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For supervised classification problems, this paper considers estimating the query's label probability through local regression using observed covariates. Well-known nonparametric kernel smoother and $k$-nearest neighbor ($k$-NN) estimator,…
In this paper, we propose a sparse least squares (SLS) optimization model for solving multilinear equations, in which the sparsity constraint on the solutions can effectively reduce storage and computation costs. By employing variational…
Nonparametric partitioning-based least squares regression is an important tool in empirical work. Common examples include regressions based on splines, wavelets, and piecewise polynomials. This article discusses the main methodological and…
We address the phase retrieval problem with errors in the sensing vectors. A number of recent methods for phase retrieval are based on least squares (LS) formulations which assume errors in the quadratic measurements. We extend this…
We address the problem of estimating a random vector X from two sets of measurements Y and Z, such that the estimator is linear in Y. We show that the partially linear minimum mean squared error (PLMMSE) estimator does not require knowing…
In practical sensing tasks, noise is usually regarded as an obstruction to better performance and will degrade the sensitivity. Fortunately, \textit{stochastic resonance} (SR), a counterintuitive concept, can utilize noise to greatly…
In this paper, we compare maximum likelihood (ML), quasi likelihood (QL) and weighted least squares (WLS) estimators for proportional error nonlinear regression models. Literature on thermoluminescence sedimentary dating revealed another…
There are many practical applications based on the Least Square Error (LSE) approximation. It is based on a square error minimization 'on a vertical' axis. The LSE method is simple and easy also for analytical purposes. However, if data…
The Mass Spectrometer and Incoherent Scatter radar (MSIS) model family has been developed and improved since the early 1970's. The most recent version of MSIS is the Naval Research Laboratory (NRL) MSIS 2.0 empirical atmospheric model.…
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 iteratively reweighted least squares method (IRLS) is a popular technique used in practice for solving regression problems. Various versions of this method have been proposed, but their theoretical analyses failed to capture the good…
Nanomechanical resonators are used in building ultra-sensitive mass and force sensors. In a widely used resonator based sensing paradigm, each modal resonance frequency is tracked with a phase-locked loop (PLL) based system. There is great…
High dimensional data reduction techniques are provided by using partial least squares within deep learning. Our framework provides a nonlinear extension of PLS together with a disciplined approach to feature selection and architecture…
This article focuses on the use of Geographically Weighted Regression (GWR) method to correct air quality low-cost sensors measurements. Those sensors are of major interest in the current era of high-resolution air quality monitoring at…
Successful quantitative measurement of carbon content in coal using laser-induced breakdown spectroscopy (LIBS) is suffered from relatively low precision and accuracy. In the present work, the spectrum standardization method was combined…
Polarization imaging can yield crucial information in multiple applications of remote sensing, such as characterization of clouds, aerosols, and the Aurora Borealis. Some applications require sub-percent polarimetric sensitivity and…
Detectors based on liquid argon (LAr) often require surfaces that can shift vacuum ultraviolet (VUV) light and reflect the visible shifted light. For the LAr instrumentation of the LEGEND-200 neutrinoless double beta decay experiment,…
It is often of interest to estimate regression functions non-parametrically. Penalized regression (PR) is one statistically-effective, well-studied solution to this problem. Unfortunately, in many cases, finding exact solutions to PR…
In the heteroscedastic linear model, the weighted least squares (WLS) estimate of the model coefficients is more efficient than the ordinary least squares (OLS) esti- mate. However, the practical application of WLS is challenging because it…
This paper provides an alternative to penalized estimators for estimation and vari- able selection in high dimensional linear regression models with measurement error or missing covariates. We propose estimation via bias corrected least…