic tools. A Monte Carlo experiment is conducted to evaluate the performances of these estimators in finite samples with a discussion of the obtained results. A real application using minerals data set collected by Department of Mines of the University of Atacama, Chile, is considered to demonstrate the practical potential of the proposed model.     

Forecasting inflation using time‐varying Bayesian model averaging

This paper presents a Bayesian model averaging regression framework for forecasting US inflation, in which the set of predictors included in the model is automatically selected from a large pool of potential predictors and the set of regressors is allowed to change over time. Using real‐time data on the 1960–2011 period, this model is applied to forecast personal consumption expenditures and gross domestic product deflator inflation. The results of this forecasting exercise show that, although it is not able to beat a simple random‐walk model in terms of point forecasts, it does produce superior density forecasts compared with a range of alternative forecasting models. Moreover, a sensitivity analysis shows that the forecasting results are relatively insensitive to prior choices and the forecasting performance is not affected by the inclusion of a very large set of potential predictors.     

Statistical inference on seemingly unrelated non‐parametric regression models with serially correlated errors

This article is concerned with the inference on seemingly unrelated non‐parametric regression models with serially correlated errors. Based on an initial estimator of the mean functions, we first construct an efficient estimator of the autoregressive parameters of the errors. Then, by applying an undersmoothing technique, and taking both of the contemporaneous correlation among equations and serial correlation into account, we propose an efficient two‐stage local polynomial estimation for the unknown mean functions. It is shown that the resulting estimator has the same bias as those estimators which neglect the contemporaneous and/or serial correlation and smaller asymptotic variance. The asymptotic normality of the resulting estimator is also established. In addition, we develop a wild block bootstrap test for the goodness‐of‐fit of models. The finite sample performance of our procedures is investigated in a simulation study whose results come out very supportive, and a real data set is analysed to illustrate the usefulness of our procedures.     

Additive hazards regression of failure time data with covariate measurement errors

This paper discusses regression analysis of failure time data under the additive hazards model, with covariates subject to measurement errors. In particular, we consider the situation where there may exist only repeated measurements or observations on the covariates with measurement errors, and for which there does not exist any method for inference. A nonparametric-correction approach is proposed for inference about regression parameters and the baseline cumulative hazards function. Both asymptotic and finite sample properties of the proposed estimators are established and the approach is applied to an AIDS clinical trial that motivated this study.     

Diagnostics analysis for log‐Birnbaum–Saunders regression models with censored data

This article develops influence diagnostics for log‐Birnbaum–Saunders (LBS) regression models with censored data based on case‐deletion model (CDM). The one‐step approximations of the estimates in CDM are given and case‐deletion measures are obtained. Meanwhile, it is shown that CDM is equivalent to mean shift outlier model (MSOM) in LBS regression models and an outlier test is presented based on MSOM. Furthermore, we discuss a score test for homogeneity of shape parameter in LBS regression models. Two numerical examples are given to illustrate our methodology and the properties of score test statistic are investigated through Monte Carlo simulations under different censoring percentages.     

Estimation and testing of crossing‐points in fixed design regression

Many phenomena in the life sciences can be analyzed by using a fixed design regression model with a regression function m that exhibits a crossing‐point in the following sense: the regression function runs below or above its mean level, respectively, according as the input variable lies to the left or to the right of that crossing‐point, or vice versa. We propose a non‐parametric estimator and show weak and strong consistency as long as the crossing‐point is unique. It is defined as maximizing point arg max of a certain marked empirical process. For testing the hypothesis H₀ that the regression function m actually is constant (no crossing‐point), a decision rule is designed for the specific alternative H₁ that m possesses a crossing‐point. The pertaining test‐statistic is the ratio max/argmax of the maximum value and the maximizing point of the marked empirical process. Under the hypothesis the ratio converges in distribution to the corresponding ratio of a reflected Brownian bridge, for which we derive the distribution function. The test is consistent on the whole alternative and superior to the corresponding Kolmogorov–Smirnov test, which is based only on the maximal value max. Some practical examples of possible applications are given where a certain study about dental phobia is discussed in more detail.     

Bayesian regression with B‐splines under combinations of shape constraints and smoothness properties

In this paper, we approach the problem of shape constrained regression from a Bayesian perspective. A B‐splines basis is used to model the regression function. The smoothness of the regression function is controlled by the order of the B‐splines, and the shape is controlled by the shape of an associated control polygon. Controlling the shape of the control polygon reduces to some inequality constraints on the spline coefficients. Our approach enables us to take into account combinations of shape constraints and to localize each shape constraint on a given interval. The performance of our method is investigated through a simulation study. Applications to a real data sets in food industry and Global Warming are provided.     

Investigating the impact of excess zeros on hurdle‐generalized Poisson regression model with right censored count data

Typically, a Poisson model is assumed for count data. In many cases, there are many zeros in the dependent variable, thus the mean is not equal to the variance value of the dependent variable. Therefore, Poisson model is not suitable anymore for this kind of data because of too many zeros. Thus, we suggest using a hurdle‐generalized Poisson regression model. Furthermore, the response variable in such cases is censored for some values because of some big values. A censored hurdle‐generalized Poisson regression model is introduced on count data with many zeros in this paper. The estimation of regression parameters using the maximum likelihood method is discussed and the goodness‐of‐fit for the regression model is examined. An example and a simulation will be used to illustrate the effects of right censoring on the parameter estimation and their standard errors.