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Autoregressive models use chain rule to define a joint probability distribution as a product of conditionals. These conditionals need to be normalized, imposing constraints on the functional families that can be used. To increase…
We study a linear random coefficient model where slope parameters may be correlated with some continuous covariates. Such a model specification may occur in empirical research, for instance, when quantifying the effect of a continuous…
We study nonlinear serial dependence tests for non-Gaussian time series and residuals of dynamic models based on portmanteau statistics involving nonlinear autocovariances. A new test with an asymptotic $\chi^2$ distribution is introduced…
We propose a new optimization framework for aleatoric uncertainty estimation in regression problems. Existing methods can quantify the error in the target estimation, but they tend to underestimate it. To obtain the predictive uncertainty…
We propose a new class of R-estimators for semiparametric VARMA models in which the innovation density plays the role of the nuisance parameter. Our estimators are based on the novel concepts of multivariate center-outward ranks and signs.…
We often seek to estimate the causal effect of an exposure on a particular outcome in both randomized and observational settings. One such estimation method is the covariate-adjusted residuals estimator, which was designed for individually…
One of the central objectives of modern risk management is to find a set of risks where the probability of multiple simultaneous catastrophic events is negligible. That is, risks are taken only when their joint behavior seems sufficiently…
This paper investigates new ways of estimating and identifying causal, noncausal, and mixed causal-noncausal autoregressive models driven by a non-Gaussian error sequence. We do not assume any parametric distribution function for the…
We study a class of iterated empirical risk minimization (ERM) procedures in which two successive ERMs are performed on the same dataset, and the predictions of the first estimator enter as an argument in the loss function of the second.…
This paper establishes the asymptotic independence between the quadratic form and maximum of a sequence of independent random variables. Based on this theoretical result, we find the asymptotic joint distribution for the quadratic form and…
This paper derives the rate of convergence and asymptotic distribution for a class of Kolmogorov-Smirnov style test statistics for conditional moment inequality models for parameters on the boundary of the identified set under general…
Risk sensitive decision making finds important applications in current day use cases. Existing risk measures consider a single or finite collection of random variables, which do not account for the asymptotic behaviour of underlying…
We consider a situation where the distribution of a random variable is being estimated by the empirical distribution of noisy measurements of that variable. This is common practice in, for example, teacher value-added models and other…
In this paper, we establish the first and the second-order asymptotics of distributions of normalized maxima of independent and non-identically distributed bivariate Gaussian triangular arrays, where each vector of the $n$th row follows…
The extremal dependence structure of a regularly varying $d$-dimensional random vector can be described by its angular measure. The standard nonparametric estimator of this measure is the empirical measure of the observed angles of the $k$…
In this paper we investigate the dependence structure for PARMA models (i.e. ARMA models with periodic coefficients) with symmetric alpha-stable innovations. In this case the covariance function is not defined and therefore other measures…
A standard approach to computing expectations with respect to a given target measure is to introduce an overdamped Langevin equation which is reversible with respect to the target distribution, and to approximate the expectation by a…
Ergodic properties and asymptotic stationarity are investigated in this paper for the pseudo-covariance matrix (PCM) of a recursive state estimator which is robust against parametric uncertainties and is based on plant output measurements…
We derive the joint asymptotic distribution of empirical quantiles and expected shortfalls under general conditions on the distribution of the underlying observations. In particular, we do not assume that the distribution function is…
In many applications, hypothesis testing is based on an asymptotic distribution of statistics. The aim of this paper is to clarify and extend multiple correction procedures when the statistics are asymptotically Gaussian. We propose a…