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Maximum likelihood style estimators possesses a number of ideal characteristics, but require prior identification of the distribution of errors to ensure exact unbiasedness. Independent of the focus of the primary statistical analysis, the…
We consider nonparametric estimation of a mixed discrete-continuous distribution under anisotropic smoothness conditions and possibly increasing number of support points for the discrete part of the distribution. For these settings, we…
We consider inference procedures, conditional on an observed ancillary statistic, for regression coefficients under a linear regression setup where the unknown error distribution is specified nonparametrically. We establish conditional…
The asymptotic variance of the maximum likelihood estimate is proved to decrease when the maximization is restricted to a subspace that contains the true parameter value. Maximum likelihood estimation allows a systematic fitting of…
The existence and consistency of a maximum likelihood estimator for the joint probability distribution of random parameters in discrete-time abstract parabolic systems are established by taking a nonparametric approach in the context of a…
The paper offers a novel unified approach to studying the accuracy of parameter estimation by the quasi likelihood method. Important features of the approach are: (1) The underlying model {is not assumed to be parametric}. (2) No conditions…
Hyperbolic space has become a popular choice of manifold for representation learning of various datatypes from tree-like structures and text to graphs. Building on the success of deep learning with prototypes in Euclidean and hyperspherical…
Exploiting a relationship between closed geodesics on a generic closed hyperbolic surface S and a certain unipotent flow on the product space T_1(S) x T_1(S), we obtain a local asymptotic equidistribution result for long closed geodesics on…
Likelihood inference for max-stable random fields is in general impossible because their finite-dimensional probability density functions are unknown or cannot be computed efficiently. The weighted composite likelihood approach that…
In this paper, we study the localization phenomena in a slender cylinder composed of an incompressible hyperelastic material subjected to axial tension. We aim to construct the analytical solutions based on a three-dimensional setting and…
Max-stable distributions and processes are important models for extreme events and the assessment of tail risks. The full, multivariate likelihood of a parametric max-stable distribution is complicated and only recent advances enable its…
A procedure for asymptotic bias reduction of maximum likelihood estimates of generic estimands is developed. The estimator is realized as a plug-in estimator, where the parameter maximizes the penalized likelihood with a penalty function…
Random hyperbolic graphs have been suggested as a promising model of social networks. A few of their fundamental parameters have been studied. However, none of them concerns their spectra. We consider the random hyperbolic graph model as…
We investigate the asymptotic behavior of high-codimensional area-minimizing locally rectifiable currents in hyperbolic space, addressing a problem posed by F.H. Lin and establishing ``boundary regularity at infinity" results for such…
We consider equilibrium statistical mechanics of a simplified model for the ideal conductor electrode in an interface contact with a classical semi-infinite electrolyte, modeled by the two-dimensional Coulomb gas of pointlike $\pm$ unit…
We present a new proof of the existence of normally hyperbolic manifolds and their whiskers for maps. Our result is not perturbative. Based on the bounds on the map and its derivative, we establish the existence of the manifold within a…
Estimating symmetric properties of a distribution, e.g. support size, coverage, entropy, distance to uniformity, are among the most fundamental problems in algorithmic statistics. While each of these properties have been studied extensively…
Given a zero-mean Gaussian random field with a covariance function that belongs to a parametric family of covariance functions, we introduce a new notion of likelihood approximations, termed truncated-likelihood functions.…
We derive the joint asymptotic distribution of the outlier eigenvalues of an additively deformed Wigner matrix $H$. Our only assumptions on the deformation are that its rank be fixed and its norm bounded. Our results extend those of [The…
Correlated random fields are a common way to model dependence struc- tures in high-dimensional data, especially for data collected in imaging. One important parameter characterizing the degree of dependence is the asymp- totic variance…