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There are many models, often called unnormalized models, whose normalizing constants are not calculated in closed form. Maximum likelihood estimation is not directly applicable to unnormalized models. Score matching, contrastive divergence…
We use the delta method and Stein's method to derive, under regularity conditions, explicit upper bounds for the distributional distance between the distribution of the maximum likelihood estimator (MLE) of a $d$-dimensional parameter and…
Spatially isotropic max-stable processes have been used to model extreme spatial or space-time observations. One prominent model is the Brown-Resnick process, which has been successfully fitted to time series, spatial data and space-time…
We propose a general framework for the estimation of observables with generative neural samplers focusing on modern deep generative neural networks that provide an exact sampling probability. In this framework, we present asymptotically…
Multivariate extreme value statistical analysis is concerned with observations on several variables which are thought to possess some degree of tail-dependence. In areas such as the modeling of financial and insurance risks, or as the…
This paper proposes a novel method for testing observability in Gaussian models using discrete density approximations (deterministic samples) of (multivariate) Gaussians. Our notion of observability is defined by the existence of the…
Estimation of density functions supported on general domains arises when the data is naturally restricted to a proper subset of the real space. This problem is complicated by typically intractable normalizing constants. Score matching…
This paper provides conditions under which subsampling and the bootstrap can be used to construct estimators of the quantiles of the distribution of a root that behave well uniformly over a large class of distributions $\mathbf{P}$. These…
Invertibility conditions for observation-driven time series models often fail to be guaranteed in empirical applications. As a result, the asymptotic theory of maximum likelihood and quasi-maximum likelihood estimators may be compromised.…
In recent years, addressing the challenges posed by massive datasets has led researchers to explore aggregated data, particularly leveraging interval-valued data, akin to traditional symbolic data analysis. While much recent research, with…
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…
The subject of robust estimation in time series is widely discussed in literature. One of the approaches is to use GM-estimation. This method incorporates a broad class of nonparametric estimators which under suitable conditions includes…
In this paper we propose methods for inference of the geometric features of a multivariate density. Our approach uses multiscale tests for the monotonicity of the density at arbitrary points in arbitrary directions. In particular, a…
We present a local density estimator based on first order statistics. To estimate the density at a point, $x$, the original sample is divided into subsets and the average minimum sample distance to $x$ over all such subsets is used to…
We give a simple conceptual proof of the consistency of a test for multivariate uniformity in a bounded set $K \subset \mathbb{R}^d$ that is based on the maximal spacing generated by i.i.d. points $X_1, \ldots,X_n$ in $K$, i.e., the volume…
Maximum margin binary classification is one of the most fundamental algorithms in machine learning, yet the role of featurization maps and the high-dimensional asymptotics of the misclassification error for non-Gaussian features are still…
The maximum score estimator of Manski (1975) provides an elegant approach to estimate slope coefficient in binary choice models without requiring parametric assumptions on the error distribution. However, under i.i.d. sampling, it admits a…
The traditional Schmidt density estimator has been proven to be unbiased and effective in a magnitude-limited sample. Previously, efforts have been made to generalize it for populations with non-uniform density and proper motion-limited…
We study weighted M-estimators for $\mathbb{R}^d$-valued clustered data and give sufficient conditions for their consistency. Their asymptotic normality is established with estimation of the asymptotic covariance matrix. We address the…
This paper generalizes recent proposals of density forecasting models and it develops theory for this class of models. In density forecasting, the density of observations is estimated in regions where the density is not observed.…