An iterative Bayesian optimisation technique is presented to find spatial designs of data that carry much information. We use the decision theoretic notion of value of information as the design criterion. Gaussian process surrogate models enable fast calculations of expected improvement for a large number of designs, while the full-scale value of information evaluations are only done for the most promising

Estimating the parameters of spatial models for large spatial datasets can be computationally challenging, as it involves repeated evaluation of sizable spatial covariance matrices. In this paper, we aim to develop Krylov subspace based methods that are computationally efficient for large spatial data. Specifically, we approximate the inverse and the log-determinant of the spatial covariance matrix

We consider a one-dimensional stochastic differential equation that is observed on a fine grid of equally-spaced time points. A novel approach for approximating the transition density of the stochastic differential equation is presented, which is based on an Itô-Taylor expansion of the sample path, combined with an application of the so-called ε-expansion. The resulting approximation is economical

For a stationary moving average random field, a non–parametric low frequency estimator of the Lévy density of its infinitely divisible independently scattered integrator measure is given. The plug–in estimate is based on the solution w of the linear integral equation v x = ∫ ℝ d g s w h s x ds where g,h: ℝ d → ℝ are given measurable functions and ν is a (weighted) L2-function on ℝ . We investigate

In this study, we consider the maximum composite likelihood estimator for spatial extremes model class of Brown–Resnick type. The composite likelihood is constructed based on the weighted tail empirical process. It is shown that the proposed estimator is consistent and asymptotically normal under some regularity conditions fulfilled by the model class. We conduct Monte Carlo simulations to evaluate

We consider estimation of the average effect of time-varying dichotomous exposure on outcome using inverse probability weighting (IPW) under the assumption that there is no unmeasured confounding of the exposure–outcome association at each time point. Despite the popularity of IPW, its performance is often poor due to instability of the estimated weights. We develop an estimating equation-based strategy

We consider high-dimensional inference for potentially misspecified Cox proportional hazard models based on low-dimensional results by Lin and Wei (1989). A desparsified Lasso estimator is proposed based on the log partial likelihood function and shown to converge to a pseudo-true parameter vector. Interestingly, the sparsity of the true parameter can be inferred from that of the above limiting parameter

A method for change point detection is proposed. We consider a univariate sequence of independent random variables with piecewise constant expectation and variance, apart from which the distribution may vary periodically. We aim to detect change points in both expectation and variance. For that, we propose a statistical test for the null hypothesis of no change points and an algorithm for change point

What is a good prior? Actual prior knowledge should be used, but for complex models this is often not easily available. The knowledge can be in the form of symmetry assumptions, and then the choice will typically be an improper prior. Also more generally, it is quite common to choose improper priors. Motivated by this we consider a theoretical framework for statistics that includes both improper priors

Generalisations of the Ornstein-Uhlenbeck process defined through Langevin equations, such as fractional Ornstein-Uhlenbeck processes, have recently received a lot of attention. However, most of the literature focuses on the one dimensional case with Gaussian noise. In particular, estimation of the unknown parameter is widely studied under Gaussian stationary increment noise. In this article, we consider

Conditional Monte Carlo refers to sampling from the conditional distribution of a random vector X given the value T ( X ) = t for a function T ( X ) . Classical conditional Monte Carlo methods were designed for estimating conditional expectations of functions ϕ ( X ) by sampling from unconditional distributions obtained by certain weighting schemes. The basic ingredients were the use of importance

In this paper we propose a class of multistate models for the analysis of multitype recurrent event and failure time data when there are past event feedbacks in longitudinal biomarkers. It can well incorporate various effects, including time-dependent and time-independent effects, of different event paths or the number of occurrences of events of different types. Asymptotic unbiased estimating equations

Generalized additive model is a powerful statistical learning and predictive modeling tool that has been applied in a wide range of applications. The need of high-dimensional additive modeling is eminent in the context of dealing with high throughput data such as genetics data analysis. In this article, we studied a two-step selection and estimation method for ultrahigh-dimensional generalized additive

We study two nonparametric tests of the hypothesis that a sequence of independent observations is identically distributed against the alternative that at a single change point the distribution changes. The tests are based on the Cramér–von Mises two-sample test computed at every possible change point. One test uses the largest such test statistic over all possible change points; the other averages

It is known that the Thresholded Lasso (TL), SCAD or MCP correct intrinsic estimation bias of the Lasso. In this paper we propose an alternative method of improving the Lasso for predictive models with general convex loss functions which encompass normal linear models, logistic regression, quantile regression, or support vector machines. For a given penalty we order the absolute values of the Lasso

When a strict subset of covariates is given, we propose conditional quantile treatment effect ( C Q T E ) to offer, compared with the unconditional quantile treatment effect ( Q T E ) and conditional average treatment effect ( C A T E ), a more complete and informative view of the heterogeneity of treatment effects via the quantile sheet that is a function of the given covariates and quantile levels

In the analysis of longitudinal or functional data, a time-varying additive model (tvAM) has been introduced that is effective at avoiding the curse of dimensionality and capturing dynamic features. The present article focuses on the unified two-step estimators of a tvAM with sparse or dense longitudinal or functional data. It is proved that the two-step estimators have the same asymptotic distribution

Generalized linear models, introduced by Nelder and Wedderburn, allowed to model the regression of normal and nonnormal data. While doing so, the analysis of these models could not be obtained without the explicit form of the variance function. In this paper, we determine the link and variance functions of the natural exponential family generated by the class of subordinated Lévy processes. In this

Model uncertainty is a pervasive problem in regression applications. Bayesian model averaging (BMA) takes model uncertainty into account and identifies robust determinants. However, it requires the specification of suitable model priors. Mixture model priors are appealing because they explicitly account for different groups of covariates as robust determinants. Specific Dirichlet process clustering

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

We introduce and develop a general paradigm for combining information across diverse data sources. In broad terms, suppose φ is a parameter of interest, built up via components ψ 1 , … , ψ k 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 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

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

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

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)

Modeling 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 nonexistence 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

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

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

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

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

In this paper, 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 of this model is not expressible in closed form, but it is easy to simulate under the model. We therefore explain how to use approximate Bayesian computation (ABC) for statistical inference

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

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

The class of inhomogeneous phase-type distributions was recently introduced as a dense extension of classical phase-type distributions that leads to more parsimonious models in the presence of heavy tails. In this paper we propose a fitting procedure for this class to given data. We furthermore consider an analogous extension of Kulkarni's multivariate phase-type class to the inhomogeneous framework

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 address here 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

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

In this paper we study some statistics linked to the average of Lipschitz-Killing (LK) curvatures of the excursion set of a stationary non-standard isotropic Gaussian field X on R 2. Under this hypothesis of unknown location and scale parameters of X, we introduce novel fundamental quantities, that we call effective level and effective spectral moment, and we derive unbiased and asymptotically normal

Regression models describing the joint distribution of multivariate response variables conditional on covariate information have become an important aspect of contemporary regression analysis. However, a limitation of such models is that they often rely on rather simplistic assumptions, e.g. a constant dependency structure that is not allowed to vary with the covariates or the restriction to linear

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 with marked empirical process approaches known from goodness-of-fit testing. The tests are consistent against general alternatives of a change

This paper deals with a situation when one is interested in 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

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

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.

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 weighted log-rank tests more robust against a broader family of alternatives, among them, considering linear combinations of weighted log-rank tests, and taking the maximum among a finite collection of them. In

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

The fitness coefficient, introduced in this paper, results from a competition between parametric and nonparametric density estimators within the likelihood of the data. As illustrated on several real datasets, the fitness coefficient generally agrees with p-values but is easier to compute and interpret. Namely, the fitness coefficient can be interpreted as the proportion of data coming from the parametric

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