An active interaction in a main effect plan may cause biased estimation of the parameters in an analysis of variance (ANOVA) model. A fractional factorial design (FFD) with higher order resolution can resolve the alias problem, however, with a considerable number of runs. Alternatively, a search design (SD), the so‐called main effect plus k plan (MEP.k ), with much less number of runs than FFD, is

In this paper, the forward selected first‐order Markov mixture (FSFOMM) is proposed for modelling heterogeneous categorical sequences with secondary components capable of detecting outlying sequences within each cluster. Such sequences are assumed to have different transition probabilities in certain states. The model provides an attractive and flexible tool for diagnostics of unusual behaviours and

In this paper we consider the low rank matrix completion problem under general bases, which intends to recover a structured matrix via a linear combination of a pre‐specified bases. Existing works focus primarily on orthonormal bases, however, it is often necessary to adopt non‐orthonormal bases in some real‐applications. Thus, there is a great need to address the feasibility of some popular estimators

Penalized splines are popular for nonparametric regression. We establish the minimax rate optimality of penalized splines for uniform convergence, thus improving the existing rate in the literature. The result is applicable to several types of penalized splines that are commonly used and holds under mild conditions on the design points.

The number of latent factors, in factor analysis, is typically unknown and motivated by a rich literature on priors distributions, which progressively penalize the number of factors in infinite factor models. Adaptive Gibbs samplers that truncate the infinite factor models are typically used for posterior inference. In this paper, we introduce a novel strategy to adaptively truncate the number of factors

Social distancing measures have been imposed across the US in order to stem the spread of COVID‐19. We quantify the reduction in doubling rate, by state, that is associated with this intervention. Using the earlier of K‐12 school closures and restaurant closures, by state, to define the start of the intervention, and considering daily confirmed cases through April 23rd, 2020, we find that social distancing

Multivariate random fields allow to simultaneously model multiple spatially indexed variables, playing a fundamental role in geophysical, environmental and climate disciplines. This paper introduces the concept of cross‐dimple for bivariate isotropic random fields on spheres, and proposes an approach to build parametric models that possess this attribute. Our findings are based on the spectral representation

With growing interest to use black‐box machine learning for complex data with many feature variables, it is critical to obtain a prediction model that only depends on a small set of features to maximize generalizability. Therefore, feature selection remains to be an important and challenging problem in modern applications. Most of existing methods for feature selection are based on either parametric

Deep learning has benefited almost every aspect of modern big data applications. Yet its statistical properties still remain largely unexplored. It is commonly believed nowadays that deep neural networks (DNNs) benefit from representational learning. To gain some statistical insights into this, we design a simple simulation setting where we generate data from some latent subspace structure with each

In recent years, there have been a large number of proposed approaches to detecting changes in mean. A natural question for an analyst is which method is most appropriate for their applications. Answering this question is difficult because current empirical studies often give conflicting conclusions. This paper aims to show the similarities and differences between different changepoint methods. We

This paper presents a new way to compute simplicial and Tukey data depths using Open Multi‐Processing parallelization, which makes it practical to compute point depths for tens of thousands of points. The definition of point depth is the order statistic depth of a single point, here in two dimensions. Using the point depths, the regional depth characteristics of the dataset as a whole can be explored

Covariance estimation is essential yet underdeveloped for analysing multivariate functional data. We propose a fast covariance estimation method for multivariate sparse functional data using bivariate penalized splines. The tensor‐product B‐spline formulation of the proposed method enables a simple spectral decomposition of the associated covariance operator and explicit expressions of the resulting

Tensor completion is among the most important tasks in tensor data analysis, which aims to fill the missing entries of a partially observed tensor. In many real applications, non‐Gaussian data such as binary or count data are frequently collected. Thus it is inappropriate to assume that observations are normally distributed, and formulate tensor completion with least squares based approach. In this

As one of the most rapidly developing artificial intelligence techniques, deep learning has been applied in various machine learning tasks, and has received great attention in data science and statistics. Regardless of the complex model structure, the deep neural networks can be viewed as non‐linear and non‐parametric generalization of existing statistical models. In this review, we introduce several

In this paper, we develop a stochastic Holling type II model from the commonly used deterministic Holling type II model by introducing Brownian motion as a stochastic perturbation, which can naturally account for the external environmental effects on a multispecies community. We study the existence and uniqueness of positive solutions to the stochastic model, and we establish sufficient conditions

Over the last few decades, various copula‐based methods have been proposed in the literature for testing independence among several random variables. But most of these tests are applicable only when all random variables are continuous. Only recently, a copula‐based test of independence has been proposed, which also works for random variables having arbitrary probability distributions. But like most

FastLORS is a software package that implements a new algorithm to solve sparse multivariate regression for expression quantitative trait loci (eQTLs) mapping. FastLORS solves the same optimization problem as LORS, an existing popular algorithm. The optimization problem is solved through inexact block coordinate descent with updates by proximal gradient steps, which reduces the computational cost compared

In many practical applications, spatial data are often collected at areal levels (i.e., block data), and the inferences and predictions about the variable at points or blocks different from those at which it has been observed typically depend on integrals of the underlying continuous spatial process. In this paper, we describe a method based on Fourier transforms by which multiple integrals of covariance

Bivariate life distributions used to model negative dependence typically possess certain limitations; in particular, the correlation coefficient takes values in a restricted subrange of [ − 1 , 0 ] . We construct a new bivariate life distribution to remedy this. Properties of the proposed distribution are studied. It is shown that the distribution satisfies most of the popular notions of negative dependence

The recurrent event data are encountered in many longitudinal studies. In many situations, there are a nonsusceptible fraction of subjects without any recurrent events, manifesting heterogeneity in risk among study participants. The frailty models have been widely used to account for this heterogeneity that does not rely on self‐reported survival data. Frailty is commonly modelled with a gamma distribution

Bayesian models use posterior predictive distributions to quantify the uncertainty of their predictions. Similarly, the point predictions of neural networks and other machine learning algorithms may be converted to predictive distributions by various bootstrap methods. The predictive performance of each algorithm can then be assessed by quantifying the performance of its predictive distribution. Previous

A major impact of globalization has been the information flow across the financial markets rendering them vulnerable to financial contagion. Research has focused on network analysis techniques to understand the extent and nature of such information flow. It is now an established fact that a stock market crash in one country can have a serious impact on other markets across the globe. It follows that

Variable screening is of fundamental importance in linear regression models when the number of predictors far exceeds the number of observations. Multicollinearity is a common phenomenon in high‐dimensional settings, in which two or more predictor variables are highly correlated, leading to the notorious difficulty for high‐dimensional variable screening. Sure independence screening (SIS) procedure

In this article, we provide the general expressions for the classic two‐player gambler's ruin problem when the decision process relies on the occurrence of m successive and nonoverlapping events. The rationale of the proposed strategy is motivated by its exhibition in various sports events. For example, in tennis, a player is required to win two successive serves to win a game after achieving deuce

Convolutional neural networks (CNNs) have exhibited superior performance in various types of classification and prediction tasks, but their interpretability remains to be low despite years of research effort. It is crucial to improve the ability of existing models to interpret deep neural networks from both theoretical and practical perspectives and to develop new neural network models with interpretable

With the development of data‐monitoring techniques in various fields of science, multivariate functional data are often observed. Consequently, an increasing number of methods have appeared to extend the general summary statistics of multivariate functional data. However, trajectory functional data, as an important subtype, have not been studied very well. This article proposes two informative exploratory

The way cell differentiate from bone marrow to peripheral blood level plays a crucial role in understanding and treating rare diseases and more common tumours. The main goal of this paper is to introduce a flexible statistical framework able to describe the cell differentiation process and to reconstruct a dependence structure along different levels of differentiation. We use next generation sequencing

In this paper, we present a class of functional linear regression models with varying coefficients of a functional response on one or multiple functional predictors and scalar predictors. In particular, the approach can accommodate densely or sparsely sampled functional responses as well as multiple scalar and functional predictors. It also allows for the combination of continuous or categorical covariates

Principal components regression (PCR) is a well‐known method to achieve dimension reduction and often improved prediction over the ordinary least squares. The conventional PCR retains the principal components with large variance and discards those with smaller variance. This operation can easily lead to poor prediction when the response variable is related to principal components with small variance

The log Gaussian Cox process (LGCP) is a frequently applied method for modeling point pattern data. The normalization constant of the LGCP likelihood involves an integral over a latent field. That integral is computationally expensive, making it troublesome to perform inference with standard methods. The so‐called stochastic partial differential equation–integrated nested Laplace approximation (SPDE‐INLA)

In multiple change‐point analysis, one of the major challenges is the determination of the number of change points, which is usually cast as a model selection problem. However, for model selection methods based on the Schwarz information criterion (SIC), it is typical that different penalization terms are required for different change‐point problems and the optimal penalization magnitude usually varies

Finite mixture models are widely used for cluster analysis, including clustering matrix data. Nowadays, high‐dimensional matrix observations arise in a variety of fields. It is known that irrelevant variables can severely affect the performance of clustering procedures. Therefore, it is important to develop algorithms capable of excluding irrelevant variables and focusing on informative attributes

In longitudinal studies in which a medical device is used to monitor outcome repeatedly and frequently on the same patients over a prespecified duration of time, two clustering goals can arise. One goal is to assess the degree of heterogeneity among patient profiles. A second yet equally important goal unique to such studies is to determine frequency and duration of monitoring sufficient to identify

Zellner's g ‐prior is one of the most popular choices for model selection in Bayesian linear regression. Despite its popularity, the asymptotic theory for high‐dimensional variable selection is not yet fully developed. In this paper, we investigate the asymptotic behaviour of Bayesian model selection under the g ‐prior as the model dimension grows with the sample size. We find a simple and intuitive

The occurrence of undetected outliers severely disrupts model building procedures and produces unreliable results. This topic has been widely addressed in the statistical literature. However, little attention has been paid to determine how large an outlier has to be for correct detection of both time and magnitude to safely take place. This issue has been the object of research mainly in geodesy. In

In functional data analysis, some regions of the domain of the functions can be of more interest than others owing to the quality of measurement, relative scale of the domain, or simply some external reason (e.g. interest of stakeholders). Weighting the domain is of interest particularly with probability density functions (PDFs), as derived from distributional data, which often aggregate measurements

Patient mortality after listing for a solid organ transplant is a relevant, patient‐centric metric, but risk factors for patient mortality after listing present severe non‐proportional hazards. We propose piecewise exponential models (PEMs) with time‐varying effects to account for the non‐proportional hazards, and we use the LASSO to minimize the risk of overfitting. We consider two parameterizations

In a wide range of applications, standard regression techniques are hard to apply because the responses may consist of a continuous part but augmented with a discrete number of additional response categories with probability greater than zero. Previous methods often assume that the process of both parts can be treated structurally independent given covariates which facilitates estimation considerably

Nonparametric estimation of the survival function for either incident or prevalent cohort failure time data, exclusively, has been well studied in the literature; the Kaplan‐Meier (KM) estimator is routinely used for right‐censored incident cohort failure time data, whereas a modified form of the KM estimator, sometimes referred to as the Tsai–Jewell–Wang (TJW) estimator, is the default estimator used

We compare two recent methods that combine conformal inference with quantile regression to produce locally adaptive and marginally valid prediction intervals under sample exchangeability (Romano, Patterson, & Candès, 2019, arXiv:1905.03222; Kivaranovic, Johnson, & Leeb, 2019, arXiv:1905.10634). First, we prove that these two approaches are asymptotically efficient in large samples, under some additional

No abstract is available for this article.

This paper establishes the asymptotic consistency of the loss‐calibrated variational Bayes (LCVB) method. LCVB is a method for approximately computing Bayesian posterior approximations in a “loss aware” manner. This methodology is also highly relevant in general data‐driven decision‐making contexts. Here, we establish the asymptotic consistency of both the loss‐ calibrated approximate posterior and

Evaluation of accuracy of diagnostic tests is frequently undertaken under nonignorable (NI) verification bias. Here, we discuss an approach, based on a mean score equation, aimed to estimate the volume under the receiver operating characteristic (ROC) surface of a diagnostic test under NI verification bias. The proposed approach rests on a parametric regression model for the verification process, which

We show the identification of the joint distribution of the potential outcomes under various parametric specifications. The key factor of the identification is the nonnormality of the distribution of the observed variables, with which we can obtain information of higher order moments that are not determined only by mean and variance. In particular, we show the identification of the joint distribution

Unit‐level models for survey data offer many advantages over their area‐level counterparts, such as potential for more precise estimates and a natural benchmarking property. However, two main challenges occur in this context: accounting for an informative survey design and handling non‐Gaussian data types. The pseudo‐likelihood approach is one solution to the former, and conjugate multivariate distribution

Graphical models have been used in many scientific fields for exploration of conditional independence relationships for a large set of random variables. Although a variety of methods have been proposed in the literature for estimating graphical models with different types of data, none of them is applicable for jointly estimating multiple mixed graphical models. To tackle this problem, we propose a

The Student‐ t distribution has proved to be a useful alternative to the traditional normal distribution, mainly to deal with heavy tails and when robust estimation is desired. We consider the multivariate Student‐ t regression model and derive the nonnull asymptotic expansions (under a sequence of Pitman alternatives) of the distribution functions of the likelihood ratio, Wald, Rao score, and gradient

As a new strategy for treatment which takes individual heterogeneity into consideration, personalized medicine is of growing interest. Discovering individualized treatment rules (ITRs) for patients who have heterogeneous responses to treatment is one of the important areas in developing personalized medicine. As more and more information per individual is being collected in clinical studies and not

Risk classification and survival probability prediction are two major goals in survival data analysis since they play an important role in patients' risk stratification, long-term diagnosis, and treatment selection. In this article, we propose a new model-free machine learning framework for risk classification and survival probability prediction based on weighted support vector machines. The new procedure

The classical methods of multivariate analysis are based on the eigenvalues of one or two sample covariance matrices. In many applications of these methods, for example to high dimensional data, it is natural to consider alternative hypotheses which are a low rank departure from the null hypothesis. For rank one alternatives, this note provides a representation for the joint eigenvalue density in terms

The pervasive use of prevalent cohort studies on disease duration increasingly calls for an appropriate methodology to account for the biases that invariably accompany samples formed by such data. It is well-known, for example, that subjects with shorter lifetime are less likely to be present in such studies. Moreover, certain covariate values could be preferentially selected into the sample, being

F-18-Fluorodeoxyglucose positron emission tomography (FDG-PET) has been used to evaluate the metabolic response of metastatic brain tumors to treatment by comparing their tumor glucose metabolism before and after treatment. The standard analysis based on regions-of-interest has the advantage of simplicity. However, it is by definition restricted to those regions and is subject to observer variability

We propose Bayesian methods for Gaussian graphical models that lead to sparse and adaptively shrunk estimators of the precision (inverse covariance) matrix. Our methods are based on lasso-type regularization priors leading to parsimonious parameterization of the precision matrix, which is essential in several applications involving learning relationships among the variables. In this context, we introduce

We consider analysis of sparsely sampled multilevel functional data, where the basic observational unit is a function and data have a natural hierarchy of basic units. An example is when functions are recorded at multiple visits for each subject. Multilevel functional principal component analysis (MFPCA; Di et al. 2009) was proposed for such data when functions are densely recorded. Here we consider

Quantile regression provides a more thorough view of the effect of covariates on a response. Nonparametric quantile regression has become a viable alternative to avoid restrictive parametric assumption. The problem of variable selection for quantile regression is challenging, since important variables can influence various quantiles in different ways. We tackle the problem via regularization in the

Clustered data analysis is characterized by the need to describe both systematic variation in a mean model and cluster-dependent random variation in an association model. Marginalized multilevel models embrace the robustness and interpretations of a marginal mean model, while retaining the likelihood inference capabilities and flexible dependence structures of a conditional association model. Although

We propose a functional random effect time-varying coefficient model to establish the dynamic relationship between the response and predictor variables in longitudinal data. This model allows us not only to interpret time-varying covariate effects, but also to depict random effects via time-varying profiles that are characterized by functional principal components. We develop the functional profiling-backfitting

It is well-known that Gaussian modeling of functional Magnetic Resonance Imaging (fMRI) magnitude time-course data, which are truly Rice-distributed, constitutes an approximation, especially at low signal-to-noise ratios (SNRs). Based on this fact, previous work has argued that Rice-based activation tests show superior performance over their Gaussian-based counterparts at low SNRs and should be preferred

Modern research data, where a large number of functional predictors is collected on few subjects are becoming increasingly common. In this paper we propose a variable selection technique, when the predictors are functional and the response is scalar. Our approach is based on adopting a generalized functional linear model framework and using a penalized likelihood method that simultaneously controls

The Mantel and Knox space-time clustering statistics are popular tools to establish transmissibility of a disease and detect outbreaks. The most commonly used null distributional approximations may provide poor fits, and researchers often resort to direct sampling from the permutation distribution. However, the exact first four moments for these statistics are available, and Pearson distributional