Weighted Least-squares Procedure Research Articles

Combination of three global Moho density contrast models by a weighted least-squares procedure

Abstract Due to different structures of the Earth’s crust and mantle, there is a significant density contrast at their boundary, the Moho Density Contrast (or shortly MDC). Frequently one assumes that the MDC is about 600 kg/m3, but seismic and gravimetric data show a considerable variation from region to region, and today there are few such studies, and global models are utterly rare. This research determines a new global model, called MDC21, which is a weighted least-squares combination of three available MDC models, pixel by pixel at a resolution of 1° × 1°. For proper weighting among the models, the study starts by estimating lacking standard errors and (frequently high) correlations among them. The numerical investigation shows that MDC21 varies from 21 to 504 kg/m3 in ocean areas and ranges from 132 to 629 kg/m3 in continental regions. The global average is 335 kg/m3. The standard errors estimated in ocean regions are mostly less than 40 kg/m3, while for continental regions it grows to 80 kg/m3. Most standard errors are small, but they reach to notable values in some specific regions. The estimated MDCs (as well as Moho depths) at mid-ocean ridges are small but show significant variations and qualities.

A continuous updating weighted least squares estimator of tail dependence in high dimensions

Likelihood-based procedures are a common way to estimate tail dependence parameters. They are not applicable, however, in non-differentiable models such as those arising from recent max-linear structural equation models. Moreover, they can be hard to compute in higher dimensions. An adaptive weighted least-squares procedure matching nonparametric estimates of the stable tail dependence function with the corresponding values of a parametrically specified proposal yields a novel minimum-distance estimator. The estimator is easy to calculate and applies to a wide range of sampling schemes and tail dependence models. In large samples, it is asymptotically normal with an explicit and estimable covariance matrix. The minimum distance obtained forms the basis of a goodness-of-fit statistic whose asymptotic distribution is chi-square. Extensive Monte Carlo simulations confirm the excellent finite-sample performance of the estimator and demonstrate that it is a strong competitor to currently available methods. The estimator is then applied to disentangle sources of tail dependence in European stock markets.

Least-Squares Estimation of the Common Pole-Zero Filter of Acoustic Feedback Paths in Hearing Aids

In adaptive feedback cancellation both the convergence speed and the computational complexity depend on the number of adaptive parameters used to model the acoustic feedback paths. To reduce the number of adaptive parameters, it has been proposed to model the acoustic feedback paths as the convolution of a time-invariant common pole-zero filter and time-varying all-zero filters, enabling to track fast changes. In this paper, a novel procedure to estimate the common pole-zero filter of acoustic feedback paths is presented. In contrast to previous approaches which minimize the so-called equation-error, we propose to approximate the desired output-error minimization by employing a weighted least-squares procedure motivated by the Steiglitz--McBride iteration. The estimation of the common pole-zero filter is formulated as a semidefinite programming problem, to which a constraint based on the Lyapunov theory is added in order to guarantee the stability of the estimated pole-zero filter. Experimental results using measured acoustic feedback paths from a two microphone behind-the-ear hearing aid show that the proposed optimization procedure using the Lyapunov constraint outperforms existing optimization procedures in terms of modelling accuracy and added stable gain.

A Continuous Updating Weighted Least Squares Estimator of Tail Dependence in High Dimensions

Likelihood-based procedures are a common way to estimate tail dependence parameters. They are not applicable, however, in non-differentiable models such as those arising from recent max-linear structural equation models. Moreover, they can be hard to compute in higher dimensions. An adaptive weighted least-squares procedure matching nonparametric estimates of the stable tail dependence function with the corresponding values of a parametrically specified proposal yields a novel minimum-distance estimator. The estimator is easy to calculate and applies to a wide range of sampling schemes and tail dependence models. In large samples, it is asymptotically normal with an explicit and estimable covariance matrix. The minimum distance obtained forms the basis of a goodness-of-fit statistic whose asymptotic distribution is chi-square. Extensive Monte Carlo simulations confirm the excellent finite-sample performance of the estimator and demonstrate that it is a strong competitor to currently available methods. The estimator is then applied to disentangle sources of tail dependence in European stock markets.

Material Balance Adjustement in Raw Material Processing

Circuit of one processing plant was studied in order to adjust the mass balance. The granulometric composition of the streams that belong to grinding and classifying processes was analyzed, while the chemical content was determined only at the streams related to separation process. Three connection matrixes are considered in this paper, one corresponding to the size fraction equations, the second corresponding to the chemical content measurements and the third, the solid flow rate balance. The technique used consisted of filtering all the data by a weighted least-squares procedure. Then running the output data in a custom designed feature of the computer program MATLAB. The raw data was then corrected and the different missing assays calculated and presented here.

Numerical Schemes for the Convection-Diffusion Equation Using a Meshless Finite-Difference Method

A meshless finite-difference method is developed for solving the steady convection-diffusion equation. A weighted least-squares procedure is used to compute a local polynomial fit which is used to find the derivatives appearing in the governing partial differential equation. A number of upwind-weighted discretization schemes for the convective operator are developed, analogous to traditional finite-difference schemes. These include a first-order upwind and a second-order upwind scheme, as well as a new scheme, the minimum gradient scheme, analogous to the essentially nonoscillatory (ENO) scheme. The order of accuracy of these methods is studied by applying them to two test problems. The first is the convection and diffusion of a scalar in a uniform velocity field, and the second pertains to scalar transport in a vortical flow field. The first-order upwind scheme results in an oscillation-free solution across the range of Peclet numbers and displays an order of accuracy close to unity. The second-order upwind scheme results in spurious oscillations for coarse nonuniform point distributions for Peclet numbers greater than 2.0, but monotonic solutions are obtained for finer point distributions across the range of Peclet numbers. The minimum gradient scheme yields nonoscillatory solutions for all Peclet numbers and point distributions explored in this work.

Denoising two-photon calcium imaging data.

Two-photon calcium imaging is now an important tool for in vivo imaging of biological systems. By enabling neuronal population imaging with subcellular resolution, this modality offers an approach for gaining a fundamental understanding of brain anatomy and physiology. Proper analysis of calcium imaging data requires denoising, that is separating the signal from complex physiological noise. To analyze two-photon brain imaging data, we present a signal plus colored noise model in which the signal is represented as harmonic regression and the correlated noise is represented as an order autoregressive process. We provide an efficient cyclic descent algorithm to compute approximate maximum likelihood parameter estimates by combing a weighted least-squares procedure with the Burg algorithm. We use Akaike information criterion to guide selection of the harmonic regression and the autoregressive model orders. Our flexible yet parsimonious modeling approach reliably separates stimulus-evoked fluorescence response from background activity and noise, assesses goodness of fit, and estimates confidence intervals and signal-to-noise ratio. This refined separation leads to appreciably enhanced image contrast for individual cells including clear delineation of subcellular details and network activity. The application of our approach to in vivo imaging data recorded in the ferret primary visual cortex demonstrates that our method yields substantially denoised signal estimates. We also provide a general Volterra series framework for deriving this and other signal plus correlated noise models for imaging. This approach to analyzing two-photon calcium imaging data may be readily adapted to other computational biology problems which apply correlated noise models.

A Meshless Finite Difference Method for Conjugate Heat Conduction Problems

A meshless finite difference method is developed for solving conjugate heat transfer problems. Starting with an arbitrary distribution of mesh points, derivatives are evaluated using a weighted least-squares procedure. The resulting system of algebraic equations is sparse and is solved using an algebraic multigrid method. The implementation of the Neumann, Dirichlet, and mixed boundary conditions within this framework is described. For conjugate heat transfer problems, continuity of the heat flux and temperature are imposed on mesh points at multimaterial interfaces. The method is verified through application to classical heat conduction problems with known analytical solutions. It is then applied to the solution of conjugate heat transfer problems in complex geometries, and the solutions so obtained are compared with more conventional unstructured finite volume methods. The method improves on existing meshless methods for conjugate heat conduction by eliminating spurious oscillations previously observed. Metrics for accuracy are provided and future extensions are discussed.

Multiple-pumped-well aquifer test to determine the anisotropic properties of a karst limestone aquifer in Pasco County, Florida, USA

Groundwater-level data from an aquifer test utilizing four pumped wells conducted in the South Pasco wellfield in Pasco County, Florida, USA, were analyzed to determine the anisotropic transmissivity tensor, storativity, and leakance in the vicinity of the wellfield. A weighted least-squares procedure was used to analyze drawdowns measured at eight observation wells, and it was determined that the major axis of transmissivity extends approximately from north to south and the minor axis extends approximately from west to east with an angle of anisotropy equal to N4.54°W. The transmissivity along the major axis $${\left( {T_{{\xi \xi }} } \right)}$$ is 14,019 m2 day–1, and the transmissivity along the minor axis $${\left( {T_{{\eta \eta }} } \right)}$$ is 4,303 m2 day–1. The equivalent transmissivity $$T_{e} = {\left( {T_{{\xi \xi }} T_{{\eta \eta }} } \right)}^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} = 7,767{{\text{m}}^{2} } \mathord{\left/ {\vphantom {{{\text{m}}^{2} } {{\text{day}}^{{ - {\text{1}}}} }}} \right. \kern-\nulldelimiterspace} {{\text{day}}^{{ - {\text{1}}}} }$$ , and the ratio of anisotropy is 3.26. The storativity of the aquifer is 7.52 × 10−4, and the leakance of the overlying confining unit is 1.37 × 10−4 day−1. The anisotropic properties determined for the South Pasco wellfield in this investigation confirm the results of previous aquifer tests conducted in the wellfield and help to quantify the NW–SE to NE–SW trends for regional fracture patterns and inferred solution-enhanced flow zones in west-central Florida.

Local Linear Estimation of Spatially Varying Coefficient Models: An Improvement on the Geographically Weighted Regression Technique

Geographically weighted regression (GWR), as a useful method for exploring spatial non-stationarity of a regression relationship, has been applied to a variety of areas. In this method a spatially varying coefficient model is locally calibrated and the spatial-variation patterns of the locally estimated regression coefficients are taken as the main evidence of spatial nonstationarity for the underlying data-generating processes. Therefore, the validity of the analysis results drawn by GWR is closely dependent on the accuracy between the underlying coefficients and their estimates. Motivated by the local polynomial-modelling technique in statistics, we propose a local linear-based GWR for the spatially varying coefficient models, in which the coefficients are locally expanded as linear functions of the spatial coordinates and then estimated by the weighted least-squares procedure. Some theoretical and numerical comparisons with GWR are conducted and the results demonstrate that the proposed method can significantly improve GWR, not only in goodness-of-fit of the whole regression function but also in reducing bias of the coefficient estimates.

IS STUDENT-RIGHT-TO-KNOW ALL YOU SHOULD KNOW? An Analysis of Community College Graduation Rates

Over the last decade, policymakers, educators, and researchers have increasingly sought to understand community college policies and practices that promote students’ success. This effort has been partly driven by an increased emphasis on outcome accountability, but it has also promoted a productive discussion about improving institutional performance. The research reported here has two related goals. One goal is to work towards strengthening the ability to assess and compare institutional performance. We thus have developed a model that can be used to adjust simple graduation rates for institutional characteristics, such as student composition, college resources, size, and location, all of which might influence those rates. Our long-term goal is to understand how to improve student outcomes, so the paper also uses the model to measure the effect of those institutional characteristics on graduation rates. We use data from the Integrated Postsecondary Education Data System (IPEDS) surveys, applying a weighted least-squares procedure for grouped data to estimate an institutional-completion rates model. This analysis confirms several hypotheses about institutional determinants of graduation rates at community colleges. Our results indicate a consistent negative relationship between enrollment size and completion. Additionally, colleges with high shares of minority students, part-time students, and women have lower graduation rates. A final significant finding among institutional characteristics is that greater instructional expenditures are related to a greater likelihood of graduation. The method developed here can be used to better assess the performance of community colleges.

Fitting the Linear Model of Coregionalization by Generalized Least Squares

In geostatistical studies, the fitting of the linear model of coregionalization (LMC) to direct and cross experimental semivariograms is usually performed with a weighted least-squares (WLS) procedure based on the number of pairs of observations at each lag. So far, no study has investigated the efficiency of other least-squares procedures, such as ordinary least squares (OLS), generalized least squares (GLS), and WLS with other weighing functions, in the context of the LMC. In this article, we compare the statistical properties of the sill estimators obtained with eight least-squares procedures for fitting the LMC: OLS, four WLS, and three GLS. The WLS procedures are based on approximations of the variance of semivariogram estimates at each distance lag. The GLS procedures use a variance–covariance matrix of semivariogram estimates that is (i) estimated using the fourth-order moments with sill estimates (GLS1), (ii) calculated using the fourth-order moments with the theoretical sills (GLS2), and (iii) based on an approximation using the correlation between semivariogram estimates in the case of spatial independence of the observations (GLS3). The current algorithm for fitting the LMC by WLS while ensuring the positive semidefiniteness of sill matrix estimates is modified to include any least-squares procedure. A Monte Carlo study is performed for 16 scenarios corresponding to different combinations of the number of variables, number of spatial structures, values of ranges, and scale dependence of the correlations among variables. Simulation results show that the mean square error is accounted for mostly by the variance of the sill estimators instead of their squared bias. Overall, the estimated GLS1 and theoretical GLS2 are the most efficient, followed by the WLS procedure that is based on the number of pairs of observations and the average distance at each lag. On that basis, GLS1 can be recommended for future studies using the LMC.

Spatial scales of 137Cs-derived soil flux by wind in a 25 km 2 arable area of eastern England

The area effected by wind erosion in England is estimated to be small, but the magnitude of the problem within this area is unknown. Direct measurement of the process is difficult because of very high spatial and temporal variability, selectivity and its slow, insidious nature. The artificial radionuclide caesium-137 ( 137Cs), offers an alternative method. It was used here to estimate the net (ca. 35 year) soil flux (erosion and deposition) in a 5×5 km area (ca. 19 km 2 area sampled) of East Anglia. It is the first study in the UK to investigate the continuous spatial variation of 137Cs over an area of such a size and one of only a few in the world to focus specifically on the redistribution of soil by wind. A two-stage, nested sampling frame captured approximately 50% of the variation that occurred between and within fields. A total of 148 samples were taken and their analysis was used to produce a variogram of the spatial variation. A spherical model was fitted to the experimental variogram using a weighted least-squares procedure. Simulations of sampling configurations on a regular grid did not provide a practical improvement to the nested sampling frame within the specified tolerance. Instead, the parameters were used in ordinary kriging to map 137Cs every 50 m at unsampled locations across the area. A tentative value for the newly established 137Cs reference inventory for the region was 2068±130 Bq m −2. Owens' mass–balance model of the relationship between 137Cs movement and soil redistribution was modified to the spatially distributed situation and also so that it could account better for the factors that control wind erosion and deposition (Towards improved interpretation of caesium-137 measurements in soil erosion studies. Unpublished PhD thesis, Exter University). A calibration relationship for each field was used to calculate the net soil flux at every 50 m. The sample region was found to approximately balance with a net soil loss of 0.6 t ha −1 year −1; the range was −32.6 to +37.5 t ha −1 year −1. Soil from the high-loss fields was accumulating in field boundaries. Despite little of the material leaving the region, the effect of soil nutrient loss on the fields may be considerable. It appears that wind erosion may have as great or greater impact in the areas where it is active than does water erosion. Net soil flux was inferred to be the result of wind erosion, but soil loss on harvested crops (primarily sugar beet), and perhaps losses during tillage (pulverizing erosion) may be other contributors, and this requires future study. Moreover, the quantity of soil lost may not be as important as its quality. Future work is therefore also required to investigate the mass–balance of soil nutrient enrichment and depletion as a consequence of soil erosion and fertiliser application.

A General Likelihood Approach to Trait-Based Multipoint Linkage Analysis in Large Groups of Half-Sibs and Super Sisters

The idea of trait-based linkage analysis in half-sibs is extended by comparing the frequency of parental marker haplotypes in animals with different phenotypes. This article first presents the likelihood of observing different classes of paternal haplotypes in a half-sib family, where only family members of a certain phenotype (e.g., affected) are genotyped and are fully informative. The likelihood function is then generalized to multiple phenotypic categories. A linear predictor allows for discontinuous as well as for continuous phenotypes and other explanatory variables. Finally, how to incorporate not fully informative offspring and how to analyze super sister families are shown. Maximum-likelihood estimates of all parameters can be found by a Newton-Raphson algorithm, which mimics an iteratively weighted least-squares procedure. The method allows for any multilocus feasible mapping function and, among others, for situations with selective or nonselective genotyping, single or multiple traits, and continuous or categorical traits. No parameters are required to describe the mode of inheritance and the method copes with virtually any family size. Fields of applications are therefore mapping experiments in species with a high reproductive capacity, such as cattle, pigs, horses, honey bees, trees, and fish.

Rational approximation with multidimensional scattered data.

Accurate and efficient rational approximation schemes are presented for interpolating multidimensional scattered data with a novel weighted least-squares procedure including domain decomposition. Two particular representations of the method are formulated and the corresponding algorithms are implemented. Numerical tests on three- and six-dimensional model systems are carried out, demonstrating high efficiency and accuracy. This work was motivated by the need for multidimensional function approximation using irregular grids when solving quantum fluid dynamics equations, and the method should have broader physical applications.

Modeling the hepatitis C virus epidemic in France using the temporal pattern of hepatocellular carcinoma deaths

Deuffic et al. developed a compartmentalized model that characterized the evolution and spread of the hepatitis C virus (HCV) within France. There were various parameters defining the age- and sex-dependent transition probabilities between chronic hepatitis and cirrhosis in need of determination to completely specify their model. These were estimated by means of a weighted least-squares procedure that was executed numerically. The objective function used was based on the distribution of the age at death from hepatocellular carcinoma (HCC) rather than the temporal pattern of deaths due to HCC from 1979 to 1995. In this report, we investigate the impact of using an objective function based on the temporal pattern of deaths. We show that the dynamics of the epidemic can be quite different, in particular, short-term prediction of HCC deaths by HCV infection and times to death from onset of disease. (HEPATOLOGY 2002;35:709-715.)

Estimation of the spectral envelope of voiced sounds using a penalized likelihood approach

Estimation of the spectral envelope (magnitude of the transfer function) of a filter driven by a periodic signal is a long-standing problem in speech and audio processing. Recently, there has been a renewed interest in this issue in connection with the rapid developments of processing techniques based on sinusoidal modeling. In this paper, we introduce a new performance criterion for spectral envelope fitting which is based on the statistical analysis of the behavior of the empirical sinusoidal magnitude estimates. We further show that penalization is an efficient approach to control the smoothness of the estimation envelope. In low-noise situations, the proposed method can be approximated by a two-step weighted least-squares procedure which also provides an interesting insight into the limitations of the previously proposed "discrete cepstrum" approach. A systematic simulation study confirms that the proposed methods perform significantly better than existing ones for high pitched and noisy signals.

Least squares estimation of nonhomogeneous poisson processes

We formulate and evaluate weighted least squares (WLS) and ordinary least squares (OLS) procedures for estimating the parametric mean-value function of a nonhomogeneous Poisson process. We focus the development on processes having an exponential rate function, where the exponent may include a polynomial component or some trigonometric components. Unanticipated problems with the WLS procedure are explained by an analysis of the associated residuals. The OLS procedure is based on a square root transformation of the "detrended" event (arrival) times - that is, the fitted mean-value function evaluated at the observed event times; and under appropriate conditions, the corresponding residuals are proved to converge weakly to a normal distribution with mean 0 and variance 0.25. The results of a Monte Carlo study indicate the advantages of the OLS procedure with respect to estimation accuracy and computational efficiency.

Sur une méthode d'analyse en composantes principales pour déterminer la variabilité haline des couches superficielles océaniques : application à l'océan Pacifique tropical ouest

We propose a new approach to estimate the vertical variability of the salinity field. The method is based on combined vertical modes of temperature and salinity, and reconstructs salinity profiles via a weighted least-squares procedure. The modes are denned as the empirical orthogonal functions along the water column. The major advantages of this new approach over using a simple T-S relationship are that interannual variability is better taken into account and that the method combines different sources of information such as temperature profiles and sea surface height in a consistent way. The present results estimate the salinity along 165°E in the western Pacific Ocean for the 1993–1997 period and emphasize the importance of the salinity on sea level variability.

Mid- and Near-Infrared Spectra, Millimeterwave Spectra, and Global Analysis of 16O12C80Se

We have recorded a total of 12 FTIR spectra of monoisotopic OC80Se in different spectral regions with a resolution (1/maximum optical path difference) between 2.7 and 13.2 × 10−3 cm−1. These spectra spanned the range from 350 to 7800 cm−1, many bands being studied with different p × L products in order to also detect weak hot bands. Altogether 18 band systems comprising 81 different bands, mostly of Σ type, were observed and analyzed by means of polynomial expansions in J(J + 1). New rotational transitions of vibrationally excited states as high as 2200 cm−1 with J" 17–25 in the 140–210 GHz and J" 53–58 in the 430–470 GHz millimeterwave regions were measured with the assistance of predictions by the global fit. This fit was performed using a weighted least-squares procedure and employing the whole body of data, and about 100 molecular parameters were determined that describe the energy level of 16O12C80Se with statistical accuracy. Improved highly accurate ground state parameters up to sextic centrifugal distortion terms were obtained by a merge of ground state combination differences and pure rotational data. The v1, v2, v3 polyad interacts anharmonically with the v1 − 1, v2 + p, v3 + q polyads with p + 2q = 4. Moreover, some local crossings with Coriolis interactions between (v1, v2, v3) and (v1 − 1, v2 + 3, v3 + 1) levels were observed and treated perturbationally.