Generalized Least-squares Method Research Articles

Positron Lifetime Analysis from Generalized Constrained Least-Squares Technique

The generalized least-squares method with non-negativity constraint is developed to analyze positron annihilation lifetime (PAL) spectra to obtain lifetimes and intensities. The method for obtaining the instrumental function from a single-component PAL spectrum is demonstrated. The present code is tested using computer simulated lifetime data.

Evaluation of Neutron Cross Sections of Carbon-12 for Energies up to 80MeV

We have evaluated the cross sections of 12C for neutrons up to 80MeV, paying more attention to the intermediate energy range above 20MeV. For energies below 20MeV, the evaluated data of JENDL-3.2 were adopted with some modifications. In the energy range above 20MeV, total cross section and its covariance matrix were evaluated using a generalized least-squares method with available experimental data. The spherical optical model was used to evaluate reaction and elastic scattering cross sections. Inelastic scattering to the first 2+ state was calculated based on the DWBA. The optical potentials used in these calculations were obtained by means of the microscopic folding model based on the Jeukenne-Lejeune-Mahaux theory. Double-differential emission cross sections for neutron, proton, deuteron, triton, 3He, alpha-particle and other heavier products were calculated using the Monte-Carlo method by which three-body simultaneous breakup process and two-body sequential decay process were taken into account in n+12C multibody breakup reactions. Kerma factors calculated from the evaluated cross sections were also compared with measurements and other evaluations.

The Prescribed Precision Estimators of the AutoregressionParameter Using the Generalized Least Square Method

A sequential estimator is proposed for the autoregression parameter of first-order (AR(1)), which is constructed on the basis of a generalized least square method (GLSM) using a special choice of the weight coefficients in the sum of residual squares. Under some natural requirements on the noise distribution function, this is the prescribed precision estimator in the sense that it provides the unknown parameter estimation with any fixed square average accuracy at the moment of termination of the observation. In contrast to the sequential least square estimator, our estimator has the important property of uniform asymptotic normality with respect to the parameter on the whole axis. Using this result one can show that the sequential least square estimator is asymptotically optimal in the minimax sense for the power loss function, in a wide class of sequential and nonsequential procedures.

Evaluation of Neutron Cross Sections of Hydrogen from 20 MeV to 1 GeV

The neutron cross sections of hydrogen (1H) have been evaluated in the energy region from 20 MeV to 1 GeV. Evaluated quantities are the total, elastic and inelastic scattering and capture cross sections, covariance matrix of total cross section and photon production cross section associated with the capture process. The total cross section was evaluated by combining the results obtained from the generalized least-squares method and the phase-shift data. The phase-shift data have been also used to calculate the elastic and inelastic scattering cross sections and their angular distributions. The capture cross section was calculated from the deuteron photo-disintegration cross section in conjunction with the principle of detailed balance. The presently evaluated data give a good description of the available experimental data in general and are also in good accord with those values given in ENDF-B/VI that are available below 100 MeV.

Estimation of factor scores in a two-level confirmatory factor analysis model

In this paper, two approaches for estimating the between-group and the within-group factor scores in a two-level confirmatory factor analysis model will be investigated. In each approach, the regression method and the generalized least-squares method are studied. These methods will be compared with each other theoretically and empirically with a simulation study.

An Error in Cota, Dion, and Evans (1993) Produced by a GLS Error in EQS Version 3.00

An error was found in an article published by the authors in this journal in 1993 entitled "A Reexamination of the Structure of the Gross Cohesiveness Scale." The value of .981 for the Bentler-Bonett Normed Fit Index (NFI) that was reported is incorrect. This research note was written to correct the error, which was caused by an inaccurate null model chi-square produced by the generalized least-squares (GLS) method of EQS Version 3.00. Implications for the conclusion reached in the previous report and for other researchers who have published NFI values using the GLS method of EQS Version 3.00 are discussed.

Doppler-broadening measurements of microvoids at the Au/GaAs interface

Recent positron lifetime studies made on the Au/GaAs interface with an applied electric field returning a significant fraction of bulk implanted positrons to the interface have revealed the presence of microvoids(≈ 1 nm diameter) at the interface. In this work an attempt has been made to study these microvoids by observing the Doppler broadening on the annihilation radiation coming from them. This is done both by observing theS-parameter as a function of applied bias and by applying the generalized least-squares method to the deconvolution of the annihilation radiation lineshape. The general conclusion is that the Doppler-broadened data are consistent with the majority of positrons trapping into microvoids, probably associated with grain boundaries. The data suggest that these open volume defects are more associated with the Au film rather than the Au-Ga alloyed interfacial region.

Relationships Between Different Chromatographic Peak Description Functions and Numerical Solutions of the Mass Balance Equation

Diverse mathematical models for chromatographic peak description-Gaussian, log-normal, gamma, Weibull, Haarhoff and der Van Linde, Littlewood, exponentially modified Gaussian, Gram-Charlier, and Edgeworth-Cramer series-are evaluated by curve fitting to solutions of the differential mass balance equation obtained numerically by an implicit finite differences method. The peak profiles generated from this equation are representative of diverse integration conditions encompassing different adsorption equilibrium isotherms (linear, Langmuir, and Freundlich), injection modes (pulse, exponential, reverse ramp, semiparabolic, and triangular), and axial longitudinal dispersion coefficients. Curve fitting is performed with a generalized least-squares method. The results show a good correspondence between the solutions of the mass balance equation, combined with a linear isotherm, and symmetric injection modes, with the Gaussian function and the functions that may approach Gaussian expressions (exponentially modified Gaussian, Gram-Charlier, Edgeworth-Cramer, log-normal, Haarhoff and der Van Linde). The exponentially modified Gaussian function gives the best fit for the profiles generated with this isotherm and the exponential injection modes. The solution of the mass balance equation, combined with the Langmuir isotherm, shows that the Haarhoff and der Van Linde function is better adapted to this type of profile. Finally, a good correlation between the log-normal function and the solutions of the mass balance equation, combined with the Freundlich isotherm, is observed

A Simple Hybrid Model for Estimating Real Estate Price Indexes

The accurate measurement of housing and real estate prices is of real theoretical importance and is crucial to understanding the operation of the housing market. Two basic techniques - hedonic and repeat sales methods - for measuring and analyzing the structure of housing prices have been developed. This paper presents an explicit model for combining samples of single sales and multipule sales for the analysis of housing prices and the computation of more efficient price indices. The procedure is based upon an explicit error structure, incorporating a random walk in housing prices. It is also based upon robust generalized least-squares methods to improve the efficiency of estimation. The technique is illustrated using a unique sample of condominium sales during a 12-year period in downtown Los Angeles.

Meuse: An origin-destination matrix estimator that exploits structure

This article proposes an improvement of existing methods of origin-destination matrix estimation by an explicit use of data describing the structure of the matrix. These data can be obtained from parking surveys. The new model is applied on both illustrative and real examples, and the results are discussed. Comparisons with the results obtained with SATURN/ME2 and the generalized least-squares method are also presented.

A generalized least-squares estimate for the origin of sporophytic self-incompatibility.

Analysis of nucleotide sequences that regulate the expression of self-incompatibility in flowering plants affords a direct means of examining classical hypotheses for the origin and evolution of this major feature of mating systems. Departing from the classical view of monophyly of all forms of self-incompatibility, the current paradigm for the origin of self-incompatibility postulates multiple episodes of recruitment and modification of preexisting genes. In Brassica, the S locus, which regulates sporophytic self-incompatibility, shows homology to a multigene family present both in self-compatible congeners and in groups for which this form of self-incompatibility is atypical. A phylogenetic analysis of S-allele sequences together with homologous sequences that do not cosegregate with self-incompatibility permits dating the change of function that marked the origin of self-incompatibility. A generalized least-squares method is introduced that provides closed-form expressions for estimates and standard errors for function-specific divergence rates and times of divergence among sequences. This analysis suggests that the age of the sporophytic self-incompatibility system expressed in Brassica exceeds species divergence within the genus by four- to fivefold. The extraordinarily high levels of sequence diversity exhibited by S alleles appears to reflect their ancient derivation, with the alternative hypothesis of hypermutability rejected by the analysis.

A medium-term probabilistic model for forecasting loads with a small proportion of air conditioners

In this paper, a medium-term load forecasting model is proposed, intended to be used for the extrapolation of loads containing a small proportion of air conditioners. The main feature of the proposed model is the decomposition of weekly load observations into two independent components: trend line and seasonal variations. The trend line is described by the combination of the polynomial regression and the first-order autoregressive model. The parameters of this model are estimated with the aid of the generalized least-squares method. The seasonal component is modeled via a discrete model, where the weather sensitive cycle is separated from the weather insensitive one. A linear regression model is further proposed in order to associate weather sensitive variations with the exogenous weather variable (temperature). This procedure enabled a simple and efficient convolution of all load components into a single forecasting model. The whole methodology is verified on a real-life example of the peak-load consumption within the power system of former Yugoslavia.

Fitting response curves for radioimmunoassays or immunoradiometric assays.

The paper describes non-linear regression methods for the evaluation of radioimmunoassay or immunoradiometric assay data. The underlying model is an overdispersed Poisson process with four regression line parameters and one parameter related to the overdispersion of the variance. A generalized least-squares algorithm is described for the parameter estimation of non-contaminated data. In the presence of outliers in Y-direction, the results are improved by a winsorized version of the generalized least-squares method.

Statistical properties of the ordinary least-squares, generalized least-squares, and minimum-evolution methods of phylogenetic inference.

Statistical properties of the ordinary least-squares (OLS), generalized least-squares (GLS), and minimum-evolution (ME) methods of phylogenetic inference were studied by considering the case of four DNA sequences. Analytical study has shown that all three methods are statistically consistent in the sense that as the number of nucleotides examined (m) increases they tend to choose the true tree as long as the evolutionary distances used are unbiased. When evolutionary distances (dij's) are large and sequences under study are not very long, however, the OLS criterion is often biased and may choose an incorrect tree more often than expected under random choice. It is also shown that the variance-covariance matrix of dij's becomes singular as dij's approach zero and thus the GLS may not be applicable when dij's are small. The ME method suffers from neither of these problems, and the ME criterion is statistically unbiased. Computer simulation has shown that the ME method is more efficient in obtaining the true tree than the OLS and GLS methods and that the OLS is more efficient than the GLS when dij's are small, but otherwise the GLS is more efficient.

Inferring the viscosity and the 3-D density structure of the mantle from geoid, topography and plate velocities

SUMMARY In a dynamic Earth, mantle mass heterogeneities induce gravity anomalies, surface velocities and surface topography. These lateral density heterogeneities can be estimated on the basis of seismic tomographic models. Recent papers have described a realistic circulation model that takes into account the observed plate geometry and is able to predict the rotation vectors of the present plates. The relationship between the surface observables and the heterogeneities is sensitive to the viscosity stratification of the mantle. Here we use this model, combined with a generalized least-squares method, in order to infer the viscosity profile of the Earth from the surface observations, and. to get some new insight into the 3-D density structure of the mantle. The computed radial viscosity profile presents a continuous increase of more than two orders of magnitude. The asthenosphere has a viscosity close to 2 x lo2’ Pa s. No sharp discontinuity is requested at the upper-lower mantle interface. The largest viscosity 7 X 10” Pas is reached in the middle of the lower mantle. At greater depth, approaching the core-mantle boundary, the viscosity decreases by one order of magnitude. The model suggests that the well-known degree-2 and order-2 anomaly in the transition zone of the upper mantle is merely the signature of the slabs. It also slightly increases the degree-2 and order-0 in the lower mantle and decreases it in the upper mantle. In other words the inversion requests a hotter lower mantle beneath the equator and a colder upper mantle at the same latitudes.

An operational GLS model for hydrologic regression

Recent Monte Carlo studies have documented the value of generalized least squares (GLS) procedures to estimate empirical relationships between streamflow statistics and physiographic basin characteristics. This paper presents a number of extensions of the GLS method that deal with realities and complexities of regional hydrologic data sets that were not addressed in the simulation studies. These extensions include: (1) a more realistic model of the underlying model errors; (2) smoothed estimates of cross correlation of flows; (3) procedures for including historical flow data; (4) diagnostic statistics describing leverage and influence for GLS regression; and (5) the formulation of a mathematical program for evaluating future gaging activities.

A New Algorithm of the Recursive Generalized Least-squares Method

A new method for estimation of ARMA model parameters is considered. A recursive version of Gauss-Markov estimate based on computation of covariance matrix elements is developed. The method uses special features of the covariance matrix. Three versions of estimators are obtained depending on the method of estimation of covariance matrix elements. Extensive simulations are made and the results of the estimation by the proposed method are compared with these ones of least squares, generalized least squares and instrumental variable methods. The results obtained by use of the new algorithm are comparable or better than these ones obtained by the existing methods.

An approach to time series analysis and ARMA spectral estimation

This paper presents an approach to time series analysis and ARMA spectral estimation from only the output data corrupted by noise. It is shown that the generalized (not well-known) modified Yule-Walker (MYW) equations hold when the residual is some correlated noise. To solve such equations, a new version of the generalized least squares (GLS) method is proposed, yielding AR parameter estimates with higher accuracy. This GLS method can also be used to enhance the estimation accuracy of AR parameters for short and noisy data in case of the MYW equation holding theoretically. Furthermore, a simple procedure for improving MA parameter estimates is studied. Our approach, as Cadzow's singular value decomposition (SVD) method, has provided significantly higher performance spectral estimates for a low-order ARMA model than those obtained via usual techniques which are based upon direct solution of the MYW equations and which use a high-order model without considering an additive noise.

Differential measurements and an evaluation of the 59Co( n, α) 56Mn reaction cross-section

The activation method is used to measure differential cross-sections for the 59Co( n, α) 56Mn reaction in the threshold region from 5.07 to 9.98 MeV. The results from this investigation, along with other recent experimental data from the literature, are employed to adjust the ENDF/B-V evaluation for this reaction by means of the generalized least-squares method, thereby producing a new evaluation which better reflects contemporary knowledge of the cross-section over the energy range which has been explicitly addressed by differential experiments (5.5-18 MeV). Nuclear-model calculations are also performed in order to develop a physically reasonable differential cross-section shape for extrapolation toward threshold so that this evaluation spans the entire energy range required for ENDF/B (threshold—20 MeV). Attention is given in this work to covariances, in both the measurement and evaluation processes. Finally, the resulting differential evaluation is employed in calculations of fission-spectrum averaged cross-sections which are then compared with corresponding measured values from the literature.

APPLICATION OF A PERTURBATION THEORY FOR EVALUATION ALGORITHMS FOR IDENTIFICATION OF A CONTINUOUS PLANT FROM DISCRETE DATA

Abstract A perturbation theory for evaluation algorithms of arithmetic expressions is applied to the generalized least-squares identification of the continuous parameters by using nonperiodic discrete data. The sampling instants are distributed in such a way that a sequence of the elemental arithmetic expressions of the identification algorithm are suboptimized according to bang-bang rules on the extrema of appropriate variation intervals. The weighting scalars in the generalized least-squares method are updated with the same purpose.