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

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.

Nonparametric estimation of a regression curve becomes crucial when the underlying dependence structure between covariates and responses is not explicit. While existing literature has addressed single change-point estimation for regression curves, the problem of multiple change points remains unresolved. In an effort to bridge this gap, this article introduces a nonparametric estimator for multiple change points by minimizing a penalized weighted sum of squared residuals, presenting consistent results under mild conditions. Additionally, we propose a cross-validation-based procedure that possesses the advantage of being tuning-free. Our simulation results showcase the competitive performance of these new procedures when compared with state-of-the-art methods. As an illustration of their utility, we apply these procedures to a real dataset.

The additive hazards model is one of the most commonly used models for regression analysis of failure time data, and many methods have been developed for its estimation. In this article, we consider the situation where one observes informatively interval-censored data arising from case-cohort studies where covariate information is collected only for a small subcohort of study subjects. By informative or dependent censoring, we mean that the failure time of interest and the censoring mechanism may be correlated. For estimation, we will develop a sieve inverse probability weighting estimation procedure with the use of Bernstein polynomials. The resulting estimators of regression parameters are shown to be consistent and asymptotically normal. An extensive simulation study is conducted and suggests that the proposed method works well in practical situations. An example is also provided.

We present methods for estimating loss-based measures of the performance of a prediction model in a target population that differs from the source population in which the model was developed, in settings where outcome and covariate data are available from the source population but only covariate data are available on a simple random sample from the target population. Prior work adjusting for differences between the two populations has used various weighting estimators with inverse odds or density ratio weights. Here, we develop more robust estimators for the target population risk (expected loss) that can be used with data-adaptive (e.g., machine learning-based) estimation of nuisance parameters. We examine the large-sample properties of the estimators and evaluate finite-sample performance in simulations. Last, we apply the methods to data from lung cancer screening using nationally representative data from the National Health and Nutrition Examination Survey (NHANES) and extend our methods to account for the complex survey design of the NHANES.

Estimating the COVID-19 infection fatality rate, inferring the latent incidence and predicting the future epidemic evolution are critical to public health surveillance, but often challenging due to limited data availability or quality. Recently, a Bayesian framework combining time series deconvolution of deaths with a parametric Susceptible–Infectious–Recovered (SIR) model was proposed by Irons and Raftery, 2021. We assess the parameter identifiability of the model using the profile likelihood approach and simulations, when only the time series of deaths and seroprevalence survey data are available. The robustness of the model to the more complex but also more realistic Susceptible–Exposed–Infectious–Recovered (SEIR)-based epidemics is evaluated through simulations; the influence of potential biases in the serosurveys on the inference is also investigated. We use a stationary first-order autoregressive prior to account for the variability of transmission rate over time. The results suggest that the model is relatively robust to SEIR-based epidemics, especially when the reproductive number is low, given sufficient information from serosurveys or priors. However, the lack of parameter identifiability under limited data availability cannot be neglected. We apply the model to infer the COVID-19 infections in Ontario and Quebec, Canada during the Omicron era.

We consider estimation of the mean squared prediction error (MSPE) for observed best prediction (OBP) in small area estimation with count data. The OBP method has been previously developed in this context by Chen et al. (Journal of Survey Statistics and Methodology, 3, 136–161, 2015). However, estimation of the MSPE remains a challenging problem due to potential model misspecification that is considered in this setting. The latter authors proposed a bootstrap method for estimating the MSPE, whose theoretical justification is not clear. We propose to use a Prasad–Rao-type linearization method to estimate the MSPE. Unlike the traditional linearization approaches, our method is computationally oriented and easier to implement in the same regard. Theoretical properties and empirical performance of the proposed method are studied. A real-data application is considered.

Order-restricted hypothesis testing problems frequently arise in practice, including studies involving regression models for longitudinal data. These tests are known to be more powerful than tests that ignore such restrictions. In this article, we consider order-restricted tests for nonlinear mixed-effects models with measurement errors in time-dependent covariates. We propose to use a multiple imputation method to address measurement errors, since this approach allows us to use existing complete-data methods for order-restricted tests. Some theoretical results are presented. We evaluate our proposed methods via simulation studies that demonstrate they are more powerful than either a competing naive method or a two-step approach to testing hypotheses. We illustrate the use of our proposed approach by analyzing data from an HIV/AIDS study.

We propose a general mixture of Markov jump processes. The key novel feature of the proposed mixture is that the generator matrices of the Markov processes comprising the mixture are entirely unconstrained. The Markov processes are mixed with distributions that depend on the initial state of the mixture process. The maximum likelihood (ML) estimates of the mixture's parameters are obtained from continuous realizations of the mixture process and their standard errors from an explicit form of the observed Fisher information matrix, which simplifies the Louis (Journal of the Royal Statistical Society Series B, 44:226–233, 1982) general formula for the same matrix. The asymptotic properties of the ML estimators are also derived. A simulation study verifies the estimates' accuracy. The proposed mixture provides an exploratory tool for identifying the homogeneous subpopulations in a heterogeneous population. This is illustrated with an application to a medical dataset.

We study the first-order stochastic dominance (SD) test in the context of two independent random samples. We introduce several test statistics that effectively capture violations of the dominance relationship, particularly in the tail regions. Additionally, we develop a resampling procedure to compute the $��p�$-values or critical values for these tests. The proposed tests have asymptotic type I error rates for frontal configurations equal to the nominal level $��\alpha �$. Furthermore, their powers approach 1 for any fixed alternatives. Through simulation experiments, we demonstrate that our SD tests outperform the recentring test proposed by Donald and Hsu (2016) as well as the integral-type test presented by Linton et al. (2010) in various scenarios discussed in existing literature. We also employ the proposed tests to analyze changes in the distribution of household income in the United Kingdom over time. The proposed tests offer some insights into potential dominance relationships within this context.

A tolerance band for a functional response provides a region that is expected to contain a given fraction of observations from the sampled population at each point in the domain. This band is a functional analogue of the tolerance interval for a univariate response. Although the problem of constructing functional tolerance bands has been considered for a Gaussian response, it has not been investigated for non-Gaussian responses, which are common in biomedical applications. We describe a methodology for constructing tolerance bands for two non-Gaussian members of the exponential family: binomial and Poisson. The approach is to first model the data using the framework of generalized functional principal components analysis. Then, a parameter is identified in which the marginal distribution of the response is stochastically monotone. We show that the tolerance limits can be readily obtained from confidence limits for this parameter, which in turn can be computed using large-sample theory and bootstrapping. Our proposed methodology works for both dense and sparse functional data. We report the results of simulation studies designed to evaluate its performance and get recommendations for practical applications. We illustrate our proposed method using two actual biomedical studies, and also provide computer source code that implements our method.