Outer power (OP) transformations of Archimedean generators are suggested to increase the modeling flexibility and statistical fitting capabilities of classical Archimedean copulas restricted to a single parameter. For OP-transformed Archimedean copulas, a formula for computing tail dependence coefficients is obtained, as well as two feasible OP Archimedean copula estimators are proposed and their properties

Quantifying the serial correlation across time lags is a crucial step in the identification and diagnosis of a time series model. Simple and partial autocorrelation functions of the time series are the most widely used tools for this purpose with scalar time series. Nevertheless, there is a lack of an established method for the identification of functional time series (FTS) models. Functional versions

An extension of the D-vine based forward regression procedure to a R-vine forward regression is proposed. In this extension any R-vine structure can be taken into account. Moreover, a new heuristic is proposed to determine which R-vine structure is the most appropriate to model the conditional distribution of the response variable given the covariates. It is shown in the simulation that the performance

Imputation and the inverse probability weighting are two commonly used approaches in missing data analysis. Parametric versions of them are not robust due to model misspecification of some unknown functions. Nonparametric ones are robust but are impractical when the number of covariates is large due to the problem of “curse of dimension”. A beyond multiple robust method is proposed in this paper. This

Sufficient dimension reduction (SDR) using distance covariance (DCOV) was recently proposed as an approach to dimension-reduction problems. Compared with other SDR methods, it is model-free without estimating link function and does not require any particular distributions on predictors. However, the DCOV-based SDR method involves optimizing a nonsmooth and nonconvex objective function over the Stiefel

Modeling longitudinal binary data is challenging but common in practice. Existing methods on modeling of binary responses take no account of the fact that the correlation coefficient of binary responses must have an upper bound which is smaller than one. Ignoring this fact can lead to incorrect statistical inferences for longitudinal binary data. A novel method is proposed to model the mean and within-subject

In many application areas, the problem of the automatic variable selection in a linear model with asymmetric errors is encountered, when the number of explanatory variables diverges with the sample size. For this high-dimensional model, the penalized least squares method is not appropriate and the quantile framework makes the inference more difficult because of the non differentiability of the loss

Linear regression with normally distributed errors–including particular cases such as ANOVA, Student’s t-test or location-scale inference–is a widely used statistical procedure. In this case the ordinary least squares estimator possesses remarkable properties but is very sensitive to outliers. Several robust alternatives have been proposed, but there is still significant room for improvement. An original

Many real-world classification problems come with costs which can vary for different types of misclassification. It is thus important to develop cost-sensitive classifiers which minimize the total misclassification cost. Although binary cost-sensitive classifiers have been well-studied, solving multicategory classification problems is still challenging. A popular approach to address this issue is to

A smooth simultaneous confidence band (SCB) is constructed for the distribution of unobserved errors in a nonparametric regression model based on a plug-in kernel distribution estimator. The normalized estimation error process is shown to converge to a Gaussian process. Simulation experiments indicate that the proposed SCB not only strikes an intelligent balance between coverage probability and precision

Regression models are widely used statistical procedures, and the validation of their assumptions plays a crucial role in the data analysis process. Unfortunately, validating assumptions usually depends on the availability of tests tailored to the specific model of interest. A novel Bayesian approach goodness-of-fit hypothesis testing approach is presented for a broad class of regression models the

The EM algorithm is a widely applicable algorithm for modal estimation but often criticized for its slow convergence. A new hybrid accelerator named APX-EM is proposed for speeding up the convergence of EM algorithm, which is based on both Linearly Preconditioned Nonlinear Conjugate Gradient (PNCG) and PX-EM algorithm. The intuitive idea is that, each step of the PX-EM algorithm can be viewed approximately

Spatial dependent data frequently occur in spatial econometrics and endemiology. In this work, we propose a class of penalized robust regression estimators based on exponential squared loss with independent and identical distributed errors for general spatial autoregressive models. A penalized exponential squared loss with the adaptive lasso penalty is employed for simultaneous model selection and

The majority of methods available to model survival data only deal with right censoring. However, there are many applications where left, right and/or interval censoring simultaneously occur. A methodology that is capable of handling all types of censoring as well as flexibly estimating several types of covariate effects is presented. The baseline hazard is modelled through monotonic P-splines. The

A self-calibrated direct estimation algorithm based on ℓ1-regularized quadratic programming is proposed. The self-calibration is achieved by an iterative algorithm for finding the regularization parameter simultaneously with the estimation target. The proposed algorithm is free of cross-validation. Two applications of this algorithm are proposed, namely precision matrix estimation and linear discriminant

The incident/dynamic time-dependent AUC (Area Under the ROC Curve) is an appealing measure to express the discriminative value of a dynamic survival model over time. However, estimation of this measure is not straightforward. Four recently proposed estimation approaches are studied. In an extensive simulation study, a head-to-head comparison between these four estimation methods is made. The estimation

Latent block models are used for probabilistic biclustering, which is shown to be an effective method for analyzing various relational data sets. However, there has been no statistical test method for determining the row and column cluster numbers of latent block models. Recent studies have constructed statistical-test-based methods for stochastic block models, which assume that the observed matrix

The Gaussian process regression (GPR) model is well-known to be susceptible to outliers. Robust process regression models based on t-process or other heavy-tailed processes have been developed to address the problem. However, due to the current definitions of heavy-tailed processes, the unknown process regression function and the random errors are always defined jointly. This definition, mainly owing

The modeling and prediction of functions that can exhibit non-stationarity characteristics is important in many applications; for example, this is often the case for simulator output. One approach to predict a function with unknown stationarity properties is to model it as a draw from a flexible stochastic process that can produce stationary or non-stationary realizations. One such model is the composite

Generalized additive models (GAMs) are a well-established statistical tool for modeling complex nonlinear relationships between covariates and a response assumed to have a conditional distribution in the exponential family. To make inference in this model class, a fast and flexible approach is considered based on Bayesian P-splines and the Laplace approximation. The proposed Laplace-P-spline model

In many complex systems studied in statistical physics, inter-arrival times between events such as solar flares, trades and neuron voltages follow a heavy-tailed distribution. The set of event times is fractal-like, being dense in some time windows and empty in others, a phenomenon which has been dubbed “bursty”. A new model for the inter-exceedance times of such events above high thresholds is proposed

A new approach is presented for learning high-dimensional Gaussian linear structural equation models from only observational data when unknown error variances are heterogeneous. The proposed method consists of three steps: inferring (1) the moralized graph using the inverse covariance matrix, (2) the ordering using conditional variances, and (3) the directed edges using conditional independence relationships

A new class of hierarchical copulas is introduced based on joint survival functions of multivariate exponential mixture distributions. The key element of this construction is the mixing random vector defined by convolutions associated to a Lévy subordinator, and leading to hierarchical copulas with Archimedean within-block copulas and asymmetric between-block pair-copulas. For the specific case of

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

In this paper, a new estimation method is introduced for the quantile spectrum, which uses a parametric form of the autoregressive (AR) spectrum coupled with nonparametric smoothing. The method begins with quantile periodograms which are constructed by trigonometric quantile regression at different quantile levels, to represent the serial dependence of time series at various quantiles. At each quantile

A new procedure is proposed for selecting the input value for the adaptation bandwidth λ in nonparametric Gaussian regression via Propagation-Separation approach. Since λ stands at the bias–variance trade-off of this estimation technique, it is its key tuning parameter. So far, however, apart from theoretical concepts, there exists no approach for a data-driven choice of its input value. This complicates

This paper considers a residual-based approach to diagnose the adequacy of both the univariate and vector multiplicative error model (MEM). Two residual-based statistics are constructed based on the parameter estimates of the linear autoregressions with the standardized residuals as dependent variables. Since the autoregressions involve estimated standardized residuals, the correct asymptotic distributions

Generalized Gaussian processes (GGPs) are highly flexible models that combine latent GPs with potentially non-Gaussian likelihoods from the exponential family. GGPs can be used in a variety of settings, including GP classification, nonparametric count regression, modeling non-Gaussian spatial data, and analyzing point patterns. However, inference for GGPs can be analytically intractable, and large

In global testing, where a large number of pointwise test statistics are aggregated to simultaneously test for a collection of null hypotheses, the handling of dependence is a crucial issue. In various fields, more particularly in genetic epidemiology and functional data analysis, many testing methods for detecting an association signal between a response and explanatory variables have been proposed

The lasso model has been widely used for model selection in data mining, machine learning, and high-dimensional statistical analysis. However, with the ultrahigh-dimensional, large-scale data sets now collected in many real-world applications, it is important to develop algorithms to solve the lasso that efficiently scale up to problems of this size. Discarding features from certain steps of the algorithm

In the study of panel regression, current existing cross-sectional dependence tests are mainly based on the normal assumption. However, in practical applications, the normal assumption is usually not valid, which weakens the usability of the tests. To develop more testing tools suitable for nonnormal panel data, we extend the rank-based framework of U-statistics to panel regressions, and derive their

A framework for determining and estimating the conditional pairwise relationships of variables in high dimensional settings when the observed samples are contaminated with measurement error is proposed. The framework is motivated by the task of establishing gene regulatory networks from microarray studies, in which measurements are taken for a large number of genes from a small sample size, but often

With the development of modern technologies, it is possible to gather an extraordinarily large number of observations. Due to the storage or transmission burden, big data are usually scattered at multiple locations. It is difficult to transfer all of data to the central server for analysis. A distributed subdata selection method for big data linear regression model is proposed. Particularly, a two-step

The problem of testing for the equality of autocovariances of two independent high-dimensional time series is studied. Tests based on the suprema or sums of suitable averages across the dimensions are adapted from the available literature. Another test based on principal component analysis (PCA) is introduced and studied in theory. An extension is also considered to the setting of testing for the equality

Gradient boosting algorithms construct a regression predictor using a linear combination of “base learners”. Boosting also offers an approach to obtaining robust non-parametric regression estimators that are scalable to applications with many explanatory variables. The robust boosting algorithm is based on a two-stage approach, similar to what is done for robust linear regression: it first minimizes

State–space models are ubiquitous in the statistical literature since they provide a flexible and interpretable framework for analyzing many time series. In most practical applications, the state–space model is specified through a parametric model. However, the specification of such a parametric model may require an important modeling effort or may lead to models which are not flexible enough to reproduce

We study a penalized logspline density estimation method using a total variation penalty. The B-spline basis is adopted to approximate the logarithm of density functions. Total variation of derivatives of splines is penalized to impart a data-driven knot selection. The proposed estimator is a bona fide density function in the sense that it is positive and integrates to one. We devise an efficient coordinate

Missing data occur in almost every field and a great deal of literature has been established for the analysis of missing data with different types of missing mechanisms and under various models. Nonignorable missing data can be analyzed using nonparametric transformation models, which has not been discussed in the literature. In particular, assume that the conditional response probability can be written

Network construction has been heavily exploited in multivariate data analysis. In many cases, connections between a large portion of variables are of minimal importance. As such, partial graphs have played an important role in network construction. Due to the existence of a multiplicative normalization constant, the existing construction approaches may bear high computational cost. To reduce the computational

Regular fractional factorial designs with 2-level factors are among the most frequently used experimental plans. In many cases, designs should be blocked for dealing with inhomogeneity of experimental units. At the same time, the research question at hand may imply a focus on specified sets of two-factor interactions, while it is not justified to assume negligibility of other low order effects. An

The local polynomial smoothing of the Kaplan–Meier estimate for fixed designs is explored and analyzed. The first benefit, in comparison to classical convolution kernel smoothing, is the development of boundary aware estimates of the distribution function, its derivatives and integrated derivative products of any arbitrary order. The advancements proceed by developing asymptotic mean integrated square

Asymmetry of dependence is an inherent property of bivariate probability distributions. Being symmetric, commonly used dependence measures such as Pearson’s r or Spearman’s ρ mask asymmetry and implicitly assume that a random variable Y is equally dependent on a random variable X as vice versa. A copula-based, hence scale-invariant dependence measure called ζ1 overcoming the just mentioned problem

Continuous-time multi-state Markov models can be used to describe transitions over time across health states. Given longitudinal interval-censored data on transitions between states, statistical inference on changing health is possible by specifying models for transition hazards. Parametric time-dependent hazards can be restrictive, and nonparametric hazard specifications using splines are presented

Meta-analyses of diagnostic test accuracy (DTA) studies have been gathering attention in research in clinical epidemiology and health technology development, and bivariate random-effects model is becoming a standard tool. However, standard inference methods usually underestimate statistical errors and possibly provide highly overconfident results under realistic situations since they ignore the variability

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

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