Canadian Journal of Statistics-Revue Canadienne De Statistique最新文献

We describe a polar coordinate transformation of the anisotropy parameters of the Matérn covariance function, which provides two benefits over the standard parameterization. First, it identifies a single point (the origin) with the special case of isotropy. Second, the posterior distribution of the transformed anisotropic angle and ratio is approximately bell-shaped and unimodal even in the case of isotropy. This has advantages for parameter inference and density estimation. We also apply a transformation to the standard deviation and range such that they are approximately orthogonal. We demonstrate this parameter transformation through two simulated and two real data sets, and conclude by considering possible extensions, such as implementing this transformation for approximate Bayesian inference methods.

Quantile-based classifiers can classify high-dimensional observations by minimizing a discrepancy of an observation to a class based on suitable quantiles of the within-class distributions, corresponding to a unique percentage for all variables. The present work extends these classifiers by introducing a way to determine potentially different optimal percentages for different variables. Furthermore, a variable-wise scale parameter is introduced. A simple greedy algorithm to estimate the parameters is proposed. Their consistency in a nonparametric setting is proved. Experiments using artificially generated and real data confirm the potential of the quantile-based classifier with variable-wise parameters.

Many common clustering methods cannot be used for clustering balanced multivariate longitudinal data in cases where the covariance of variables is a function of the time points. In this article, a copula kernel mixture model (CKMM) is proposed for clustering data of this type. The CKMM is a finite mixture model that decomposes each mixture component's joint density function into a copula and marginal distribution functions. In this decomposition, the Gaussian copula is used due to its mathematical tractability and Gaussian kernel functions are used to estimate the marginal distributions. A generalized expectation-maximization algorithm is used to estimate the model parameters. The performance of the proposed model is assessed in a simulation study and on two real datasets. The proposed model is shown to have effective performance in comparison with standard methods, such as $��K�$-means with dynamic time warping clustering, latent growth models and functional high-dimensional data clustering.

The susceptible-infected-recovered (SIR) model is the cornerstone of epidemiological models. However, this specification depends on two parameters only, which results in its lack of flexibility and explains its difficulty to replicate the volatile reproduction numbers observed in practice. We extend the standard SIR model to a semiparametric SIR model, by first introducing a functional parameter of transmission, and then making this function stochastic. This leads to a SIR model with stochastic transmission. Our model is particularly tractable. We derive its closed-form solution and use it to compute key indicators, such as the condition (and the threshold) of herd immunity and the timing of the peak. When the population size is finite and the observations are in discrete time, there is also observational uncertainty. We propose a nonlinear state-space framework under which we analyze the relative magnitudes of the observational and intrinsic uncertainties during the evolution of the epidemic. We emphasize the lack of robustness of the notion of herd immunity when the SIR model is time-discretized.

In this article, we propose a flexible Bayesian modelling framework and investigate the probabilistic weighted Dirichlet process mixture (pWDPM). The construction and properties of a probabilistic weight function are illustrated. The advantage of the pWDPM under the log-squared transformed stochastic volatility (SV) model is demonstrated. We achieve greater modelling flexibility by relaxing the distributional assumption of the error term. Bayesian inference for the pWDPM under SV and sampling procedures are provided. The performance of the pWDPM is evaluated using simulation studies and empirical results. Both computational efficiency and model accuracy are achieved through the pWDPM.

Maximin distance Latin hypercube designs have been widely used in computer experiments because they can achieve one-dimensional stratification and full-dimensional space-filling properties. In this article, we propose a new method for constructing a class of Latin hypercube designs that can accommodate many columns. We show that the resulting designs are asymptotically optimal under the maximin distance criterion, and enjoy a large proportion of low-dimensional stratification properties that strong orthogonal arrays should have. In addition, the proposed method can be used to construct a class of asymptotically optimal sliced maximin distance Latin hypercube designs. These designs are well suited to computer experiments due to their good space-filling properties.

In this article, we use e-values in the context of multiple hypothesis testing, assuming that the base tests produce independent, or sequential, e-values. Our simulation and empirical studies, as well as theoretical considerations, suggest that, under this assumption, our new algorithms are superior to the known algorithms using independent p-values and to our recent algorithms designed for e-values without the assumption of independence.

Large observational databases are often subject to missing data. As such, methods for causal inference must simultaneously handle confounding and missingness; surprisingly little work has been done at this intersection. Motivated by this, we propose an efficient and robust estimator of the causal average treatment effect from cohort studies when confounders are missing at random. The approach is based on a novel factorization of the likelihood that, unlike alternative methods, facilitates flexible modelling of nuisance functions (e.g., with state-of-the-art machine learning methods) while maintaining nominal convergence rates of the final estimators. Simulated data, derived from an electronic health record-based study of the long-term effects of bariatric surgery on weight outcomes, verify the robustness properties of the proposed estimators in finite samples. Our approach may serve as a theoretical benchmark against which ad hoc methods may be assessed.

We propose a parametric kernel mode–based regression built on the mode value, which provides robust and efficient estimators for datasets containing outliers or heavy-tailed distributions. To address the challenges posed by massive datasets, we integrate this regression method with distributed statistical learning techniques, which greatly reduces the required amount of primary memory and simultaneously accommodates heterogeneity in the estimation process. By approximating the local kernel objective function with a least squares format, we are able to preserve compact statistics for each worker machine, facilitating the reconstruction of estimates for the entire dataset with minimal asymptotic approximation error. Additionally, we explore shrinkage estimation through local quadratic approximation, showcasing that the resulting estimator possesses the oracle property through an adaptive LASSO approach. The finite-sample performance of the developed method is illustrated using simulations and real data analysis.

We develop a general semisupervised framework for statistical inference in the two-sample comparison setting. Although the supervised Mann–Whitney statistic outperforms many estimators in the two-sample problem for nonnormally distributed responses, it is excessively inefficient because it ignores large amounts of unlabelled information. To borrow strength from unlabelled data, we propose a class of efficient and adaptive estimators that use two-step semiparametric imputation. The probabilistic index model is adopted primarily to achieve dimension reduction for multivariate covariates, and a follow-up reweighting step balances the contributions of labelled and unlabelled data. The asymptotic properties of our estimator are derived with variance comparison through a phase diagram. Efficiency theory shows our estimators achieve the semiparametric variance lower bound if the probabilistic index model is correctly specified, and are more efficient than their supervised counterpart when the model is not degenerate. The asymptotic variance is estimated through a two-step perturbation resampling procedure. To gauge the finite sample performance, we conducted extensive simulation studies which verify the adaptive nature of our methods with respect to model misspecification. To illustrate the merits of our proposed method, we analyze a dataset concerning homelessness in Los Angeles.