Least squares
On the Equivalence of the Weighted Least Squares and the Generalised Least Squares Estimators, with Applications to Kernel Smoothing
... The paper establishes the conditions under which the generalised least squares estima- tor of the regression parameters is equivalent to the weighted least squares estimator. The equivalence ...
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Kernel Partial Least Squares for Stationary Data
... partial least squares algorithm is competitive with other regression methods such as ridge regression and principal component regression, needing generally fewer iterations than the latter to achieve ...
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Orthogonal least squares regression with tunable kernels
... A basic principle in practical nonlinear data modelling is the parsimonious principle of ensuring the smallest possible model that explains the training data. The existing sparse kernel modelling methods [1]–[6] place ...
5
A Least-squares Approach to Direct Importance Estimation
... LSIF is shown to be efficient in computation, but it tends to share a common weakness of reg- ularization path tracking algorithms, that is, accumulation of numerical errors (Scheinberg, 2006). The numerical problem ...
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GURLS: A Least Squares Library for Supervised Learning
... Figure 1: Prediction accuracy vs. computing time. The color represents the training method and the library used. In blue: the Matlab implementation of RLS with RBF kernel, in red: its C++ counterpart. In dark red: ...
5
A note on approximating moments of least squares estimators
... We present results to facilitate the asymptotic approximation of the mo- ments of least squares coefficient estimators under similar assumptions to Phillips (2000), but focussing on the OLS estimator. The ...
13
ORDINARY LEAST SQUARES METHOD AND ITS VARIANTS
... Let us a rewrite OLS estimator of β from (2) β ˆ = A − 1 X′ Y, where A = ( X′ X) − 1 is a matrix, termed as the inverse of A such that A A − 1 = A − 1 A = I. From time to time, the corresponding problem in the case where ...
14
APPLICATION OF RESTRICTED LEAST SQUARES TO ECONOMETRIC DATA
... (O'Donnell, 2006) opined that Economic theory often provides information on the variables to be included in economic relationships (e.g., demands are functions of prices) and sometimes provides information on the signs ...
12
Theory of Errors and Least Squares Adjustment
... Theory of errors and least squares adjustment is an important subject within the geomatics programme o¤ered at KTH. This is due to the fact that surveying and mapping (or production of spatial data) often ...
14
3D Deformation Using Moving Least Squares
... We present a 3d deformation method based on Moving Least Squares that extends the work by Schaefer et al. [Schaefer et al. 2006] to the 3d setting. The user controls the deformation by ma- nipulating a set ...
7
AIC under the framework of least squares estimation
... In this note we explain the use of the Akiake Information Criterion and its related model compar- ison indices (usually derived for maximum likelihood estimator inverse problem formulations) for use with least ...
16
An Introduction to Partial Least Squares Regression
... The next section gives a brief overview of how PLS works, relating it to other multivariate techniques such as principal components regression and maximum re- dundancy analysis. An extended chemometric exam- ple is ...
8
Least squares regret and partially strategic players
... apply least-squares regret to a number of well-known games, in particular, the Dollar Auction; Bertrand competition; inspection games; Matching Pennies; Chicken; coordination games; Battle of the Sexes; and ...
138
Iterative least squares method for global positioning system
... Abstract. The efficient implementation of positioning algo- rithms is investigated for Global Positioning System (GPS). In order to do the positioning, the pseudoranges between the receiver and the satellites are ...
6
Least Squares Support Vector Fuzzy Regression
... LS_SVFR is constructed based on least squares support vector regression [11] in this paper. Due to the equality constraints in the formulation, LS_SVFR is solved by a set of linear equations instead of a ...
6
Least squares estimation of a shift in linear processes
... The least squares (LS) estimation of a shift is not new. Hawkins (1986) examined the LS method for a shift in an i.i.d. sequence. He proved that T 1/2−δ (ˆ τ − τ ) → 0 in probability for any δ > 0, where ...
31
Linear least squares localization in sensor networks
... In order to avoid the explicit minimization problem and obtain a closed form solution, the nonlinear expres- sions of observations can be linearized using the linear least squares (LLS) algorithms. ...
7
Extremiles: a new perspective on asymmetric least squares
... for being too pessimistic since it only depends on the tail event. The quantile-based VaR and ES may therefore be considered as too liberal or too conservative, depending on the tail shape of the underlying distribution. ...
41
On the computation of the structured total least squares estimator
... We consider numerical methods for the solution of the optimization problem (5). One approach is to use standard algorithms for local optimization. The choice of the optimization method is inspired by the need to use as ...
18
Completely Recursive Least Squares and Its Applications
... Most power system state estimation (SE) programs are formulated as static weighted-least-squares (WLS) problems with one-scan data [Monticelli00]. Dynamic state estimation (DSE) is not popularly applied due ...
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