Vector random fields with compactly supported covariance matrix functions

The objective of this paper is to construct covariance matrix functions whose entries are compactly supported, and to use them as building blocks to formulate other covariance matrix functions for second-order vector stochastic processes or random fields. In terms of the scale mixture of compactly supported covariance matrix functions, we derive a class of second-order vector stochastic processes on the real line whose direct and cross covariance functions are of Pólya type. Then some second-order vector random fields in R^d${\mathbb{R}}^d$ whose direct and cross covariance functions are compactly supported are constructed by using a convolution approach and a mixture approach.     

Statistical inference for partially time-varying coefficient errors-in-variables models

This paper studies the partially time-varying coefficient models where some covariates are measured with additive errors. In order to overcome the bias of the usual profile least squares estimation when measurement errors are ignored, we propose a modified profile least squares estimator of the regression parameter and construct estimators of the nonlinear coefficient function and error variance. The proposed three estimators are proved to be asymptotically normal under mild conditions. In addition, we introduce the profile likelihood ratio test and then demonstrate that it follows an asymptotically χ²${\chi }^2$ distribution under the null hypothesis. Finite sample behavior of the estimators is investigated via simulations too.     

Model-based confidence bands for survival functions

This paper focuses on a novel method of developing one-sample confidence bands for survival functions from right censored data. The approach is model-based, relying on a parametric model for the conditional expectation of the censoring indicator given the observed minimum, and derives its strength from easy access to a good-fitting model among a plethora of choices available for binary response data. The substantive methodological contribution is in exploiting a semiparametric estimator of the survival function to produce improved simultaneous confidence bands. To obtain critical values for computing the confidence bands, a two-stage bootstrap approach that combines the classical bootstrap with the more recent model-based regeneration of censoring indicators is proposed and a justification of its asymptotic validity is also provided. Several different confidence bands are studied using the proposed approach. Numerical studies, including robustness of the proposed bands to misspecification, are carried out to check efficacy. The method is illustrated using two lung cancer data sets.     

Bayesian inference with misspecified models

This article reviews Bayesian inference from the perspective that the designated model is misspecified. This misspecification has implications in interpretation of objects, such as the prior distribution, which has been the cause of recent questioning of the appropriateness of Bayesian inference in this scenario. The main focus of this article is to establish the suitability of applying the Bayes update to a misspecified model, and relies on representation theorems for sequences of symmetric distributions; the identification of parameter values of interest; and the construction of sequences of distributions which act as the guesses as to where the next observation is coming from. A conclusion is that a clear identification of the fundamental starting point for the Bayesian is described.     

Generalized estimating equations for mixtures with varying concentrations

A finite mixture model is considered in which the mixing probabilities vary from observation to observation. A parametric model is assumed for one mixture component distribution, while the others are nonparametric nuisance parameters. Generalized estimating equations (GEE) are proposed for the semi‐parametric estimation. Asymptotic normality of the GEE estimates is demonstrated and the lower bound for their dispersion (asymptotic covariance) matrix is derived. An adaptive technique is developed to derive estimates with nearly optimal small dispersion. An application to the sociological analysis of voting results is discussed. The Canadian Journal of Statistics 41: 217–236; 2013 © 2013 Statistical Society of Canada     

A likelihood ratio test for goodness‐of‐fit of recessive and dominant models for case–control studies

Testing goodness‐of‐fit of commonly used genetic models is of critical importance in many applications including association studies and testing for departure from Hardy–Weinberg equilibrium. Case–control design has become widely used in population genetics and genetic epidemiology, thus it is of interest to develop powerful goodness‐of‐fit tests for genetic models using case–control data. This paper develops a likelihood ratio test (LRT) for testing recessive and dominant models for case–control studies. The LRT statistic has a closed‐form formula with a simple $\chi^{2}(1)$ null asymptotic distribution, thus its implementation is easy even for genome‐wide association studies. Moreover, it has the same power and optimality as when the disease prevalence is known in the population. The Canadian Journal of Statistics 41: 341–352; 2013 © 2013 Statistical Society of Canada     

A Markov regime‐switching model for crude‐oil markets: Comparison of composite likelihood and full likelihood

We use the two‐state Markov regime‐switching model to explain the behaviour of the WTI crude‐oil spot prices from January 1986 to February 2012. We investigated the use of methods based on the composite likelihood and the full likelihood. We found that the composite‐likelihood approach can better capture the general structural changes in world oil prices. The two‐state Markov regime‐switching model based on the composite‐likelihood approach closely depicts the cycles of the two postulated states: fall and rise. These two states persist for on average 8 and 15 months, which matches the observed cycles during the period. According to the fitted model, drops in oil prices are more volatile than rises. We believe that this information can be useful for financial officers working in related areas. The model based on the full‐likelihood approach was less satisfactory. We attribute its failure to the fact that the two‐state Markov regime‐switching model is too rigid and overly simplistic. In comparison, the composite likelihood requires only that the model correctly specifies the joint distribution of two adjacent price changes. Thus, model violations in other areas do not invalidate the results. The Canadian Journal of Statistics 41: 353–367; 2013 © 2013 Statistical Society of Canada     

Fast and Accurate Inference for the Smoothing Parameter in Semiparametric Models

A fast and accurate method of confidence interval construction for the smoothing parameter in penalised spline and partially linear models is proposed. The method is akin to a parametric percentile bootstrap where Monte Carlo simulation is replaced by saddlepoint approximation, and can therefore be viewed as an approximate bootstrap. It is applicable in a quite general setting, requiring only that the underlying estimator be the root of an estimating equation that is a quadratic form in normal random variables. This is the case under a variety of optimality criteria such as those commonly denoted by maximum likelihood (ML), restricted ML (REML), generalized cross validation (GCV) and Akaike's information criteria (AIC). Simulation studies reveal that under the ML and REML criteria, the method delivers a near‐exact performance with computational speeds that are an order of magnitude faster than existing exact methods, and two orders of magnitude faster than a classical bootstrap. Perhaps most importantly, the proposed method also offers a computationally feasible alternative when no known exact or asymptotic methods exist, e.g. GCV and AIC. An application is illustrated by applying the methodology to well‐known fossil data. Giving a range of plausible smoothed values in this instance can help answer questions about the statistical significance of apparent features in the data.     

Forecasting Multivariate Road Traffic Flows Using Bayesian Dynamic Graphical Models,Splines and Other Traffic Variables

Traffic flow data are routinely collected for many networks worldwide. These invariably large data sets can be used as part of a traffic management system, for which good traffic flow forecasting models are crucial. The linear multiregression dynamic model (LMDM) has been shown to be promising for forecasting flows, accommodating multivariate flow time series, while being a computationally simple model to use. While statistical flow forecasting models usually base their forecasts on flow data alone, data for other traffic variables are also routinely collected. This paper shows how cubic splines can be used to incorporate extra variables into the LMDM in order to enhance flow forecasts. Cubic splines are also introduced into the LMDM to parsimoniously accommodate the daily cycle exhibited by traffic flows. The proposed methodology allows the LMDM to provide more accurate forecasts when forecasting flows in a real high‐dimensional traffic data set. The resulting extended LMDM can deal with some important traffic modelling issues not usually considered in flow forecasting models. Additionally, the model can be implemented in a real‐time environment, a crucial requirement for traffic management systems designed to support decisions and actions to alleviate congestion and keep traffic flowing.     

Distance-based approach in univariate longitudinal data analysis

In this paper, we propose a methodology to analyze longitudinal data through distances between pairs of observations (or individuals) with regard to the explanatory variables used to fit continuous response variables. Restricted maximum-likelihood and generalized least squares are used to estimate the parameters in the model. We applied this new approach to study the effect of gender and exposure on the deviant behavior variable with respect to tolerance for a group of youths studied over a period of 5 years. Were performed simulations where we compared our distance-based method with classic longitudinal analysis with both AR(1) and compound symmetry correlation structures. We compared them under Akaike and Bayesian information criterions, and the relative efficiency of the generalized variance of the errors of each model. We found small gains in the proposed model fit with regard to the classical methodology, particularly in small samples, regardless of variance, correlation, autocorrelation structure and number of time measurements.