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In this paper, we introduce a new estimator for the emission densities of a nonparametric hidden Markov model. It is adaptive and minimax with respect to each state's regularity--as opposed to globally minimax estimators, which adapt to the…
We estimate the support of a uniform density, when it is assumed to be a convex polytope or, more generally, a convex body in $\R^d$. In the polytopal case, we construct an estimator achieving a rate which does not depend on the dimension…
A theory of superefficiency and adaptation is developed under flexible performance measures which give a multiresolution view of risk and bridge the gap between pointwise and global estimation. This theory provides a useful benchmark for…
Recent work has focused on the problem of nonparametric estimation of information divergence functionals. Many existing approaches are restrictive in their assumptions on the density support set or require difficult calculations at the…
We discuss the problem of adaptive discrete-time signal denoising in the situation where the signal to be recovered admits a "linear oracle" -- an unknown linear estimate that takes the form of convolution of observations with a…
This paper considers the problem of estimating probabilities of the form $\mathbb{P}(Y \leq w)$, for a given value of $w$, in the situation that a sample of i.i.d.\ observations $X_1, \ldots, X_n$ of $X$ is available, and where we…
It has long been known that galaxy shapes align coherently with the large-scale density field. Characterizing this effect is essential to interpreting measurements of weak gravitational lensing, the deflection of light from distant galaxies…
This paper is concerned with a numerical solution to the scattering of a time-harmonic electromagnetic wave by a bounded and impenetrable obstacle in three dimensions. The electromagnetic wave propagation is modeled by a boundary value…
This paper introduces a straightforward sieve-based approach for estimating and conducting inference on regression parameters in panel data models with interactive fixed effects. The method's key assumption is that factor loadings can be…
The multiscale complexity of modern problems in computational science and engineering can prohibit the use of traditional numerical methods in multi-dimensional simulations. Therefore, novel algorithms are required in these situations to…
Distributed minimax estimation and distributed adaptive estimation under communication constraints for Gaussian sequence model and white noise model are studied. The minimax rate of convergence for distributed estimation over a given Besov…
We study the isotonic regression estimator over a general countable pre-ordered set. We obtain the limiting distribution of the estimator and study its properties. It is proved that, under some general assumptions, the limiting distribution…
High-dimensional data are ubiquitous in contemporary science and finding methods to compress them is one of the primary goals of machine learning. Given a dataset lying in a high-dimensional space (in principle hundreds to several thousands…
The Dirichlet prior is widely used in estimating discrete distributions and functionals of discrete distributions. In terms of Shannon entropy estimation, one approach is to plug-in the Dirichlet prior smoothed distribution into the entropy…
In this paper we consider the stacking of isotonic regression and the method of rearrangement with the empirical estimator to estimate a discrete distribution with an infinite support. The estimators are proved to be strongly consistent…
Assume a time-harmonic elastic wave is incident onto a penetrable anisotropic body embedded into a homogeneous isotropic background medium. We propose an equivalent variational formulation in a truncated bounded domain and show the…
This paper considers inference for conditional moment inequality models using a multiscale statistic. We derive the asymptotic distribution of this test statistic and use the result to propose feasible critical values that have a simple…
In this work we present an adaptive Newton-type method to solve nonlinear constrained optimization problems in which the constraint is a system of partial differential equations discretized by the finite element method. The adaptive…
In this paper, we analyze the convergence and optimality of a standard adaptive nonconforming linear element method for the Stokes problem. After establishing a special quasi--orthogonality property for both the velocity and the pressure in…
This paper presents a novel methodology of local adaptivity for the frequency-domain analysis of the vibrations of Reissner-Mindlin plates. The adaptive discretization is based on the recently developed Geometry Independent Field…