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For a stationary moving average random field, a nonparametric 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)=∫ℝdg(s)w(h(s)x)ds, where g,h:ℝd→ℝ are given measurable functions and v is a (weighted) L2‐function on ℝ. We investigate conditions for the existence and uniqueness of this solution and give L2‐error bounds for the resulting estimates. An application to pure jump moving averages and a simulation study round off the paper. [ABSTRACT FROM AUTHOR]

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 in the log‐likelihood function via conjugate gradient and stochastic Lanczos on a Krylov subspace. These methods reduce the computational complexity from O(N3) to O(N2logN) and O(NlogN) for dense and sparse matrices, respectively. Moreover, we quantify the difference between the approximated log‐likelihood function and the original log‐likelihood function and establish the consistency of parameter estimates. Simulation studies are conducted to examine the computational efficiency as well as the finite‐sample properties. For illustration, our methodology is applied to analyze a large dataset comprising LiDAR estimates of forest canopy height in western Alaska. [ABSTRACT FROM AUTHOR]

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 sampling and change of variables. In the present paper we reformulate the problem by introducing an artificial parametric model in which X is a pivotal quantity, and next representing the conditional distribution of X given T(X)=t within this new model. The approach is illustrated by several examples, including a short simulation study and an application to goodness‐of‐fit testing of real data. The connection to a related approach based on sufficient statistics is briefly discussed. [ABSTRACT FROM AUTHOR]

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 framework, we introduce a class of variance functions that depends on the Lambert function. In this regard, we call it the Lambert class, which covers the variance functions of the natural exponential families generated by the subordinated gamma processes and the subordinated Lévy processes by the Poisson subordinator. Notice that the gamma process subordinated by the Poisson one is excluded from this class. The concept of reciprocity in natural exponential families was given in order to obtain an exponential family from another one. In this context, we get the reciprocal class of the natural exponential family generated by the class of subordinated Lévy processes. It is well known that the variance function represents an essential element for the determination of the quasi‐likelihood and deviance functions. Then, we use the expression of our variance function in order to maintain them. This leads us to analyze the proposed generalized linear model. We illustrate some of our models with applications to the daily exchange rate returns of the Tunisian Dinar against the U.S. Dollar and the damage incidents of ships. [ABSTRACT FROM AUTHOR]

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 nonzero coefficients and then select the final model from a small nested family by the Generalized Information Criterion. We derive exponential upper bounds on the selection error of the method. These results confirm that, at least for normal linear models, our algorithm seems to be the benchmark for the theory of model selection as it is constructive, computationally efficient and leads to consistent model selection under weak assumptions. Constructivity of the algorithm means that, in contrast to the TL, SCAD or MCP, consistent selection does not rely on the unknown parameters as the cone invertibility factor. Instead, our algorithm only needs the sample size, the number of predictors and an upper bound on the noise parameter. We show in numerical experiments on synthetic and real‐world datasets that an implementation of our algorithm is more accurate than implementations of studied concave regularizations. Our procedure is included in the R package DMRnet and available in the CRAN repository. [ABSTRACT FROM AUTHOR]

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 based on polynomial splines approximation are developed. The consistency and asymptotic normality of the proposed estimators are provided. Simulation studies show that the naive estimators which either ignore the past event feedback or the measurement errors are biased. Our method has a better coverage probability of the time‐varying/constant coefficients, compared to the naive methods. An application to the dataset from the Atherosclerosis Risk in Communities Study, which is also the motivating example to develop the method, is presented. [ABSTRACT FROM AUTHOR]

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 target matrix into factors and estimate these factors in turn by the kernel approach. The resulting estimator is further regularized by thresholding and optimal shrinkage. Under certain mixing and sparsity conditions, we show that the proposed estimator is well‐conditioned and uniformly consistent with the underlying matrix function even when the sample is dependent. Simulation studies suggest that the proposed estimator significantly outperforms its competitors in terms of integrated root‐squared estimation error. We present an application to financial return data. [ABSTRACT FROM AUTHOR]

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 parameter of the kernel function and the stability index of the driving Lévy motion. We extend their work to allow for a multiparametric framework that in particular includes the important examples of the linear fractional stable motion, the stable Ornstein–Uhlenbeck process, certain CARMA(2, 1) models, and Ornstein–Uhlenbeck processes with a periodic component among other models. We present both the consistency and the associated central limit theorem of the minimal contrast estimator. Furthermore, we demonstrate numerical analysis to uncover the finite sample performance of our method. [ABSTRACT FROM AUTHOR]

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) moment‐based measure as well as difficult statistical inference and strange behaviour for discrete distributions for quantile‐based measures. Therefore, in this paper, we introduce skewness measures based on or connected with expectiles. Since expectiles can be seen as smoothed versions of quantiles, they preserve the advantages over the moment‐based measure while not exhibiting most of the disadvantages of quantile‐based measures. We introduce corresponding empirical counterparts and derive asymptotic properties. Finally, we conduct a simulation study, comparing the newly introduced measures with established ones, and evaluating the performance of the respective estimators. [ABSTRACT FROM AUTHOR]

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 (MCMC) methods are commonly used to allow us to infer such missing or censored data. However, for large disease systems, these methods can be highly computationally expensive. In this paper, we propose two methods of approximate inference for such situations based on so‐called emulation techniques. Here, both methods are set in a Bayesian MCMC framework but replace the computationally expensive likelihood function by a Gaussian process‐based likelihood approximation. In the first method, we build an emulator of the discrepancy between summary statistics of simulated and observed epidemic data. In the second method, we develop an emulator of an importance sampling‐based likelihood approximation. We show how both methods offer substantial computational efficiency gains over standard Bayesian MCMC‐based method, and can be used to infer the transmission of complex infectious disease systems. We also show that importance sampling‐based methods tend to perform more satisfactorily. [ABSTRACT FROM AUTHOR]

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 from an application‐oriented standpoint, it requires a new method of proof to replace the established ones for the univariate case. The main purpose of this paper is to show the uniform consistency and to provide the rates of convergence of the considered nonparametric estimator for both multivariate random covariates and multivariate deterministic design points. To demonstrate the performance of the estimators, the small sample behavior is investigated in a simulation study in dimension two and three. [ABSTRACT FROM AUTHOR]

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 copula offers additional flexibility and accuracy in describing the dependence structure. We propose a two‐step semi‐parametric estimation method and develop asymptotic properties of the estimators. Moreover, we introduce model selection procedures to select the component copulas of the conditional mixture copula model. Simulation results suggest that the proposed procedures have a good performance in estimating and selecting conditional mixture copulas with different model specifications. The proposed model is then applied to investigate how the dependence structures among international equity markets evolve with the volatility in the exchange rate markets. [ABSTRACT FROM AUTHOR]

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 class to given data. We furthermore consider an analogous extension of Kulkarni's multivariate PH class (Kulkarni, 1989) to the inhomogeneous framework and study parameter estimation for the resulting new and flexible class of multivariate distributions. As a by‐product, we amend a previously suggested fitting procedure for the homogeneous multivariate PH case and provide appropriate adaptations for censored data. The performance of the algorithms is illustrated in several numerical examples, both for simulated and real‐life insurance data. [ABSTRACT FROM AUTHOR]

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. However, expectiles and their sample versions do not benefit from a simple explicit form, making their analysis significantly harder than that of quantiles and order statistics. This difficulty is compounded when one wishes to integrate auxiliary information about the phenomenon of interest through a finite‐dimensional covariate, in which case the problem becomes the estimation of conditional expectiles. In this paper, we exploit the fact that the expectiles of a distribution F are in fact the quantiles of another distribution E explicitly linked to F, in order to construct nonparametric kernel estimators of extreme conditional expectiles. We analyze the asymptotic properties of our estimators in the context of conditional heavy‐tailed distributions. Applications to simulated data and real insurance data are provided. [ABSTRACT FROM AUTHOR]

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 the maximum pseudo‐likelihood method. It is proved that under some appropriate regularity assumptions the estimator calculated from the residuals has the same asymptotic distribution as the estimator based on the unobserved errors. In such case one can ignore the fact that the response is first adjusted for the effect of the covariate. The theoretical results are accompanied by a Monte Carlo simulation study which illustrates that the maximum pseudo‐likelihood estimator based on residuals may behave poorly when the stated regularity assumptions are not satisfied. [ABSTRACT FROM AUTHOR]

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. In addition to the theoretical results of similar methods we prove the consistency of our estimate for divergent number of p. Finally, we demonstrate the advantages of our algorithm using simulated and real datasets. [ABSTRACT FROM AUTHOR]

This role for alternatives (or similar) in non-decision HT ht -values is not new: after first discussing some exceptions Cox ([2], section 2.7) acknowledges how alternatives generally drive choice of divergence measures. Finally, I very much doubt this process will be compatible with the strong likelihood principle - but if so, that would be a problem for the strong likelihood principle, and not divergence HT ht -values. Decision P$$ P $$-values: A Distinction Worth Making in Theory and Keeping in Practice - or, How Divergence P$$ P $$-values Measure Evidence Even When Decision P$$ P $$-values Do Not" by Sander Greenland. [Extracted from the article]