Journal of Statistical Planning and Inference最新文献

We study the kernel estimators of the transition density of bifurcating Markov chains. Under some ergodic and regularity properties, we prove that these estimators are consistent and asymptotically normal. Next, in the numerical studies, we propose two data-driven methods to choose the bandwidth parameters. These methods, based on the so-called two bandwidths approach, are adaptation for bifurcating Markov chains of the least squares Cross-Validation and the rule of thumb method. Finally, we provide an example with real data.

The explosion of data volume and the expansion in data dimensionality have led to a critical challenge in analyzing high-dimensional matrix time series for big data-related applications. In this regard, factor models for matrix-valued high-dimensional time series provide a powerful tool, that reduces the dimensionality of the variables with low-rank structures. However, existing high-dimensional matrix factor models suffer from two limitations in complex scenarios. One is that it is difficult to make robust inferences for datasets with heavy-tailed distributions. The other is that existing models require additional parameters for fine-tuning to guarantee performance. We propose an adaptively robust high-dimensional matrix factor model based on a specified Huber loss function to tackle the challenges mentioned above. An efficient iterative algorithm is provided to consistently determine the additional parameters of our model for robust estimation. The robustness of the model estimation is greatly improved by incorporating the Huber loss. Furthermore, we theoretically investigate the proposed method and derive the convergence rates of the robust estimators to examine its performance. Simulations show that the proposed method outperforms previous models in the estimation of heavy-tailed data. A real-world data analysis on a financial portfolio dataset illustrates that the method can be used to extract useful knowledge from high-dimensional matrix time series.

Massive survival data has become common in survival analysis. In this study, a subsampling algorithm is proposed for Cox proportional hazards model with time-dependent covariates when the sample size is extraordinarily large but the computing resources are relatively limited. A subsample estimator is developed by maximizing a weighted partial likelihood, and shown to have consistency and asymptotic normality. By minimizing the asymptotic mean squared error of the subsample estimator, the optimal subsampling probabilities are formulated with explicit expression. Simulation studies show that the proposed method has satisfactory performances in approximating the full data estimator. The proposed method is applied to the corporate loan data and breast cancer data, with different censoring rates, and the outcome also confirms the practical advantages.

In linear models, omitting a covariate that is orthogonal to covariates in the model does not result in biased coefficient estimation. This generally does not hold for longitudinal data, where additional assumptions are needed to get an unbiased coefficient estimation in addition to the orthogonality between omitted longitudinal covariates and longitudinal covariates in the model. We propose methods to mitigate the omitted variable bias under weaker assumptions. A two-step estimation procedure is proposed to infer the asynchronous longitudinal covariates when such covariates are observed. For mixed synchronous and asynchronous longitudinal covariates, we get a parametric convergence rate for the coefficient estimation of the synchronous longitudinal covariates by the two-step method. Extensive simulation studies provide numerical support for the theoretical findings. We illustrate the performance of our method on a dataset from the Alzheimer’s Disease Neuroimaging Initiative study.

Maximum correntropy criterion regression (MCCR) models have been well studied within the theoretical framework of statistical learning when the scale parameters take fixed values or go to infinity. This paper studies MCCR models with tending-to-zero scale parameters. It is revealed that the optimal learning rate of MCCR models is $O\left(n^{-1}\right)$ in the asymptotic sense when the sample size $n$ goes to infinity. In the case of finite samples, the performance and robustness of MCCR, Huber and the least square regression models are compared. The applications of these three methods to real data are also demonstrated.

We investigate the validity of two resampling techniques when carrying out inference on the underlying unknown copula using a recently proposed class of smooth, possibly data-adaptive nonparametric estimators that contains empirical Bernstein copulas (and thus the empirical beta copula). Following Kiriliouk et al. (2021), the first resampling technique is based on drawing samples from the smooth estimator and can only can be used in the case of independent observations. The second technique is a smooth extension of the so-called sequential dependent multiplier bootstrap and can thus be used in a time series setting and, possibly, for change-point analysis. The two studied resampling schemes are applied to confidence interval construction and the offline detection of changes in the cross-sectional dependence of multivariate time series, respectively. Monte Carlo experiments confirm the possible advantages of such smooth inference procedures over their non-smooth counterparts. A by-product of this work is the study of the weak consistency and finite-sample performance of two classes of smooth estimators of the first-order partial derivatives of a copula which can have applications in mean and quantile regression.

Multivariate functional data are prevalent in various fields such as biology, climatology, and finance. Motivated by the World Health Data applications, in this study, we propose and examine a global test for assessing the equality of multiple mean functions in multivariate functional data. This test addresses the one-way Functional Multivariate Analysis of Variance (FMANOVA) problem, which is a fundamental issue in the analysis of multivariate functional data. While numerous analysis of variance tests have been proposed and studied for univariate functional data, only a limited number of methods have been developed for the one-way FMANOVA problem. Furthermore, our global test has the ability to handle heteroscedasticity in the unknown covariance function matrices that underlie the multivariate functional data, which is not possible with existing methods. We establish the asymptotic null distribution of the test statistic as a chi-squared-type mixture, which depends on the eigenvalues of the covariance function matrices. To approximate the null distribution, we introduce a Welch–Satterthwaite type chi-squared-approximation with consistent parameter estimation. The proposed test exhibits root-$n$ consistency, meaning it possesses nontrivial power against a local alternative. Additionally, it offers superior computational efficiency compared to several permutation-based tests. Through simulation studies and applications to the World Health Data, we highlight the advantages of our global test.

Misclassification of binary responses, if ignored, may severely bias the maximum likelihood estimators (MLEs) of regression parameters. For such data, a binary regression model incorporating non-differential classification errors is extensively used by researchers in different application contexts. We strongly caution against indiscriminate use of this model considering the fact that it suffers from a serious estimation problem due to confounding of the unknown misclassification probabilities with the regression parameters, and thus, may lead to a highly biased estimate. To overcome this problem, we propose here the use of an internal validation sample in addition to the main sample. Assuming differential classification errors, we consider MLEs of the regression parameters based on the joint likelihood of the main sample and the internal validation sample. We then develop a rigorous asymptotic theory for the joint MLEs under standard assumptions. To facilitate its easy implementation for inference, we propose a bootstrap approximation to the asymptotic distribution and prove its consistency. The results of the simulation studies suggest that even an extremely small validation sample may lead to a vastly improved inference. Finally, the methodology is illustrated with a real-life survey data.

Modern experiments typically involve a very large number of variables. Screening designs allow experimenters to identify active factors in a minimum number of trials. To save costs, only low-level factorial designs are considered for screening experiments, especially two- and three-level designs. In this article, we provide a systematic method to construct screening designs that contain both two- and three-level factors based on Hadamard matrices with the fold-over structure. The proposed designs have good performance in terms of D-optimal and A-optimal criteria, and the estimates of the main effects are unbiased by the second-order effects, making them very suitable for screening experiments. Besides, some theoretical results on D- and A-optimality are obtained as a by-product.

Missing data is a common problem in real data analysis. In this paper, a Mallows model averaging method based on kernel regression imputation is proposed for the linear regression models with responses missing at random. We prove that our method asymptotically achieves the lowest possible squared error. Compared with the existing model averaging methods, the new method does not require the use of a parameter model to characterize the missing generation mechanism. The Monte Carlo simulation and a practical application demonstrate the usefulness of the proposed method.