Systems Analysis of Tides

Quite a long time the analysis of tidal observations has been based on the knowledge of the frequencies of the tidal components. These frequencies follow from an analysis of the tidal potentialor the tide generating force. This analysis also yields amplitudes and phases, but they are not equal to those of the real tidal components, called tqe...

Estimation of a convex function: Characterizations and asymptotic theory

We study nonparametric estimation of convexregression and density functions by methods of least squares (in the regression and density cases) and maximum likelihood (in the density estimation case).We provide characterizations of these estimators, prove that they are consistent and establish their asymptotic distributions at a fixed point of...

A canonical process for estimation of convex functions: The "invelope" of integrated Brownian motion +t4

A process associated with integrated Brownian motion is introduced that characterizes the limit behavior of nonparametric least squares and maximum likelihood estimators of convex functions and convex densities, respectively. We call this process “the invelope” and show that it is an almost surely uniquely defined function of integrated Brownian...

Application of Least-Squares Spectral Element Methods to Polynomial Chaos

This papers describes the use of the Least-Squares Spectral Element Method to polynomial Chaos to solve stochastic partial differential equations. The method will be described in detail and a comparison will be presented between the least-squares projection and the conventional Galerkin projection.

Application of Least-Squares Spectral Element Methods to Polynomial Chaos

This papers describes the use of the Least-Squares Spectral Element Method to polynomial Chaos to solve stochastic partial differential equations. The method will be described in detail and a comparison will be presented between the least-squares projection and the conventional Galerkin projection.

Estimating a concave distribution function from data corrupted with additive noise

We consider two nonparametric procedures for estimating a concave distribution function based on data corrupted with additive noise generated by a bounded decreasing density on (0, ?). For the maximum likelihood (ML) estimator and least squares (LS) estimator, we state qualitative properties, prove consistency and propose a computational...

Least squares estimation of Generalized Space Time AutoRegressive (GSTAR) model and its properties

In this paper we studied a least squares estimation parameters of the Generalized Space Time AutoRegressive (GSTAR) model and its properties, especially in consistency and asymptotic normality. We use R software to estimate the GSTAR parameter and apply the model toward real phenomena of data, such as an oil production data at volcanic layer.

Power spectral density of the heterogeneous fracture compliance from scattered elastic wavefields

Using the scattered elastic wavefield, a method to derive the power spectral density (PSD) of the heterogeneous compliance distribution, along the plane of a single fracture, is formulated. The method involves estimation of the stress field at the fracture depth from the scattered wavefield followed by least-squares optimization of the PSD of...

Conservative Taylor least squares reconstruction with application to material point methods

Within the standard material point method (MPM), the spatial errors are partially caused by the direct mapping of material-point data to the background grid. In order to reduce these errors, we introduced a novel technique that combines the least squares method with the Taylor basis functions, called the Taylor least squares (TLS), to...

Eligibility traces and forgetting factor in recursive least-squares-based temporal difference

We propose a new reinforcement learning method in the framework of Recursive Least Squares-Temporal Difference (RLS-TD). Instead of using the standard mechanism of eligibility traces (resulting in RLS-TD((Formula presented.))), we propose to use the forgetting factor commonly used in gradient-based or least-square estimation, and we show that...

Least Squares Calibration of MIMO Radars with Collocated Arrays

The calibration of a collocated MIMO radar is addressed by means of independent calibration of transmit and receive arrays. The solutions for both arrays' elements gain and phase terms only and the full coupling matrix estimation are presented. The proposed solution significantly improves over the conventional calibration of the virtual array...