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

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

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

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

State space models (SSMs) are now ubiquitous in many fields and increasingly complicated with observed and unobserved variables often interacting in non‐linear 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

In health research interest often lies in modeling a failure time process but in many cohort studies failure status is only determined at scheduled assessment times. While the assessment times may be fixed upon study entry, individuals may become lost to follow‐up and miss visits subsequent to the time of loss to follow‐up. We consider a three‐state model to characterize a joint failure and loss to

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

In the present paper, 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. Simulation

This manuscript 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

The nonlinear responses of species to environmental variability can play an important role in the maintenance of ecological diversity. Nonetheless, many models use parametric nonlinear terms which pre‐determine the ecological conclusions. Motivated by this concern, we study the estimate of the second derivative (curvature) of the link function in a functional single index model. Since the coefficient

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

We study a novel class of affine invariant and consistent tests for normality in any dimension in an i.i.d.‐setting. The tests are based on a characterization of the standard d ‐variate normal distribution as the unique solution of an initial value problem of a partial ifferential equation motivated by the harmonic oscillator, which is a special case of a Schrodinger operator. We derive the asymptotic

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 this paper, we investigate a new procedure for the estimation of a linear quantile regression with possibly right‐censored responses. Contrary to the main literature on the subject, we propose in this context to circumvent the formulation of conditional quantiles through the socalled “check” loss function that stems from the influential work of Koenker and Bassett (1978). Instead, our suggestion

In this article we study the theoretical properties of the simultaneous multiscale change point estimator (SMUCE) in piecewise‐constant signal models with dependent error processes. Empirical studies suggest that in this case the change point estimate is inconsistent, but it is not known if alternatives suggested in the literature for correlated data are consistent. We propose a modification of SMUCE

No abstract is available for this article.

The case‐cohort study design is widely used to reduce cost when collecting expensive covariates in large cohort studies with survival or competing risks outcomes. A case‐cohort study dataset consists of two parts: (a) a random sample and (b) all cases or failures from a specific cause of interest. Clinicians often assess covariate effects on competing risks outcomes. The proportional subdistribution

The classical multivariate extreme‐value theory concerns the modeling of extremes in a multivariate random sample, suggesting the use of max‐stable distributions. In this work, the classical theory is extended to the case where aggregated data, such as maxima of a random number of observations, are considered. We derive a limit theorem concerning the attractors for the distributions of the aggregated

We address the identifiability and estimation of recursive max‐linear structural equation models represented by an edge‐weighted directed acyclic graph (DAG). Such models are generally unidentifiable and we identify the whole class of DAG s and edge weights corresponding to a given observational distribution. For estimation, standard likelihood theory cannot be applied because the corresponding families

We study nonparametric maximum likelihood estimation for two classes of multivariate distributions that imply strong forms of positive dependence; namely log‐supermodular (MTP2) distributions and log‐L♮‐concave (LLC) distributions. In both cases we also assume log‐concavity in order to ensure boundedness of the likelihood function. Given n independent and identically distributed random vectors from

The analysis of natural direct and principal stratum direct effects has a controversial history in statistics and causal inference as these effects are commonly identified with either untestable cross world independence or graphical assumptions. This paper demonstrates that the presence of individual level natural direct and principal stratum direct effects can be identified without cross world independence

No abstract is available for this article.

There is a growing need for flexible methods to analyze interval‐valued data, which can provide efficient data representations for very large data sets. However, the existing descriptive frameworks to achieve this ignore the process by which interval‐valued data are typically constructed, namely, by the aggregation of real‐valued data generated from some underlying process. In this paper, we develop

In this paper, we revisit the construction of confidence intervals for extreme quantiles of Pareto‐type distributions. A novel asymptotic pivotal quantity is proposed for these quantile estimators, which leads to new asymptotic confidence intervals that exhibit more accurate coverage probability. This pivotal quantity also allows for the construction of a saddle‐point approximation, from which a second

We study the asymptotic behavior of the marginal expected shortfall when the two random variables are asymptotic independent but positively associated, which is modeled by the so‐called tail dependent coefficient. We construct an estimator of the marginal expected shortfall, which is shown to be asymptotically normal. The finite sample performance of the estimator is investigated in a small simulation

When the primary outcome is hard to collect, a surrogate endpoint is typically used as a substitute. However, even when a treatment has a positive average causal effect (ACE) on a surrogate endpoint, which also has a positive ACE on the primary outcome, it is still possible that the treatment has a negative ACE on the primary outcome. Such a phenomenon is called the surrogate paradox and greatly challenges

This paper studies cyclic long‐memory processes with Gegenbauer‐type spectral densities. For a semiparametric statistical model, new simultaneous estimates for singularity location and long‐memory parameters are proposed. This generalized filtered method‐of‐moments approach is based on general filter transforms that include wavelet transformations as a particular case. It is proved that the estimates

This paper deals with the nonparametric estimation of the mean and variance functions of univariate time series data. We propose a nonparametric dimension reduction technique for both mean and variance functions of time series. This method does not require any model specification and instead we seek directions in both the mean and variance functions such that the conditional distribution of the current

The degrees are a classical and relevant way to study the topology of a network. They can be used to assess the goodness of fit for a given random graph model. In this paper, we introduce goodness‐of‐fit tests for two classes of models. First, we consider the case of independent graph models such as the heterogeneous Erdös‐Rényi model in which the edges have different connection probabilities. Second

There are many approaches in the estimation of spectral density. With regard to parametric approaches, different divergences are proposed in fitting a certain parametric family of spectral densities. Moreover, nonparametric approaches are also quite common considering the situation when we cannot specify the model of process. In this paper, we develop a local Whittle likelihood approach based on a

We present a Bayesian model selection approach to estimate the intrinsic dimensionality of a high‐dimensional dataset. To this end, we introduce a novel formulation of the probabilisitic principal component analysis model based on a normal‐gamma prior distribution. In this context, we exhibit a closed‐form expression of the marginal likelihood which allows to infer an optimal number of components.

We describe inferactive data analysis, so‐named to denote an interactive approach to data analysis with an emphasis on inference after data analysis. Our approach is a compromise between Tukey's exploratory and confirmatory data analysis allowing also for Bayesian data analysis. We see this as a useful step in concrete providing tools (with statistical guarantees) for current data scientists. The basis

A new nonparametric quantile regression method based on the concept of optimal quantization was developed recently and was showed to provide estimators that often dominate their classical, kernel‐type, competitors. In the present work, we extend this method to multiple‐output regression problems. We show how quantization allows approximating population multiple‐output regression quantiles based on

This article presents a clustering approach that allows for rigorous statistical error control similar to a statistical test. We develop estimators for both the unknown number of clusters and the clusters themselves. The estimators depend on a tuning parameter α which is similar to the significance level of a statistical hypothesis test. By choosing α, one can control the probability of overestimating

Variable selection over a potentially large set of covariates in a linear model is quite popular. In the Bayesian context, common prior choices can lead to a posterior expectation of the regression coefficients that is a sparse (or nearly sparse) vector with a few nonzero components, those covariates that are most important. This article extends the “global‐local” shrinkage idea to a scenario where

A common goal in observational research is to estimate marginal causal effects in the presence of confounding variables. One solution to this problem is to use the covariate distribution to weight the outcomes such that the data appear randomized. The propensity score is a natural quantity that arises in this setting. Propensity score weights have desirable asymptotic properties, but they often fail

Variable screening for censored survival data is most challenging when both survival and censoring times are correlated with an ultrahigh‐dimensional vector of covariates. Existing approaches to handling censoring often make use of inverse probability weighting by assuming independent censoring with both survival time and covariates. This is a convenient but rather restrictive assumption which may

In this article, we propose a new technique for constructing confidence intervals for the mean of a noisy sequence with multiple change‐points. We use the weighted bootstrap to generalize the bootstrap aggregating or bagging estimator. A standard deviation formula for the bagging estimator is introduced, based on which smoothed confidence intervals are constructed. To further improve the performance

In genetic association studies, detecting phenotype–genotype association is a primary goal. We assume that the relationship between the data—phenotype, genetic markers and environmental covariates—can be modeled by a generalized linear model. The number of markers is allowed to be far greater than the number of individuals of the study. A multivariate score statistic is used to test each marker for

In a high‐dimensional multiple testing framework, we present new confidence bounds on the false positives contained in subsets S of selected null hypotheses. These bounds are post hoc in the sense that the coverage probability holds simultaneously over all S, possibly chosen depending on the data. This article focuses on the common case of structured null hypotheses, for example, along a tree, a hierarchy

Consider the problem of pointwise estimation of f in a multivariate isotonic regression model Z=f(X1,…,Xd)+ϵ, where Z is the response variable, f is an unknown nonparametric regression function, which is isotonic with respect to each component, and ϵ is the error term. In this article, we investigate the behavior of the least squares estimator of f. We generalize the greatest convex minorant characterization

In this article, we define a new boosting‐type algorithm for multiplicative model combination using as loss function the Hyvärinen scoring rule. In particular, we focus on density estimation problems and the aim is to define a suitable estimator, using a multiplicative combination of elementary density functions, which correspond to simplified or partially specified probability models for the interest

Let f ^ n be the nonparametric maximum likelihood estimator of a decreasing density. Grenander characterized this as the left‐continuous slope of the least concave majorant of the empirical distribution function. For a sample from the uniform distribution, the asymptotic distribution of the L2‐distance of the Grenander estimator to the uniform density was derived in an article by Groeneboom and Pyke

We propose a survey weighted quadratic inference function method for the analysis of data collected from longitudinal surveys, as an alternative to the survey weighted generalized estimating equation method. The procedure yields estimators of model parameters, which are shown to be consistent and have a limiting normal distribution. Furthermore, based on the inference function, a pseudolikelihood ratio

Estimating function inference is indispensable for many common point process models where the joint intensities are tractable while the likelihood function is not. In this article, we establish asymptotic normality of estimating function estimators in a very general setting of nonstationary point processes. We then adapt this result to the case of nonstationary determinantal point processes, which

We propose a new model for regression and dependence analysis when addressing spatial data with possibly heavy tails and an asymmetric marginal distribution. We first propose a stationary process with t marginals obtained through scale mixing of a Gaussian process with an inverse square root process with Gamma marginals. We then generalize this construction by considering a skew‐Gaussian process, thus

We propose a novel method for tensorial‐independent component analysis. Our approach is based on TJADE and k‐JADE, two recently proposed generalizations of the classical JADE algorithm. Our novel method achieves the consistency and the limiting distribution of TJADE under mild assumptions and at the same time offers notable improvement in computational speed. Detailed mathematical proofs of the statistical

We define a nonlinear autoregressive time series model based on the generalized hyperbolic distribution in an attempt to model time series with non‐Gaussian features such as skewness and heavy tails. We show that the resulting process has a simple condition for stationarity and it is also ergodic. An empirical example with a forecasting experiment is presented to illustrate the features of the proposed

In this work, we introduce a class of dynamic models for time series taking values on the unit interval. The proposed model follows a generalized linear model approach where the random component, conditioned on the past information, follows a beta distribution, while the conditional mean specification may include covariates and also an extra additive term given by the iteration of a map that can present

We estimate model parameters of Lévy‐driven causal continuous‐time autoregressive moving average random fields by fitting the empirical variogram to the theoretical counterpart using a weighted least squares (WLS) approach. Subsequent to deriving asymptotic results for the variogram estimator, we show strong consistency and asymptotic normality of the parameter estimator. Furthermore, we conduct a

Unequal probability sampling is commonly used for sample selection. In the context of spatial sampling, the variables of interest often present a positive spatial correlation, so that it is intuitively relevant to select spatially balanced samples. In this article, we study the properties of pivotal sampling and propose an application to tesselation for spatial sampling. We also propose a simple conservative

Testing the existence of a quantitative trait locus (QTL) effect is an important task in QTL mapping studies. Most studies concentrate on the case where the phenotype distributions of different QTL groups follow normal distributions with the same unknown variance. In this paper we make a more general assumption that the phenotype distributions come from a location‐scale distribution family. We derive

We investigate a generalized semiparametric regression. Such a model can avoid the risk of wrongly choosing the base measure function. We propose a profile likelihood to efficiently estimate both parameter and nonparametric function. The main difference from the classical profile likelihood is that the profile likelihood proposed is a functional of the base measure function, instead of a function of

This paper shows that the term structure of conditional (i.e. predictive) distributions allows for closed form expression in a large family of (possibly higher order or infinite order) thinning‐based count processes such as INAR(p), INARCH(p), NBAR(p), and INGARCH(1,1). Such predictive distributions are currently often deemed intractable by the literature and existing approximation methods are usually

The prediction error for mixed models can have a conditional or a marginal perspective depending on the research focus. We introduce a novel conditional version of the optimism theorem for mixed models linking the conditional prediction error to covariance penalties for mixed models. Different possibilities for estimating these conditional covariance penalties are introduced. These are bootstrap methods

In this article, we consider clustering based on principal component analysis (PCA) for high‐dimensional mixture models. We present theoretical reasons why PCA is effective for clustering high‐dimensional data. First, we derive a geometric representation of high‐dimension, low‐sample‐size (HDLSS) data taken from a two‐class mixture model. With the help of the geometric representation, we give geometric

In this paper, the maximum spacing method is considered for multivariate observations. Nearest neighbor balls are used as a multidimensional analogue to univariate spacings. A class of information‐type measures is used to generalize the concept of maximum spacing estimators of model parameters. Asymptotic normality of these generalized maximum spacing estimators is proved when the assigned model class

The conditional tail expectation (CTE) is an indicator of tail behavior that takes into account both the frequency and magnitude of a tail event. However, the asymptotic normality of its empirical estimator requires that the underlying distribution possess a finite variance; this can be a strong restriction in actuarial and financial applications. A valuable alternative is the median shortfall (MS)

Methods for constructing confidence intervals for variance component ratios in general unbalanced mixed models are developed. The methods are based on inverting the distribution of the signed root of the log‐likelihood ratio statistic constructed from either the restricted maximum likelihood or the full likelihood. As this distribution is intractable, the inversion is rather based on using a saddlepoint