To avoid the effect of distributional misspecification in the model-based regression, we propose an essentially nonparametric symmetric error distribution and construct a so-called doubly smoothed (DS) likelihood function by applying the same amount of smoothing to both the model and given data. To compute the DS maximum likelihood estimator based on the DS likelihood, we propose an approximated DS

In this paper, we study the model detection and estimation for varying coefficient panel data models with fixed effects. We first propose a data transformation approach to eliminate fixed effects. Then, using the basis function approximations and the group SCAD penalty, we develop a combined penalization procedure to select the significant covariates, detect the true structure of the model, i.e., identify

A class of random graph models is considered, combining features of exponential-family models and latent structure models, with the goal of retaining the strengths of both of them while reducing the weaknesses of each of them. An open problem is how to estimate such models from large networks. A novel approach to large-scale estimation is proposed, taking advantage of the local structure of such models

Dynamic networks are commonly used to model relational data that are observed over time. Statistical models for such data should capture both the temporal variation of the relational system as well as the structural dependencies within each network. As a consequence, effectively making inference on dynamic networks is a computationally challenging task, and many models are intractable even for moderately

The stochastic block model (SBM) is a popular model for capturing community structure and interaction within a network. Network data with non-Boolean edge weights is becoming commonplace; however, existing analysis methods convert such data to a binary representation to apply the SBM, leading to a loss of information. A generalisation of the SBM is considered, which allows edge weights to be modelled

Two matrix-variate distributions, both elliptical heavy-tailed generalization of the matrix-variate normal distribution, are introduced. They belong to the normal scale mixture family, and are respectively obtained by choosing a convenient shifted exponential or uniform as mixing distribution. Moreover, they have a closed-form for the probability density function that is characterized by only one additional

Given a large sample of observations from an unknown univariate continuous distribution, it is often of interest to empirically estimate the global mode of the underlying density. Applications include samples obtained by Monte Carlo methods with independent observations, or Markov Chain Monte Carlo methods with weakly dependent samples from the underlying stationary density. In either case, often the

The Pietra ratio (Pietra index) is also known as the Robin Hood index or Schutz coefficient (Ricci–Schutz index). It is a measure of statistical heterogeneity in positive random variables. In this paper, we propose the jackknife empirical likelihood (JEL), the adjusted JEL, the extended JEL, and the balanced adjusted JEL method, for interval estimation of the Pietra ratio. We compare the performance

Modelling genetic diversity needs an underlying genealogy model. To choose a fitting model based on genetic data, one can perform model selection between classes of genealogical trees, e.g. Kingman’s coalescent with exponential growth or multiple merger coalescents. Such selection can be based on many different statistics measuring genetic diversity. A random forest based Approximate Bayesian Computation

The hidden Markov framework is adapted to construct a compelling model for simulation of sub-daily rainfall, capable of capturing important characteristics of sub-daily rainfall well, including: long dry periods or droughts; seasonal and temporal variation in occurrence and intensity; and propensity for extreme values. These adaptations include both clone states and temporally non-homogeneous state

Spatial dynamic microsimulations allow for the multivariate analysis of complex systems with geographic segmentation. A synthetic replica of the system is stochastically projected into future periods using micro-level transition probabilities. These should accurately represent the dynamics of the system to allow for reliable simulation outcomes. In practice, transition probabilities are unknown and

The recovery properties of nonconvex regularized M-estimators are analysed, under the general sparsity assumption on the true parameter. In the statistical aspect, the recovery bound for any stationary point of the nonconvex regularized M-estimator is established under some regularity conditions. In the computational aspect, the proximal gradient method is used to solve the nonconvex optimization problem

A wide class of Bayesian nonparametric priors leads to the representation of the distribution of the observable variables as a mixture density with an infinite number of components. Such a representation induces a clustering structure in the data. However, due to label switching, cluster identification is not straightforward a posteriori and some post-processing of the MCMC output is usually required

Model-based clustering approaches generally assume that the observations to be clustered are generated from a mixture of distributions, each component of the mixture corresponding to a particular parametric distribution. Most commonly, the underlying distribution is assumed to be normal, which is inadequate for many situations, for example when skewness or multimodality is present within the components

Sufficient dimension reduction that replaces original predictors with their low- dimensional linear combinations without loss of information is a critical tool in modern statistics and has gained considerable research momentum in the past decades since the two pioneers sliced inverse regression and principal Hessian directions. The classical sufficient dimension reduction methods do not handle sparse

Semi-functional linear regression models postulate a linear relationship between a scalar response and a functional covariate, and also include a non-parametric component involving a univariate explanatory variable. It is of practical importance to obtain estimators for these models that are robust against high-leverage outliers, which are generally difficult to identify and may cause serious damage

A novel test statistic is proposed to identify important predictors for the conditional mean function in regression. The stepwise regression algorithm based on the proposed test statistic guarantees variable selection consistency without specifying the functional form of the conditional mean. When the predictors are ultrahigh dimensional, a model-free screening procedure is introduced to precede the

A prescription is presented for a new and practical correlation coefficient, ϕK, based on several refinements to Pearson’s hypothesis test of independence of two variables. The combined features of ϕK form an advantage over existing coefficients. Primarily, it works consistently between categorical, ordinal and interval variables, in essence by treating each variable as categorical, and can therefore

The classification of normally distributed data in a high-dimensional setting when variables are more numerous than observations is considered. Under the assumption that the inverse covariance matrices (the precision matrices) are the same over all groups, the method of the linear discriminant analysis (LDA) is adapted by including a sparse estimate of these matrices. Furthermore, a variable selection

Partially varying coefficient model (PVCM) provides a useful class of tools for modeling complex data by incorporating a combination of constant and time-varying covariate effects. One natural question is that how to decide which covariates correspond to constant coefficients and which correspond to time-dependent coefficient functions. To handle this two-type structure selection problem on PVCM, those

The Delaunay triangulation learner (DTL), which is a new piecewise linear learner, is proposed for both regression and classification tasks. Based on the data samples in a p-dimensional feature space, the Delaunay triangulation algorithm provides a unique way of triangulating the space. The triangulation separates the convex hull of the samples into a series of disjoint p-simplices, where the samples

The functional principal component analysis is widely used to explore major sources of variation in a sample of random curves. These major sources of variation are represented by functional principal components (FPCs). The FPCs from the conventional FPCA method are often nonzero in the whole domain, and are hard to interpret in practice. The main focus is to estimate functional principal components

Various approaches for spectral analysis based on regularly spaced data have already been well-established, but the spectral inference based on irregularly spaced data are still essentially limited. Under the Bayesian framework, a detouring approach for spectral estimation is proposed for analyzing irregularly spaced data. The detouring process is accomplished by three steps: (1) normalizing the data

Functional variables are often used as predictors in regression problems. A commonly used parametric approach, called scalar-on-function regression, uses the L2 inner product to map functional predictors into scalar responses. This method can perform poorly when predictor functions contain undesired phase variability, causing phases to have disproportionately large influence on the response variable

In order to learn the complex features of large spatio-temporal data, models with a large number of parameters are often required. However, inference is often infeasible due to the computational and memory costs of maximum likelihood estimation (MLE). The class of marginally parameterized (MP) models is introduced, where estimation can be performed efficiently with a sequence of marginal likelihood

Quasi-Monte Carlo (QMC) methods using quasi-random sequences, as opposed to pseudo-random samples, are proposed for use in the joint modelling of time-to-event and multivariate longitudinal data. The QMC integration framework extends the Monte Carlo Expectation Maximisation approaches that are commonly adopted, namely using ordinary and antithetic variates. The motivation of QMC integration is to increase

The single index model is one of the most popular semiparametric models in applied quantitative sciences. This paper studies a single index model with unknown jumps (SIMJ) that occur in the link function. An adaptive semiparametric estimation procedure is proposed for estimating the index coefficient and link function. The asymptotic normality of the resulting estimators for both the parametric and

Factor copula models have been recently proposed for describing the joint distribution of a large number of variables in terms of a few common latent factors. A Bayesian procedure is employed in order to make fast inferences for multi-factor and structured factor copulas. To deal with the high dimensional structure, a Variational Inference (VI) algorithm is applied to estimate different specifications

The complexity of X-chromosome inactivation arouses the X-linked genetic association being overlooked in most of the genetic studies, especially for genetic association analysis on time to event outcomes. To fill this gap, we propose novel methods to analyze the X-linked genetic association for competing risk failure time data based on a subdistribution hazard function. Specifically, we consider two

In principal component analysis (PCA), principal components are identified by maximizing the component score variance around the mean. However, a practitioner might be interested in capturing the variation in the tail rather than the center of a distribution to, for example, identify the major pollutants from air pollution data. To address this problem, we introduce a new method called Huber-type principal

A two-part latent variable model is proposed to analyze semicontinuous data in the presence of latent variables. The proposed model comprises two major components. The first component is a structural equation model (SEM), which characterizes latent variables using corresponding multiple attributes and examines the interrelationships among them. The second component is a two-part model to assess a semicontinuous

A wide set of recent and classical symmetry tests is compared in terms of empirical power against some flexible skew-symmetric alternatives. The comparison is done for i.i.d. data, as well as for linear and GARCH time series models. In addition, the tests are analyzed in terms of computational efficiency. The role of distribution-free tests that avoid time-consuming resampling techniques for determining

The problem of species richness estimation using complete monotonicity of the distribution of species abundances is considered. Complete monotonicity is the most natural surrogate for k-monotonicity when k is large. The latter model has been considered in the same estimation problem adopting two different approaches which both necessitate selecting the unknown degree of monotonicity k via some chosen

Developing effective individualized treatment rules (ITRs) for diseases is an important goal of clinical research. Much effort has been devoted to estimating individualized treatment effects in the recent literature. However, there have not been systematic studies on the robust inference for individualized treatment effects when there exist potential outliers. We propose a monotone ITR in the framework

Testing the equality of two mean vectors is a classical problem in multivariate analysis. In this article, we consider the test in the high-dimensional setting. Existing tests often assume that the covariance matrix (or its inverse) of the underlying variables is sparse, which is rarely true in social science due to the existence of latent common factors. In the article, we introduce a maximum-type

In functional magnetic resonance imaging (fMRI), there is a rise in evidence that time-varying functional connectivity, or dynamic functional connectivity (dFC), which measures changes in the synchronization of brain activity, provides additional information on brain networks not captured by time-invariant (i.e., static) functional connectivity. While there have been many developments for statistical

The performance of Bayes estimators is examined, in comparison with the MLE, in multinomial models with a relatively large number of cells. The prior for the Bayes estimator is taken to be the conjugate Dirichlet, i.e., the multivariate Beta, with exchangeable distributions over the coordinates, including the non-informative uniform distribution. The choice of the multinomial is motivated by its many

A generalization of the classical Ornstein Uhlenbeck diffusion process including some deterministic time dependent functions in the infinitesimal moments is considered. The inference based on discrete sampling in time is provided by means of an iterative procedure that, in each step, combines the classical maximum likelihood estimation and a generalized method of moments. The validity of the suggested

Predicting the onset time of Alzheimer’s disease is of great importance in preventive medicine. Structural changes in brain regions have been actively investigated in the association study of Alzheimer’s disease diagnosis and prognosis. In this study, we propose a functional linear regression model to predict the conversion time to Alzheimer’s disease among mild cognitive impairment patients. Midsagittal

In this paper, we study the partially functional linear regression model in which there are both functional predictors and traditional multivariate predictors. The existing approach is based on approximation using functional principal component analysis which has some limitations. We propose an alternative framework based on reproducing kernel Hilbert spaces (RKHS) which has not been investigated in

Empirical likelihood offers a nonparametric approach to estimation and inference, which replaces the probability density-based likelihood function with a function defined by estimating equations. While this eliminates the need for a parametric specification, the restriction of numerical optimization greatly decreases the applicability of empirical likelihood for large data problems. A solution to this

It is well-known that the conventional CUSUM tests are over-sized in the presence of high persistence and misspecification. In this article, we propose a block wild bootstrap-based CUSUM test (CUSUM-BWB) for detecting changes in mean and variance shifts under possible high persistence and misspecification. We establish the asymptotic properties of the proposed test and our simulation study shows that

The linearity condition and the constant conditional variance assumption popularly used in sufficient dimension reduction are respectively close to elliptical symmetry and normality. However, it is always the concern about their restrictiveness. In this article, we give systematic studies to provide insight into the reasons why the popularly used sliced inverse regression and sliced average variance

Augmented designs play an important role in early-generation plant breeding when many varieties are tested and sufficient seeds are unavailable to permit each variety to be replicated more than once. The key idea is to include some replicated varieties to adjust for environmental heterogeneity and provide an estimate of error. The simplest form of augmented design is constructed using randomized complete

Biclustering is an important exploratory analysis tool that simultaneously clusters rows (e.g., samples) and columns (e.g., variables) of a data matrix. Checkerboard-like biclusters reveal intrinsic associations between rows and columns. However, most existing methods rely on Gaussian assumptions and only apply to matrix data. In practice, non-Gaussian and/or multi-way tensor data are frequently encountered

Bayesian quasi-likelihoods constructed from estimating functions extend the scope of Bayesian inference to a wide range of semi-parametric problems. Nonetheless, when the estimating functions possess complex structure, like containing highly irregular weighting matrices, the quasi-likelihoods constructed from those estimating functions may deform with multiple modes, and thus lose their nice statistical

A copula graphic estimator for the competing risks duration model with multiple spells is presented. By adopting a nested copula structure the dependencies between risks and spells are modelled separately. This breaks up an implicit restriction of popular duration models such as multivariate mixed proportional hazards. It is shown that the dependence structure between spells is identifiable and can

Many applications of regression models involve ordinal categorical predictors. Two common approaches for handling ordinal predictors are to form a set of dummy variables, or employ a two stage approach where dimension reduction is first applied and then the response is regressed against the predicted latent indices. Both approaches have drawbacks, with the former running into a high-dimensional problem

A new sampling design for populations whose units can be arranged as an N×M matrix is proposed. The sample must satisfy some constraints: row and column sample sizes are set in advance. The proposed sampling method gives the same selection probability to all the sample matrices that satisfy the constraints. Three algorithms to select a sample uniformly in the feasible set are presented: an exact algorithm

A nonparametric approach for testing independence among groups of continuous random variables is proposed. Gaussian-centered multivariate finite Polya tree priors are used to model the underlying probability distributions. Integrating out the random probability measure, a tractable empirical Bayes factor is derived and used as the test statistic. The Bayes factor is consistent in the sense that it

Functional data analysis can be seriously impaired by abnormal observations, which can be classified as either magnitude or shape outliers based on their way of deviating from the bulk of data. Identifying magnitude outliers is relatively easy, while detecting shape outliers is much more challenging. We propose turning the shape outliers into magnitude outliers through data transformation and detecting

A thorough investigation into the model degrees of freedom in k-means clustering is conducted. An extension of Stein’s lemma is used to obtain an expression for the effective degrees of freedom in the k-means model. Approximating the degrees of freedom in practice requires simplifications of this expression, however empirical studies evince the appropriateness of the proposed approach. The practical

This article develops a model-free variable screening technique with the non-ignorable missing response in ultrahigh-dimensional data analysis. Based on the common logistic model assumption of the propensity function, a novel screening procedure is proposed by borrowing hidden information of missingness indicator such that any variable screening method for ultrahigh-dimensional covariates with full

When huge amounts of data arrive in streams, online updating is an important method to alleviate both computational and data storage issues. The scope of previous research for online updating is extended in the context of the classical linear measurement error model. In the case where some covariates are unknowingly measured with error at the beginning of the stream, but then are measured without error

The study of the dynamic behavior of cross-sectional ranks over time for functional data and the ranks of the observed curves at each time point and their temporal evolution can yield valuable insights into the time dynamics of functional data. This approach is of interest in various application areas. For the analysis of the dynamics of ranks, estimation of the cross-sectional ranks of functional

Estimation of nonlinear curves and surfaces has long been the focus of semiparametric and nonparametric regression analysis. What has been less studied is the comparison of nonlinear functions. In lower-dimensional situations, inference typically involves comparisons of curves and surfaces. The existing comparative procedures are subject to various limitations, and few computational tools have been

This article proposes three tests for proportionality hypotheses regrading high-dimensional covariance matrices. Compared with currently available tests in the literature that fail in situations involving a “large p small n” or require knowledge of the underlying normal distributions, these tests are nonparametric, and do not require specifying any known distribution to derive asymptotic distributions

A novel borrowing strength measure and an overall borrowing index to characterize the strength of borrowing behaviors among subgroups are proposed for a given Bayesian hierarchical model. The constructions of the proposed indexes are based on the Mallow's distance and can be easily computed using MCMC samples for univariate or multivariate posterior distributions. Consequently, the proposed indexes

Three-arm non-inferiority (NI) trial including the experimental treatment, an active reference treatment, and a placebo where the outcome of interest is binary are considered. While the risk difference (RD) is the most common and well explored functional form for testing efficacy (or effectiveness), however, recent FDA guideline suggested measures such as relative risk (RR), odds ratio (OR), number