Coming Attractions of The Canadian Journal of Statistics: 2018 Issue 2
In the second issue of 2018, The Canadian Journal of Statistics presents nine papers covering a number of topics including the analysis of censored data, model robustness and assessment, prediction, optimal designs, and the goodness-of-fit of stochastic processes.
The first two articles consider censored data from different perspectives. For multiple samples with censored observations, CAI and CHEN develop a semiparametric approach for the estimation of population quantiles and distribution functions. By pooling information across multiple censored samples through a semiparametric density ratio model, they develop an empirical likelihood approach to achieve high efficiency without making restrictive model assumptions.
Focusing on the modelling of censored data, WANG and WANG examine a transformation regression model where both the transformation function and the error distribution function are left unspecified. Such a model is more flexible than traditional semiparametric models, which require one of these to be specified. The authors estimate the transformation function using the kernel estimation method and estimate the regression parameters using weighted estimation equations.
To generalize classical quantile linear regression models, GIJBELS, IBRAHIM and VERHASSELT consider quantile varying coefficient models (VCMs), which allow the coefficients to depend on other variables. To allow for heteroscedasticity, they explore various variance structures for the VCM errors. In addition to presenting estimation procedures, they develop likelihood-ratio-based tests for choosing between two variability functions with heteroscedastic error structure.
The fourth paper concerns the precision matrix that is often used to describe the association information for multiple variables. Since the performance of such a matrix is quite sensitive to the presence of outliers, CHUN, LEE, KIM and OH propose a robust precision-matrix estimation method via weighted median regression with regularization. The approach is shown to be consistent under various distributional assumptions, including multivariate t distributions and contaminated Gaussian distributions. The development focuses on the situation where either the dimension p of the variables is fixed or p >> n where n is the sample size.
Frequentist model averaging has often been used to incorporate model uncertainty. In particular, the model averaged tail area (MATA) confidence interval is useful. With a large number of linear regression models KABAILA constructs MATA confidence intervals and provides an easily computed upper bound on the minimum coverage probability of these intervals. This bound provides evidence against the use of a model weight based on the Bayesian information criterion.
Typically, diagnostic tests are assessed over multiple studies. Receiver operating characteristic (ROC) curves can be used to evaluate the properties of a diagnostic test based on the distribution of a variable in the healthy and diseased populations. Using the minimum averaged mean squared error weights, PLANTE and DÉBORDÈS infer the ROC curve of a diagnostic test based on raw data obtained from multiple studies. The estimates are consistent, and Monte Carlo simulations show good finite-sample performance.
In some applications, the covariate values in the prediction model are different from those in the model for the observed data. Referring to this as covariate shift, KAWAKUBO, SUGASAWA and KUBOKAWA discuss a criterion for selecting the explanatory variables for the fixed effects in linear mixed models. To demonstrate the usefulness of the criterion, they explore covariate shift in small-area estimation based on conditional Akaike information.
In the eighth article, ZHAI and FANG explore locally optimal designs for nonlinear dose-response models with binary outcomes. Applying the theory of Tchebycheff Systems, the authors show that the locally D-, A- and c-optimal designs for three binary dose-response models are minimally supported in finite, closed design intervals. Construction methods and examples are provided for these locally optimal designs.
In the final paper, ABDELRAZEQ, IVANOFF and KULIK propose goodness-of-fit tests for Levy-driven Ornstein–Uhlenbeck (or CAR(1)) processes that have been used to model stochastic volatility. The authors develop a general formula to recover the unobserved driving process from a continuously observed CAR(1). When the CAR(1) process is observed at discrete times, the driving process is approximated, and approximated increments are used to test the hypothesis that the CAR(1) belongs to a specified class of Levy processes.
Enjoy the new issue!
Grace Y. Yi, CJS Editor