Statistical analysis of point processes often assumes that the underlying process is isotropic in the sense that its distribution is invariant under rotation. For point processes on ℝ2, some tests based on the K‐ and nearest neighbour orientation functions have been proposed to check such an assumption. However, anisotropy and directional analysis need proper caution when dealing with point processes

In this paper, we develop a group learning approach to analyze the underlying heterogeneity structure of shot selection among professional basketball players in the NBA. We propose a mixture of finite mixtures (MFM) model to capture the heterogeneity of shot selection among different players based on Log Gaussian Cox process (LGCP). Our proposed method can simultaneously estimate the number of groups

The identification of outliers is mainly based on unannotated data and therefore constitutes an unsupervised problem. The lack of a label leads to numerous challenges that do not occur or only occur to a lesser extent when using annotated data and supervised methods. In this paper, we focus on two of these challenges: the selection of hyperparameters and the selection of informative features. To this

In this paper we propose a linear variable screening method for computer experiments when the number of input variables is larger than the number of runs. This method uses a linear model to model the nonlinear data, and screens the important variables by existing screening methods for linear models. When the underlying simulator is nearly sparse, we prove that the linear screening method is asymptotically

The success of deep learning neural network models often relies on the accessibility of a large number of labelled training data. In many health care settings, however, only a small number of accurately labelled data are available while unlabelled data are abundant. Further, input variables such as clinical events in the medical settings are usually of longitudinal nature, which poses additional challenges

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 prespecified bases. Existing works focus primarily on orthonormal bases; however, it is often necessary to adopt nonorthonormal bases in some real applications. Thus, there is a great need to address the feasibility of some popular estimators

We propose the notion of sub‐Weibull distributions, which are characterised by tails lighter than (or equally light as) the right tail of a Weibull distribution. This novel class generalises the sub‐Gaussian and sub‐Exponential families to potentially heavier‐tailed distributions. Sub‐Weibull distributions are parameterized by a positive tail index θ and reduce to sub‐Gaussian distributions for θ =1/2

We study the nested model averaging method on the solution path for a high‐dimensional linear regression problem. In particular, we propose to combine model averaging with regularized estimators (e.g., {lasso, elastic net, and SLOPE}) on the solution path for high‐dimensional linear regression. In simulation studies, we first conduct a systematic investigation on the impact of predictor ordering on

We propose a visual test of goodness of fit for families of elliptically symmetric distributions based on a test statistic derived from scale‐scale plots. The scale‐scale plots are constructed based on the volume functionals of the central rank regions. The test is motivated through the multivariate normal distributions, and extended to a test of elliptical symmetry. We derive the asymptotic properties

For high dimensional data, the standard empirical estimator for the covariance matrix is very poor, and thus many methods have been proposed to more accurately estimate the covariance structure of high dimensional data. In this article, we consider estimation under the assumption of sparsity, but regularize with respect to the individual false positive rate for incorrectly including a matrix entry

Expectile is a generalization of the expected value in probability and statistics. In finance and risk management, the expectile is considered to be an important risk measure due to its connection with gain‐loss ratio and its coherent and elicitable properties. Linear multiple expectile regression was proposed in 1987 for estimating the conditional expectiles of a response given a set of covariates

The non‐asymptotic tail bounds of random variables play crucial roles in probability, statistics, and machine learning. Despite much success in developing upper bounds on tail probability in literature, the lower bounds on tail probabilities are relatively fewer. In this paper, we introduce systematic and user‐friendly schemes for developing non‐asymptotic lower bounds of tail probabilities. In addition

When multiple measures are collected repeatedly over time, redundancy typically exists among responses. The envelope method was recently proposed to reduce the dimension of responses without loss of information in regression with multivariate responses. It can gain substantial efficiency over the standard least squares estimator. In this paper, we generalize the envelope method to mixed effects models

Consider semi‐supervised learning for classification, where both labeled and unlabeled data are available for training. The goal is to exploit both datasets to achieve higher prediction accuracy than just using labeled data alone. We develop a semi‐supervised logistic learning method based on exponential tilt mixture models, by extending a statistical equivalence between logistic regression and exponential

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, deep neural networks can be viewed as a nonlinear and nonparametric generalization of existing statistical models. In this review, we introduce several popular

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

Multivariate count data are commonly encountered through high‐throughput sequencing technologies in bioinformatics, text mining, or in sports analytics. Although the Poisson distribution seems a natural fit to these count data, its multivariate extension is computationally expensive. In most cases mutual independence among the variables is assumed, however this fails to take into account the correlation

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 approaches. In this

Covariance operators are fundamental concepts and modeling tools for many functional data analysis methods, such as functional principal component analysis. However, the empirical (or estimated) covariance operator becomes too costly to compute when the functional dataset gets big. This paper studies a randomized algorithm for covariance operator estimation. The algorithm works by sampling and rescaling

Since the mid‐2000s, there has been a resurrection of interest in modern modifications of fiducial inference. To date, the main computational tool to extract a generalized fiducial distribution is Markov chain Monte Carlo (MCMC). We propose an alternative way of computing a generalized fiducial distribution that could be used in complex situations. In particular, to overcome the difficulty when the

We discuss an approach of robust fitting on nonlinear regression models, both in a frequentist and a Bayesian approach, which can be employed to model and predict the contagion dynamics of COVID‐19 in Italy. The focus is on the analysis of epidemic data using robust dose‐response curves, but the functionality is applicable to arbitrary nonlinear regression models.

Despite being a well‐known problem, feature weighting and feature selection is a major predicament for clustering. Most of the algorithms, which provide weighting or selection of features, require the number of clusters to be known in advance. On the other hand, the existing automatic clustering procedures that can determine the number of clusters are computationally expensive and often do not make

Sparseness of the regression coefficient vector is often a desirable property, since, among other benefits, sparseness improves interpretability. In practice, many true regression coefficients might be negligibly small, but non‐zero, which we refer to as quasi‐sparseness. Spike‐and‐slab priors can be tuned to ignore very small regression coefficients, and, as a consequence provide a trade‐off between

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 the existing methods for feature selection are based on either parametric

In this work, we construct a lack‐of‐fit test for testing parametric single‐index quantile regression models. We apply the kernel smoothing technique for the multivariate nonparametric estimation involved in this task. To avoid the “curse of dimensionality” in multivariate nonparametric estimation and to fully utilize the information contained in the model, we employ a sufficient dimension reduction

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 able

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

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

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 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)

Social distancing measures have been imposed across the United States in order to stem the spread of COVID‐19. We quantify the reduction in the 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 23, 2020, we find that

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 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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