This article is concerned with the estimation of a varying-coefficient regression model when the explanatory variables are measured with additive errors and the response variable is sometimes missing. Estimated coefficient function in complete observational data and interpolation data respectively, and all the proposed estimators for the coefficient function are proved to be asymptotic normalit...

The sensitivity of generalized matrix Lyapunov equations relative to perturbations in the coefficient matrices is studied. New local and non-local perturbation bounds are obtained.

Pearson’s correlation coefficient is used to describe dependence between random variables X and Y . In some practical situations, however, we have strong correlation for some values X and/or Y and no correlation for other values ofX and Y . To describe such a local dependence, we come up with a natural localized version of Pearson’s correlation coefficient. We also study the properties of the n...

In this paper, we present a detailed analysis of the global clustering coefficient in scale-free graphs. Many observed real-world networks of diverse nature have a power-law degree distribution. Moreover, the observed degree distribution usually has an infinite variance. Therefore, we are especially interested in such degree distributions. In addition, we analyze the clustering coefficient for ...

We develop a numerical scheme to determine which planar snake motions are optimal for locomotory efficiency, across a wide range of frictional parameter space. For a large coefficient of transverse friction, we show that retrograde traveling waves are optimal. We give an asymptotic analysis showing that the optimal wave amplitude decays as the -1/4 power of the coefficient of transverse frictio...

This paper provides ANOVA inference for nonparametric local polynomial regression (LPR) in analogy with ANOVA tools for the classical linear regression model. A surprisingly simple and exact local ANOVA decomposition is established, and a local R-squared quantity is defined to measure the proportion of local variation explained by fitting LPR. A global ANOVA decomposition is obtained by integra...

A synthesis of a globally convergent numerical method for a coefficient inverse problem and the adaptivity technique is presented. First, the globally convergent method provides a good approximation for the unknown coefficient. Next, this approximation is refined via the adaptivity technique. The analytical effort is focused on a posteriori error estimates for the adaptivity. A numerical test i...

Improving the detection of relevant variables using a new bivariate measure could importantly impact variable selection and large network inference methods. In this paper, we propose a new statistical coefficient that we call the rank minrelation coefficient. We define a minrelation of X to Y (or equivalently a majrelation of Y to X) as a measure that estimate p(X ≤ Y ) when X and Y are continu...

A globally convergent numerical method is developed for a 2-d Coefficient Inverse Problem for a hyperbolic PDE with the backscattering data. An important part of this technique is the quasi-reversibility method. A global convergence theorem is proven via a Carleman estimate. Results of numerical experiments for the problem modeling imaging of plastic land mines are presented.