The Rosenbrock function is a ubiquitous benchmark problem in numerical optimization, and variants have been proposed to test the performance of Markov chain Monte Carlo algorithms on distributions with a curved and narrow shape. In this work we discuss the Rosenbrock distribution and the advantages and limitations of its current n‐dimensional extensions. We then propose a new extension to arbitrary

We propose a log‐linear Poisson regression model driven by a stationary latent gamma autoregression. This process has negative binomial (NB) marginals to analyze overdispersed count time series data. Estimation and statistical inference are performed using a composite (CL) likelihood function. We establish theoretical properties of the proposed count model, in particular, the strong consistency and

In this article we present a parametric estimation method for certain multiparameter heavy‐tailed Lévy‐driven moving averages. The theory relies on recent multivariate central limit theorems obtained via Malliavin calculus on Poisson spaces. Our minimal contrast approach is related to previous papers, which propose to use the marginal empirical characteristic function to estimate the one‐dimensional

Estimation of covariate‐dependent conditional covariance matrix in a high‐dimensional space poses a challenge to contemporary statistical research. The existing kernel estimators may not be locally adaptive due to using a single bandwidth to explore the smoothness of all entries of the target matrix function. In this paper, we propose a novel framework to address this issue, where we factorize the

For the multivariate COGARCH process, we obtain explicit expressions for the second‐order structure of the “squared returns” process observed on an equidistant grid. Based on this, we present a generalized method of moments estimator for its parameters. Under appropriate moment and strong mixing conditions, we show that the resulting estimator is consistent and asymptotically normal. Sufficient conditions

In prevalent cohort studies where subjects are recruited at a cross‐section, the time to an event may be subject to length‐biased sampling, with the observed data being either the forward recurrence time, or the backward recurrence time, or their sum. In the regression setting, assuming a semiparametric accelerated failure time model for the underlying event time, where the intercept parameter is absorbed

Magnetic resonance imaging (MRI) is a technique that scans the anatomical structure of the brain, whereas functional magnetic resonance imaging (fMRI) uses the same basic principles of atomic physics as MRI scans but image metabolic function. A major goal of MRI and fMRI study is to precisely delineate various types of tissues, anatomical structure, pathologies, and detect the brain regions that react

We introduce and develop a general paradigm for combining information across diverse data sources. In broad terms, suppose &ip.phi is a parameter of interest, built up via components ψ1,...,ψk from data sources 1,...,k. The proposed scheme has three steps. First, the Independent Inspection (II) step amounts to investigating each separate data source, translating statistical information to a confidence

The Greenwood statistic Tn and its functions, including sample coefficient of variation, often arise in testing exponentiality or detecting clustering or heterogeneity. We provide a general result describing stochastic behavior of Tn in response to stochastic behavior of the sample data. Our result provides a rigorous base for constructing tests and assuring that confidence regions are actually intervals

Mechanistic models of infectious disease spread are key to inferring spatiotemporal infectious disease transmission dynamics. Ideally, covariate data and the infection status of individuals over time would be used to parameterize such models. However, in reality, complete data are rarely available; for example, infection times are almost never observed. Bayesian data‐augmented Markov chain Monte Carlo

In this work, we consider a multivariate regression model with one‐sided errors. We assume for the regression function to lie in a general Hölder class and estimate it via a nonparametric local polynomial approach that consists of minimization of the local integral of a polynomial approximation lying above the data points. While the consideration of multivariate covariates offers an undeniable opportunity

For any given multivariate distribution, explicit formulae for the asymptotic covariances of cumulant vectors of the third and the fourth order are provided here. General expressions for cumulants of elliptically symmetric multivariate distributions are also provided. Utilizing these formulae one can extend several results currently available in the literature, as well as obtain practically useful

We study functional central limit theorems for persistent Betti numbers obtained from networks defined on a Poisson point process. The limit is formed in large volumes of cylindrical shape stretching only in one dimension. The results cover a directed sublevel‐filtration for stabilizing networks and the Čech and Vietoris–Rips complex on the random geometric graph. The presented functional central limit

In the literature, quite a few measures have been proposed for quantifying the deviation of a probability distribution from symmetry. The most popular of these skewness measures are based on the third centralized moment and on quantiles. However, there are major drawbacks in using these quantities. These include a strong emphasis on the distributional tails and a poor asymptotic behavior for the (empirical)

Preliminary test estimation is a methodology that combines goodness‐of‐fit testing and estimation. It is a classical procedure when it is suspected that the parameter to be estimated satisfies some prespecified constraints. In the present paper, we establish general results on the asymptotic behavior of preliminary test estimators. More precisely, we show that, in uniformly locally asymptotically normal

The question whether structural changes in time‐resolved images are of statistical significance or merely emerge from random noise is of great relevance in many practical applications such as live cell fluorescence microscopy, where intracellular diffusion processes are investigated. Using bootstrap‐methods, we construct nonparametric confidence bands for time‐resolved images from fluorescence microscopy

Modelling conditional distributions for functional data extends the concept of a mean response in functional regression settings, where vector predictors are paired with functional responses. This extension is challenging because of the non‐existence of well‐defined densities, cumulative distributions or quantile functions in the Hilbert space where the response functions are located. To address this

Conditional copula models allow the dependence structure among variables to vary with covariates, and thus can describe the evolution of the dependence structure with those factors. This paper proposes a conditional mixture copula which is a weighted average of several individual conditional copulas. We allow both the weights and copula parameters to vary with a covariate so that the conditional mixture

We propose a projection‐based cross‐validation method for estimating a low‐dimensional parameter in the presence of a high‐dimensional nuisance parameter in the Cox regression model. We show that the proposed estimator is asymptotically normal, which enables us to conduct hypothesis test for the parameter of interest with high‐dimensional nuisance parameters. Three decision rules are presented to avoid

This article provides a novel approach to nonstationarity by considering a bridge between differential equations and spatial fields. We consider the dynamical transformation of a given spatial process undergoing the action of a temporal flow of space diffeomorphisms. Such dynamical deformations are shown to be connected to certain classes of ordinary and partial differential equations. The natural

Various statistical problems can be formulated in terms of a bilinear form of the covariance matrix. Examples are testing whether coordinates of a high‐dimensional random vector are uncorrelated, constructing confidence intervals for the risk of optimal portfolios or testing for the stability of a covariance matrix, especially for factor models. Extending previous works to a general high‐dimensional

A new lack‐of‐fit test for quantile regression models will be presented for the case where the response variable is right‐censored. The test is based on the cumulative sum of residuals, and it extends the ideas of He and Zhu (2003) to censored quantile regression. It will be shown that the empirical process associated with the test statistic converges to a Gaussian process under the null hypothesis

In this article, we propose a doubly stochastic spatial point process model with both aggregation and repulsion. This model combines the ideas behind Strauss processes and log Gaussian Cox processes. The likelihood for this model is not expressible in closed form but it is easy to simulate realizations under the model. We therefore explain how to use approximate Bayesian computation (ABC) to carry

Disease progression is often monitored by intermittent follow‐up “visits” in longitudinal cohort studies, resulting in interval‐censored failure time outcomes. Furthermore, the timing and frequency of visits is often found related to a person's history of disease‐related variables in practice. This article develops a semiparametric estimation approach using weighted binomial regression and a kernel

Analysis of time‐to‐event data using Cox's proportional hazards (PH) model is ubiquitous in scientific research. A sample is taken from the population of interest and covariate information is collected on everyone. If the event of interest is rare and covariate information is difficult to collect, the nested case‐control (NCC) design reduces costs with minimal impact on inferential precision. Under

In this article, we propose an adaptive‐to‐model test for conditional independence through groupwise dimension reduction developed in sufficient dimension reduction field. The test statistic under the null hypothesis is asymptotically normally distributed. Although it is also based on nonparametric estimation like any local smoothing tests for conditional independence, its behavior is similar to existing

The class of inhomogeneous phase‐type distributions (IPH) was recently introduced in Albrecher & Bladt (2019) as an extension of the classical phase‐type (PH) distributions. Like PH distributions, the class of IPH is dense in the class of distributions on the positive halfline, but leads to more parsimonious models in the presence of heavy tails. In this paper we propose a fitting procedure for this

We consider a stochastic individual‐based model in continuous time to describe a size‐structured population for cell divisions. This model is motivated by the detection of cellular aging in biology. We here address the problem of nonparametric estimation of the kernel ruling the divisions based on the eigenvalue problem related to the asymptotic behavior in large population. This inverse problem involves

We construct and study a test to detect possible change points in the regression parameters of a linear model when the model errors and covariates may exhibit heteroscedasticity. Being based on a new trimming scheme for the CUSUM process introduced in Horváth et al. (2020), this test is particularly well suited to detect changes that might occur near the endpoints of the sample. A complete asymptotic

In the present article we study the average of Lipschitz‐Killing (LK) curvatures of the excursion set of a stationary isotropic Gaussian field X on ℝ 2 . The novelty is that the field can be nonstandard, that is, with unknown mean and variance, which is more realistic from an applied viewpoint. To cope with the unknown location and scale parameters of X, we introduce novel fundamental quantities called

Regression models describing the joint distribution of multivariate responses conditional on covariate information have become an important aspect of contemporary regression analysis. However, a limitation of such models are the rather simplistic assumptions often made, for example, a constant dependence structure not varying with covariates or the restriction to linear dependence between the responses

Expectiles and quantiles can both be defined as the solution of minimization problems. Contrary to quantiles though, expectiles are determined by tail expectations rather than tail probabilities, and define a coherent risk measure. For these two reasons in particular, expectiles have recently started to be considered as serious candidates to become standard tools in actuarial and financial risk management

We consider a nonparametric heteroscedastic time series regression model and suggest testing procedures to detect changes in the conditional variance function. The tests are based on a sequential marked empirical process and thus combine classical CUSUM tests from change point analysis with marked empirical process approaches known from goodness‐of‐fit testing. The tests are consistent against general

This paper deals with an estimation of the dependence structure of a multidimensional response variable in the presence of a multivariate covariate. It is assumed that the covariate affects only the marginal distributions through regression models while the dependence structure, which is described by a copula, is unaffected. A parametric estimation of the copula function is considered with focus on

Bias approximation has played an important rôle in statistical inference, and numerous bias calculation techniques have been proposed under different contexts. We provide a unified approach to approximating the bias of the maximum likelihood estimator and the l2 penalized likelihood estimator for both linear and nonlinear models, where the design variables are allowed to be random and the sample size

No abstract is available for this article.

In this paper, we consider a one‐dimensional Cox‐Ingersoll‐Ross (CIR) process whose drift coefficient depends on unknown parameters. Considering the process discretely observed at high frequency, we prove the local asymptotic normality property in the subcritical case, the local asymptotic quadraticity in the critical case, and the local asymptotic mixed normality property in the supercritical case

Case‐cohort design has been demonstrated to be an economical and efficient approach in large cohort studies when the measurement of some covariates on all individuals is expensive. Various methods have been proposed for case‐cohort data when the dimension of covariates is smaller than sample size. However, limited work has been done for high‐dimensional case‐cohort data which are frequently collected

Weighted log‐rank tests are arguably the most widely used tests by practitioners for the two‐sample problem in the context of right‐censored data. Many approaches have been considered to make them more robust against a broader family of alternatives, including taking linear combinations, or the maximum among a finite collection of them. In this article, we propose as test statistic the supremum of

Olkin and Spiegelman introduced a semiparametric estimator of the density defined as a mixture between the maximum likelihood estimator and the kernel density estimator. Due to the absence of any leave‐one‐out strategy and the hardness of estimating the Kullback–Leibler loss of kernel density estimate, their approach produces unsatisfactory results. This article investigates an alternative approach

We apply a three‐step sequential procedure to estimate the change‐point of count time series. Under certain regularity conditions, the estimator of change‐point converges in distribution to the location of the maxima of a two‐sided random walk. We derive a closed‐form approximating distribution for the maxima of the two‐sided random walk based on the invariance principle for the strong mixing processes

Inspired by the problem of gait reproducibility (reidentifying individuals across doctor's visits) we develop two‐sample permutation tests under a sample‐specific group action on Lie groups with a bi‐invariant Riemannian metric. These tests rely on consistent estimators and pairwise curve alignment. To this end, we propose Gaussian perturbation models and for the special case of curves on the group

When dealing with Bayesian inference the choice of the prior often remains a debatable question. Empirical Bayes methods offer a data‐driven solution to this problem by estimating the prior itself from an ensemble of data. In the nonparametric case, the maximum likelihood estimate is known to overfit the data, an issue that is commonly tackled by regularization. However, the majority of regularizations

Various assumptions on a right‐censoring mechanism to ensure consistency of the Kaplan–Meier and Aalen–Johansen estimators in a competing risks setting are studied. Specifically, eight different assumptions are seen to fall in two categories: a weaker identifiability assumption, which is the weakest possible assumption in a precise sense, and a stronger representativity assumption which ensures the

We propose a new Gini correlation to measure dependence between a categorical and numerical variables. Analogous to Pearson R2 in ANOVA model, the Gini correlation is interpreted as the ratio of the between‐group variation and the total variation, but it characterizes independence (zero Gini correlation mutually implies independence). Closely related to the distance correlation, the Gini correlation

The functional linear model with functional response (FLMFR) is one of the most fundamental models to assess the relation between two functional random variables. In this article, we propose a novel goodness‐of‐fit test for the FLMFR against a general, unspecified, alternative. The test statistic is formulated in terms of a Cramér–von Mises norm over a doubly projected empirical process which, using

In nonignorable missing response problems, we study a semiparametric model with unspecified missingness mechanism model and a exponential family model for response conditional density. Even though existing methods are available to estimate the parameters in exponential family, estimation or testing of the missingness mechanism model nonparametrically remains to be an open problem. By defining a “synthesis"

For many environmental processes, recent studies have shown that the dependence strength is decreasing when quantile levels increase. This implies that the popular max‐stable models are inadequate to capture the rate of joint tail decay, and to estimate joint extremal probabilities beyond observed levels. We here develop a more flexible modeling framework based on the class of max‐infinitely divisible

We consider importance sampling (IS) type weighted estimators based on Markov chain Monte Carlo (MCMC) targeting an approximate marginal of the target distribution. In the context of Bayesian latent variable models, the MCMC typically operates on the hyperparameters, and the subsequent weighting may be based on IS or sequential Monte Carlo (SMC), but allows for multilevel techniques as well. The IS

The main challenge in ensemble‐based filtering methods is the updating of a prior ensemble to a posterior ensemble. In the ensemble Kalman filter (EnKF), a linear‐Gaussian model is introduced to overcome this issue, and the prior ensemble is updated with a linear shift. In the current article, we consider how the underlying ideas of the EnKF can be applied when the state vector consists of binary variables

We consider inference for local maxima of the marginal density function of strongly dependent linear processes. Weak consistency of the estimated modular set and the number of modes is derived. A uniform reduction principle for kernel density estimators is used to obtain confidence sets for the set of modes. The results can be extended to multivariate modes. Simulations illustrate the asymptotic results

In this paper, we introduce a sufficient dimension reduction (SDR) algorithm based on distance‐weighted discrimination (DWD). Our methods is shown to be robust on the dimension p of the predictors in our problem, and it also utilizes some new computational results in the DWD literature to propose a computationally faster algorithm than previous classification‐based algorithms in the SDR literature

This article pertains to the analysis of recurrent event data in the presence of spatial correlation. Consider units located at n possibly spatially correlated geographical areas described by their longitude and latitude and monitored for the occurrence of an event that can recur. We propose a new class of semiparametric models for recurrent events that simultaneously account for risk factors and correlation

We analyze the ordinal structure of long‐range dependent time series. To this end, we use so called ordinal patterns which describe the relative position of consecutive data points. We provide two estimators for the probabilities of ordinal patterns and prove limit theorems in different settings, namely stationarity and (less restrictive) stationary increments. In the second setting, we encounter a

In the present article, we discuss the regression of a point on the surface of a unit sphere in d dimensions given a point on the surface of a unit sphere in p dimensions, where p may not be equal to d. Point projection is added to the rotation and linear transformation for regression link function. The identifiability of the model is proved. Then, parameter estimation in this set up is discussed.

Multiple imputation provides an effective way to handle missing data. When several possible models are under consideration for the data, multiple imputation is typically performed under a single‐best model selected from the candidate models. This single‐model selection approach ignores the uncertainty associated with the model selection and so leads to underestimation of the variance of multiple imputation

We introduce a model for recurrent event data subject to left‐, right‐, and intermittent‐censoring. The observations consist of binary sequences (along with covariates) for each individual under study. These sequences are modeled as generated by latent Ornstein–Uhlenbeck processes being above or below certain thresholds. Features of the latent process and the thresholds are taken as functions of covariates

We study theoretical foundation of model comparison for ergodic stochastic differential equation (SDE) models and an extension of the applicable scope of the conventional Bayesian information criterion. Different from previous studies, we suppose that the candidate models are possibly misspecified models, and we consider both Wiener and a pure‐jump Lévy noise‐driven SDE. Based on the asymptotic behavior

State space models (SSMs) are now ubiquitous in many fields and increasingly complicated with observed and unobserved variables often interacting in nonlinear fashions. The crucial task of validating model assumptions thus becomes difficult, particularly since some assumptions are formulated about unobserved states and thus cannot be checked with data. Motivated by the complex SSMs used for the assessment

Let X 1,X 2,… be independent and identically distributed random elements taking values in a separable Hilbert space ℍ . With applications for functional data in mind, ℍ may be regarded as a space of square‐integrable functions, defined on a compact interval. We propose and study a novel test of the hypothesis H 0 that X 1 has some unspecified nondegenerate Gaussian distribution. The test statistic