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Statistical modeling of multivariate and spatial extreme events has attracted broad attention in various areas of science. Max-stable distributions and processes are the natural class of models for this purpose, and many parametric families…
We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. The model considered in the paper is very general as we do not impose any…
This paper studies theory and inference of an observation-driven model for time series of counts. It is assumed that the observations follow a Poisson distribution conditioned on an accompanying intensity process, which is equipped with a…
In this article, a discrete analogue of continuous Teissier distribution is presented. Its several important distributional characteristics have been derived. The estimation of the unknown parameter has been done using the method of maximum…
This paper investigates the {\em nonasymptotic} properties of Bayes procedures for estimating an unknown distribution from $n$ i.i.d.\ observations. We assume that the prior is supported by a model $(\scr{S},h)$ (where $h$ denotes the…
This study develops a non-asymptotic Gaussian approximation theory for distributions of M-estimators, which are defined as maximizers of empirical criterion functions. In existing mathematical statistics literature, numerous studies have…
In this work, we consider an estimation method in sparse Poisson models inspired by [1] and provide novel sign consistency results under mild conditions.
We propose a principal components regression method based on maximizing a joint pseudo-likelihood for responses and predictors. Our method uses both responses and predictors to select linear combinations of the predictors relevant for the…
We present a new method of estimating the dispersion of a distribution which is based on the surprising property of a function that measures information processing intensity. It turns out that this function has a maximum at its fixed point.…
We propose a novel estimation approach for a general class of semi-parametric time series models where the conditional expectation is modeled through a parametric function. The proposed class of estimators is based on a Gaussian…
In this article, we study the problem of parameter estimation for a discrete Ornstein - Uhlenbeck model driven by Poisson fractional noise. Based on random walk approximation for the noise, we study least squares and maximum likelihood…
Observational cohort studies with oversampled exposed subjects are typically implemented to understand the causal effect of a rare exposure. Because the distribution of exposed subjects in the sample differs from the source population,…
We investigate a Poisson sampling design in the presence of unknown selection probabilities when applied to a population of unknown size for multiple sampling occasions. The fixed-population model is adopted and extended upon for inference.…
We generalize Taylor's theorem by introducing a stochastic formulation based on an underlying Poisson point process model. We utilize this approach to propose a novel non-linear regression framework and perform statistical inference of the…
We develop a novel asymptotic theory for local polynomial extremum estimators of time-varying parameters in a broad class of nonlinear time series models. We show the proposed estimators are consistent and follow normal distributions in…
We present a new, analytic, Poisson likelihood derived, technique to account for the statistical uncertainties inherent in simulation samples of limited size. This method has better coverage properties than other techniques, is valid for…
Any limiting point process for the time normalized exceedances of high levels by a stationary sequence is necessarily compound Poisson under appropriate long range dependence conditions. Typically exceedances appear in clusters. The…
This paper gives a review of concentration inequalities which are widely employed in non-asymptotical analyses of mathematical statistics in a wide range of settings, from distribution-free to distribution-dependent, from sub-Gaussian to…
Complex simulator-based models are now routinely used to perform inference across the sciences and engineering, but existing inference methods are often unable to account for outliers and other extreme values in data which occur due to…
We propose a novel approach for density estimation called histogram trend filtering. Our estimator arises from looking at surrogate Poisson model for counts of observations in a partition of the support of the data. We begin by showing…