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

General or case II interval-censored data are commonly encountered in practice. We develop methods for model-checking and goodness-of-fit testing for the additive hazards model with case II interval-censored data. We propose test statistics based on the supremum of the stochastic processes derived from the cumulative sum of martingale-based residuals over time and covariates. We approximate the distribution of the stochastic process via a simulation technique to conduct a class of graphical and numerical techniques for various purposes of model-fitting evaluations. Simulation studies are conducted to assess the finite-sample performance of the proposed method. A real dataset from an AIDS observational study is analyzed for illustration.

Heterogeneity exists in populations, and people may benefit differently from the same treatments or services. Correctly identifying subgroups corresponding to outcomes such as treatment response plays an important role in data-based decision making. As few discussions exist on subgroup analysis with measurement error, we propose a new estimation method to consider these two components simultaneously under the linear regression model. First, we develop an objective function based on unbiased estimating equations with two repeated measurements and a concave penalty on pairwise differences between coefficients. The proposed method can identify subgroups and estimate coefficients simultaneously when considering measurement error. Second, we derive an algorithm based on the alternating direction method of multipliers algorithm and demonstrate its convergence. Third, we prove that the proposed estimators are consistent and asymptotically normal. The performance and asymptotic properties of the proposed method are evaluated through simulation studies. Finally, we apply our method to data from the Lifestyle Education for Activity and Nutrition study and identify two subgroups, of which one has a significant treatment effect.

Data collected from distributed sources or sites commonly have different distributions or contaminated observations. Active learning procedures allow us to assess data when recruiting new data into model building. Thus, combining several active learning procedures together is a promising idea, even when the collected data set is contaminated. Here, we study how to conduct and integrate several adaptive sequential procedures at a time to produce a valid result via several machines or a parallel-computing framework. To avoid distraction by complicated modelling processes, we use confidence set estimation for linear models to illustrate the proposed method and discuss the approach's statistical properties. We then evaluate its performance using both synthetic and real data. We have implemented our method using Python and made it available through Github at https://github.com/zhuojianc/dsep.

In multigroup data settings with small within-group sample sizes, standard $��F�$-tests of group-specific linear hypotheses can have low power, particularly if the within-group sample sizes are not large relative to the number of explanatory variables. To remedy this situation, in this article we derive alternative test statistics based on information sharing across groups. Each group-specific test has potentially much larger power than the standard $��F�$-test, while still exactly maintaining a target type I error rate if the null hypothesis for the group is true. The proposed test for a given group uses a statistic that has optimal marginal power under a prior distribution derived from the data of the other groups. This statistic approaches the usual $��F�$-statistic as the prior distribution becomes more diffuse, but approaches a limiting “cone” test statistic as the prior distribution becomes extremely concentrated. We compare the power and $��P�$-values of the cone test to that of the $��F�$-test in some high-dimensional asymptotic scenarios. An analysis of educational outcome data is provided, demonstrating empirically that the proposed test is more powerful than the $��F�$-test.

We propose a new model averaging approach to investigate segment regression models with multiple threshold variables and multiple structural breaks. We first fit a series of models, each with a single threshold variable and multiple breaks over its domain, using a two-stage change point detection method. Then these models are combined together to produce a weighted ensemble through a frequentist model averaging approach. Consequently, our segment regression model averaging (SRMA) method may help identify complicated subgroups in a heterogeneous study population. A crucial step is to determine the optimal weights in the model averaging, and we follow the familiar non-concave penalty estimation approach. We provide theoretical support for SRMA by establishing the consistency of individual fitted models and estimated weights. Numerical studies are carried out to assess the performance in low- and high-dimensional settings, and comparisons are made between our proposed method and a wide range of existing alternative subgroup estimation methods. Two real economic data examples are analyzed to illustrate our methodology.

As a popular tool for nonlinear models, additive models work efficiently with nonparametric estimation. However, naively applying the existing regularization method can result in misleading outcomes because of the basis sparsity in each variable. In this article, we consider variable selection in additive models via a combination of variable selection and basis selection, yielding a joint selection of variables and basis functions. A novel penalty function is proposed for basis selection to address the hierarchical structure as well as the sparsity assumption. Under some mild conditions, we establish theoretical properties including the support recovery consistency. We also derive the necessary and sufficient conditions for the estimator and develop an efficient algorithm based on it. Our new methodology and results are supported by simulation and real data examples.

We begin by showing that the standard repeated-sampling interpretation of the variance of a parameter estimate in a finite-dimensional parametric model is ambiguous and open to misinterpretation. Three operational interpretations are given, all numerically different in general and all compatible with repeated sampling from the same population with a fixed parameter. One of these is compatible with the standard large-sample calculation based on the inverse Fisher information. The others are not. One interpretation coincides with what Fisher appears to have had in mind in his 1943 derivation of the log-series model for species abundances. The different interpretations help to resolve an apparent contradiction between the Fisherian variance and the inverse-information variance obtained from the Ewens model.

Low-frequency historical data, high-frequency historical data, and option data are three primary sources that can be used to forecast an underlying security's volatility. In this article, we propose an explicit model integrating the three information sources. Instead of directly using option price data, we extract option-implied volatility from option data and estimate its dynamics. We provide joint quasimaximum likelihood estimators for the parameters and establish their asymptotic properties. Real data examples demonstrate that the proposed model has better out-of-sample volatility forecasting performance than other popular volatility models.

Although log-likelihood is widely used in model selection, the log-likelihood ratio has had few applications in this area. We develop a log-likelihood ratio based method for selecting regression models by focusing on the set of models deemed plausible by the likelihood ratio test. We show that when the sample size is large and the significance level of the test is small, there is a high probability that the smallest model in this set is the true model; thus, we select this smallest model. The significance level of the test serves as a tuning parameter of this method. We consider three levels of this parameter in a simulation study and compare this method with the Akaike information criterion (AIC) and Bayesian information criterion (BIC) to demonstrate its excellent accuracy and adaptability to different sample sizes. This method is a frequentist alternative and a strong competitor to AIC and BIC for selecting regression models.

The pioneering work on parameter orthogonalization by Cox and Reid is presented as an inducement of abstract population-level sparsity. This is taken as a unifying theme for this article, in which sparsity-inducing parameterizations or data transformations are sought. Three recent examples are framed in this light: sparse parameterizations of covariance models, the construction of factorizable transformations for the elimination of nuisance parameters, and inference in high-dimensional regression. Strategies for the problem of exact or approximate sparsity inducement appear to be context-specific and may entail, for instance, solving one or more partial differential equations or specifying a parameterized path through transformation or parameterization space. Open problems are emphasized.