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

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

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

An optimal and flexible multiple hypotheses testing procedure is constructed for dependent data based on Bayesian techniques, aiming at handling two challenges, namely dependence structure and non-null distribution specification. Ignoring dependence among hypotheses tests may lead to loss of efficiency and bias in decision. Misspecification in the non-null distribution, on the other hand, can result

The problem of determining cut-points of a continuous scale according to an establish categorical scale is often encountered in practice for the purposes such as making diagnosis or treatment recommendation, determining study eligibility, or facilitating interpretations. A general analytic framework was recently proposed for assessing optimal cut-points defined based on some pre-specified criteria

In regression applications, the presence of nonlinearity and correlation among observations offer computational challenges not only in traditional settings such as least squares regression, but also (and especially) when the objective function is nonsmooth as in the case of quantile regression. Methods are developed for the modelling and estimation of nonlinear conditional quantile functions when data

The practice of employing empirical likelihood (EL) components in place of parametric likelihood functions in the construction of Bayesian-type procedures has been well-addressed in the modern statistical literature. The EL prior, a Jeffreys-type prior, which asymptotically maximizes the Shannon mutual information between data and the parameters of interest, is rigorously derived. The focus of the

Correlated survival data naturally arise from many clinical and epidemiological studies. For the analysis of such data, the Gamma-frailty proportional hazards (PH) model is a popular choice because the regression parameters have marginal interpretations and the statistical association between the failure times can be explicitly quantified via Kendall's tau. Despite their popularity, Gamma-frailty PH

Modern bio-technologies have produced a vast amount of high-throughput data with the number of predictors far greater than the sample size. In order to identify more novel biomarkers and understand biological mechanisms, it is vital to detect signals weakly associated with outcomes among ultrahigh-dimensional predictors. However, existing screening methods, which typically ignore correlation information

Truncated survival data arise when the event time is observed only if it falls within a subject-specific region, known as the truncation set. Left-truncated data arise when there is delayed entry into a study, such that subjects are included only if their event time exceeds some other time. Quasi-independence of truncation and failure refers to factorization of their joint density in the observable

A novel jackknife empirical likelihood method for constructing confidence intervals for multiply robust estimators is proposed in the context of missing data. Under mild regularity conditions, the proposed jackknife empirical likelihood ratio has been shown to converge to a standard chi-square distribution. A simulation study supports the findings and shows the benefits of the proposed method. The

In logistic regression, separation occurs when a linear combination of predictors perfectly discriminates the binary outcome. Because finite-valued maximum likelihood parameter estimates do not exist under separation, Bayesian regressions with informative shrinkage of the regression coefficients offer a suitable alternative. Classical studies of separation imply that efficiency in estimating regression

Penalization is a popular tool for multi- and high-dimensional data. Most of the existing computational algorithms have been developed for convex loss functions. Nonconvex loss functions can sometimes generate more robust results and have important applications. Motivated by the BLasso algorithm, this study develops the Forward and Backward Stagewise (Fabs) algorithm for nonconvex loss functions with

A multivariate functional joint model framework is proposed which enables the repeatedly measured functional outcomes, scalar outcomes, and survival process to be modeled simultaneously while accounting for association among the multiple (functional and scalar) longitudinal and survival processes. This data structure is increasingly common across medical studies of neurodegenerative diseases and is

A robust probabilistic classifier for functional data is developed to predict class membership based on functional input measurements and to provide a reliable probability estimates for class membership. The method combines a Bayes classifier and semi-parametric mixed effects model with robust tuning parameter to make the method robust to outlying curves, and to improve the accuracy of the risk or

Model misspecification is a potential problem for any parametric-model based analysis. However, the measurement and consequences of model misspecification have not been well formalized in the context of causal inference. A measure of model misspecification is proposed, and the consequences of model misspecification in non-experimental causal inference methods are investigated. The metric is then used

Screening procedures for infectious diseases, such as HIV, often involve pooling individual specimens together and testing the pools. For diseases with low prevalence, group testing (or pooled testing) can be used to classify individuals as diseased or not while providing considerable cost savings when compared to testing specimens individually. The pooling literature is replete with group testing

The cumulative incidence function quantifies the probability of failure over time due to a specific cause for competing risks data. The generalized semiparametric regression models for the cumulative incidence functions with missing covariates are investigated. The effects of some covariates are modeled as non-parametric functions of time while others are modeled as parametric functions of time. Different

Nonparametric regression models do not require the specification of the functional form between the outcome and the covariates. Despite their popularity, the amount of diagnostic statistics, in comparison to their parametric counter-parts, is small. We propose a goodness-of-fit test for nonparametric regression models with linear smoother form. In particular, we apply this testing framework to smoothing

A joint design for sampling functional data is proposed to achieve optimal prediction of both functional data and a scalar outcome. The motivating application is fetal growth, where the objective is to determine the optimal times to collect ultrasound measurements in order to recover fetal growth trajectories and to predict child birth outcomes. The joint design is formulated using an optimization

Cluster analysis methods are used to identify homogeneous subgroups in a data set. In biomedical applications, one frequently applies cluster analysis in order to identify biologically interesting subgroups. In particular, one may wish to identify subgroups that are associated with a particular outcome of interest. Conventional clustering methods generally do not identify such subgroups, particularly

Expectile regression is a useful tool for exploring the relation between the response and the explanatory variables beyond the conditional mean. A continuous threshold expectile regression is developed for modeling data in which the effect of a covariate on the response variable is linear but varies below and above an unknown threshold in a continuous way. The estimators for the threshold and the regression

In longitudinal studies, serial dependence of repeated outcomes must be taken into account to make correct inferences on covariate effects. As such, care must be taken in modeling the covariance matrix. However, estimation of the covariance matrix is challenging because there are many parameters in the matrix and the estimated covariance matrix should be positive definite. To overcomes these limitations

A model is presented for the supervised learning problem where the observations come from a fixed number of pre-specified groups, and the regression coefficients may vary sparsely between groups. The model spans the continuum between individual models for each group and one model for all groups. The resulting algorithm is designed with a high dimensional framework in mind. The approach is applied to