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In a recent paper, the authors proposed a general methodology for probabilistic learning on manifolds. The method was used to generate numerical samples that are statistically consistent with an existing dataset construed as a realization…
In practice, data often contain discrete variables. But most of the popular nonparametric estimation methods have been developed in a purely continuous framework. A common trick among practitioners is to make discrete variables continuous…
This paper deals with the problem of estimating a slope parameter in a simple linear regression model, where independent variables have functional measurement errors. Measurement errors in independent variables, as is well known, cause…
A parameter estimation method is devised for a slow-fast stochastic dynamical system, where often only the slow component is observable. By using the observations only on the slow component, the system parameters are estimated by working on…
We propose a new series expansion method for the periapsis shift. The method formulates the periapsis shift in various spacetimes analytically without using special functions and provides simple and highly accurate approximate formulae. We…
We investigate high-dimensional nonconvex penalized regression, where the number of covariates may grow at an exponential rate. Although recent asymptotic theory established that there exists a local minimum possessing the oracle property…
Assume a (semi)parametrically efficient estimator is given of the Euclidean parameter in a (semi)parametric model. A submodel is obtained by constraining this model in that a continuously differentiable function of the Euclidean parameter…
The ability to obtain reliable point estimates of model parameters is of crucial importance in many fields of physics. This is often a difficult task given that the observed data can have a very high number of dimensions. In order to…
We study a nonlinear regression problem of fitting a circle (or a circular arc) to scattered data. We prove that under any standard assumptions on the statistical distribution of errors that are commonly adopted in the literature, the…
Given observations from a circular random variable contaminated by an additive measurement error, we consider the problem of minimax optimal goodness-of-fit testing in a non-asymptotic framework. We propose direct and indirect testing…
We consider a problem in parametric estimation: given $n$ samples from an unknown distribution, we want to estimate which distribution, from a given one-parameter family, produced the data. Following Schulman and Vazirani, we evaluate an…
We propose a stochastic variance-reduced cubic regularized Newton algorithm to optimize the finite-sum problem over a Riemannian submanifold of the Euclidean space. The proposed algorithm requires a full gradient and Hessian update at the…
Consider the setting where there are B>1 candidate statistical models, and one is interested in model selection. Two common approaches to solve this problem are to select a single model or to combine the candidate models through model…
Gradient information on the sampling distribution can be used to reduce the variance of Monte Carlo estimators via Stein's method. An important application is that of estimating an expectation of a test function along the sample path of a…
This paper proposes the estimation of a mutual shape from a set of different segmentation results using both active contours and information theory. The mutual shape is here defined as a consensus shape estimated from a set of different…
In this work, we propose a method for determining a non-uniform sampling scheme for multi-dimensional signals by solving a convex optimization problem reminiscent of the sensor selection problem. The resulting sampling scheme minimizes the…
The work develops further the theory of the following inversion problem, which plays the central role in the rapidly developing area of thermoacoustic tomography and has intimate connections with PDEs and integral geometry: {\it Reconstruct…
The field of machine have seen rising applications of equivariance criterion. However, there is no systematic way to justify its usage, including why it works, whether there is an optimal solution and if so, what form it carries. In this…
The technique of wrapping of a univariate probability distribution is very effective in getting a circular form of the underlying density. In this article, we introduce the circular (wrapped) version of xgamma distribution and study its…
The problem of recovering the configuration of points from their partial pairwise distances, referred to as the Euclidean Distance Matrix Completion (EDMC) problem, arises in a broad range of applications, including sensor network…