The backfitting algorithm commonly used in estimating additive models is used to decompose the component shares explained by a set of predictors on a dependent variable in the presence of linear dependencies (multicollinearity) among the predictors. Multicollinearity of independent variables affects the consistency and efficiency of ordinary least squares estimates of the parameters. We propose...

Measurement uncertainty is a recurrent concern in visual reconstruction. Image formation and 3D structure recovery are essentially projective processes that do not quite fit into the classical framework of affine least squares, so intrinsically projective error models must be developed. This paper describes initial theoretical work on a fully projective generalization of affine least squares. T...

The difference based estimation in partially linear models is an approach designed to estimate parametric component by using the ordinary least squares estimator after removing the nonparametric component from the model by differencing. However, it is known that least squares estimates do not provide useful information for the majority of data when the error distribution is not normal, particul...

In this work, we propose a continuous-domain stochastic model that can be applied to image data. This model is autoregressive, and accounts for Gaussian-type as well as for non-Gaussian-type innovations. In order to estimate the corresponding parameters from the data, we introduce two possible error criteria; namely, Gaussian maximum-likelihood, and least-squares autocorrelation fit. Exploiting...

The coefficient of prediction 2 j P is derived from the PRESS (prediction sum of squares) statistic just as 2 j R is derived from SSE, the error sum of squares. While 2 j R measures quality of fit, 2 j P measures quality of point predictions. Unlike SSE and PRESS, 2 j R and 2 j P are bounded, relative measures ideally suited for statistical modeling. This paper describes the limits, properties,...

For magnetic resonance imaging (MRI) with Cartesian k-space sampling, a simple inverse FFT usually suffices for image reconstruction. More sophisticated image reconstruction methods are needed for non-Cartesian k-space acquisitions. Regularized least-squares methods for image reconstruction involve minimizing a cost function consisting of a least-squares data fit term plus a regularizing roughn...

Rosin, P.L., A note on the least squares fitting of ellipses, Pattern Recognition Letters 14 (1993) 799-808. The characteristics of two normalisations for the general conic equation are investigated for use in least squares fitting: either setting F = 1 or A + C= 1. The normalisations vary in three main areas: curvature bias, singularities, transformational invariance. It is shown that setting ...

The digital Fourier transform (DFT) and the adaptive least mean square (LMS) algorithm have existed for some time. This paper establishes a connection between them. The result is the “LMS spectrum analyzer,” a new means for the calculation of the DFT. The method uses a set of N periodic complex phasors whose frequencies are equally spaced from dc to the sampling frequency. The phasors are weigh...