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We analyze fluctuations of random walks with generally distributed increments. Integral representations for key performance measures are obtained by extending an inversion theorem of Hewitt [11] for Laplace-Stieltjes transforms. Another…
A significant obstacle in the development of robust machine learning models is covariate shift, a form of distribution shift that occurs when the input distributions of the training and test sets differ while the conditional label…
We define a class of multivariate maxima of moving multivariate maxima, generalising the M4 processes. For these stationary multivariate time series we characterise the joint distribution of extremes and compute the multivariate extremal…
After having closely re-examined the notion of a L\'evy's stable vector, it is shown that the notion of a stable multivariate distribution is more general than previously defined. Indeed, a more intrinsic vector definition is obtained with…
In modeling multivariate time series for either forecast or policy analysis, it would be beneficial to have figured out the cause-effect relations within the data. Regression analysis, however, is generally for correlation relation, and…
Atar, Chowdhary and Dupuis have recently exhibited a variational formula for exponential integrals of bounded measurable functions in terms of R\'enyi divergences. We develop a variational characterization of the R\'enyi divergences between…
Varying coefficient models are useful in applications where the effect of the covariate might depend on some other covariate such as time or location. Various applications of these models often give rise to case-specific prior distributions…
This paper shows that the degree of approximate multicollinearity in a linear regression model increases simply by including independent variables, even if these are not highly linearly related. In the current situation where it is…
Individual-specific, time-constant, random effects are often used to model dependence and/or to account for omitted covariates in regression models for longitudinal responses. Longitudinal studies have known a huge and widespread use in the…
The multivariate version of the Mixed Tempered Stable is proposed. It is a generalization of the Normal Variance Mean Mixtures. Characteristics of this new distribution and its capacity in fitting tails and capturing dependence structure…
In this paper we consider a variety of procedures for numerical statistical inference in the family of univariate and multivariate stable distributions. In connection with univariate distributions (i) we provide approximations by finite…
An approach to inference for relative sparsity was developed in prior work, and an adaptive lasso asymptotic normality theorem was given there, but this theorem was not fully used when estimating the variance of the policy coefficients.…
We construct and analyze an estimator of association between random variables based on their similarity in both direction and magnitude. Under special conditions, the proposed measure becomes a robust and consistent estimator of the linear…
We provide a unified approach to MM-estimation with auxiliary scale for balanced linear models with structured covariance matrices. This approach leads to estimators that are highly robust against outliers and highly efficient for normal…
We define a model for the joint distribution of multiple continuous latent variables which includes a model for how their correlations depend on explanatory variables. This is motivated by and applied to social scientific research questions…
The problem of inferring the distribution of a random vector given that its norm is large requires modeling a homogeneous limiting density. We suggest an approach based on graphical models which is suitable for high-dimensional vectors. We…
This survey provides a self-contained account of $M$-estimation of multivariate scatter. In particular, we present new proofs for existence of the underlying $M$-functionals and discuss their weak continuity and differentiability. This is…
In this paper we obtain advances for the concept of directional $\rho$-coefficients, originally defined for the trivariate case in [Nelsen, R.B., \'Ubeda-Flores, M. (2011). Directional dependence in multivariate distributions. Ann. Inst.…
This paper presents a new class of regression models for continuous data restricted to the interval $(0,1)$, such as rates and proportions. The proposed class of models assumes a beta distribution for the variable of interest with…
Models based on assumptions of multivariate regular variation and hidden regular variation provide ways to describe a broad range of extremal dependence structures when marginal distributions are heavy tailed. Multivariate regular variation…