Related papers: Optimal R-Estimation of a Spherical Location

We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a…

The real Ginibre spherical ensemble consists of random matrices of the form $A B^{-1}$, where $A,B$ are independent standard real Gaussian $N \times N$ matrices. The expected number of real eigenvalues is known to be of order $\sqrt{N}$. We…

We present algorithms for solving spatially nonlocal diffusion models on the unit sphere with spectral accuracy in space. Our algorithms are based on the diagonalizability of nonlocal diffusion operators in the basis of spherical harmonics,…

We prove localization at the bottom of the spectrum for a random Schr\"odinger operator in the continuum with a single-site potential probability distribution supported by a Cantor set of zero Lebesgue measure. This distribution is too…

This paper proposes consistent estimators for transformation parameters in semiparametric models. The problem is to find the optimal transformation into the space of models with a predetermined regression structure like additive or…

We provide novel theoretical results regarding local optima of regularized $M$-estimators, allowing for nonconvexity in both loss and penalty functions. Under restricted strong convexity on the loss and suitable regularity conditions on the…

The distribution of the spacing, or the difference between consecutive order statistics, is known only for uniform and exponential random variates. We add here logistic and Gumbel variates, and present an estimator for distributions with a…

The SLAM problem is known to have a special property that when robot orientation is known, estimating the history of robot poses and feature locations can be posed as a standard linear least squares problem. In this work, we develop a SLAM…

Sampling from multimodal distributions is a challenging task in scientific computing. When a distribution has an exact symmetry between the modes, direct jumps among them can accelerate the samplings significantly. However, the…

We revisit the problem of estimating the center of symmetry $\theta$ of an unknown symmetric density $f$. Although Stone (1975), Van Eden (1970), and Sacks (1975) constructed adaptive estimators of $\theta$ in this model, their estimators…

We study the problem of signal source localization using angle of arrival (AOA) measurements. We begin by presenting verifiable geometric conditions for sensor deployment that ensure the model's asymptotic localizability. Then we establish…

One-dimensional scattering mediated by non-Hermitian Hamiltonians is studied. A schematic set of models is used which simulate two point interactions at a variable strength and distance. The feasibility of the exact construction of the…

We consider one of the most important problems in directional statistics, namely the problem of testing the null hypothesis that the spike direction $\theta$ of a Fisher-von Mises-Langevin distribution on the $p$-dimensional unit…

The asymptotic efficiency of the spatial sign covariance matrix (SSCM) relative to affine equivariant estimates of scatter is studied in detail. In particular, the SSCM is shown to be asymptoticaly inadmissible, i.e. the asymptotic…

This paper deals with the asymptotic statistical properties of a class of redescending M-estimators in linear models with increasing dimension. This class is wide enough to include popular high breakdown point estimators such as…

We study the approximation of the radiative transfer equation with a relatively few moments in the spherically symmetric case. We propose a three-moment model based on choosing the beta distribution as the ansatz for the specific intensity.…

Robust estimators, like the median of a point set, are important for data analysis in the presence of outliers. We study robust estimators for locationally uncertain points with discrete distributions. That is, each point in a data set has…

Let $(X_i)_{i=1,...,n}$ be a possibly nonstationary sequence such that $\mathscr{L}(X_i)=P_n$ if $i\leq n\theta$ and $\mathscr{L}(X_i)=Q_n$ if $i>n\theta$, where $0<\theta <1$ is the location of the change-point to be estimated. We…

Scattering of nonstationary electromagnetic fields from axially symmetrical bodies is numerically investigated. Simulations are performed using the time- and frequency-domain approaches. Computational results obtained for a finite perfectly…

M-estimation, aka empirical risk minimization, is at the heart of statistics and machine learning: Classification, regression, location estimation, etc. Asymptotic theory is well understood when the loss satisfies some smoothness…