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Approximate least squares parameter estimation with structured observations

Atulya Yellepeddi, James C. Preisig
2014 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)  
We present an approximate least squares method which takes advantage of the structure to reduce the complexity of least squares.  ...  It is shown that the proposed method is asymptotically equivalent to least squares parameter estimation for a large number of observations. The properties of the algorithm are verified by simulation.  ...  CONCLUSIONS In this work, an algorithm was introduced to solve the problem of parameter estimation with structured observations.  ... 
doi:10.1109/icassp.2014.6854689 dblp:conf/icassp/YellepeddiP14 fatcat:shdkhygovfbytcjtkutk6twaqm

The analysis of structural equation models by means of derivative free nonlinear least squares

Sik-Yum Lee, Robert I. Jennrich
1984 Psychometrika  
It is shown that the PAR Derivative-Free Nonlinear Regression program in BMDP can be used to fit structural equation models, producing generalized least squares estimates, standard errors, and goodness-of-fit  ...  The approach is particularly useful for dealing with new non-standard models and experimenting with alternate methods of estimation.  ...  The generalized least squares estimates obtained from PAR and Lee (1980) are reported in Table 2 . Again, we observe that these two sets of estimates are very close.  ... 
doi:10.1007/bf02302589 fatcat:ry5oxplytvbvbkceabq7sunxue

NONLINEAR REGRESSION FOR SPLIT PLOT EXPERIMENTS

Marcia L. Gumpertz, John O. Rawlings
1990 Conference on Applied Statistics in Agriculture  
The advantage of estimated generalized least squares is that it produces proper estimates of the variances of the parameters and of estimated yields, which take the covariance structure into account.  ...  We propose an estimated generalized least squares (EGLS) method of estimation for this model.  ...  GENERALIZED LEAST SQUARES ESTIMATION OF PARAMETERS In ordinary nonlinear least squares (OLS) the parameters are estimated by minimizing the sum of the squared residuals: (y -g(X,8 »)'(y -g(X,8 ».  ... 
doi:10.4148/2475-7772.1441 fatcat:u5fjq2dplbaqlct5nn3z2ieilm

Estimation of parameters in linear structural relationships: Sensitivity to the choice of the ratio of error variances

MANI Y. LAKSHMINARAYANAN, RICHARD F. GUNST
1984 Biometrika  
Figures 2 and 3 compare the asymptotic mean squared errors of the structural nodel estimator (1.2) with the least squares estimator, the latter mean squared error calculated from equation (2.6).  ...  [insert Tables 6 and 7] Erroneous use of least squares when the predictor variable is measured with error is especially unwarranted when X can be estimated with replicated observations.  ... 
doi:10.1093/biomet/71.3.569 fatcat:6c6djp7sbrhujez7wgjbqp42ue

Wavelet-Generalized Least Squares: A New BLU Estimator of Linear Regression Models with 1/f Errors

M.J. Fadili, E.T. Bullmore
2002 NeuroImage  
Here we introduce a novel method, called wavelet-generalized least squares (WLS), which is (to a good approximation) the best linear unbiased (BLU) estimator of regression model parameters in the context  ...  Compared to ordinary least squares and ARMA-based estimators, WLS is shown to be more efficient and to give excellent type 1 error control.  ...  Normal quantile plots of linear model parameters estimated by wavelet-generalized least squares (WLS), ordinary least squares (OLS), and autoregressive-based least squares (ARLS) in simulated data with  ... 
doi:10.1006/nimg.2001.0955 pmid:11771991 fatcat:t35uetmaejhn3jc64wswbf6pcu

Page 30 of American Society of Civil Engineers. Collected Journals Vol. 129, Issue 1 [page]

2003 American Society of Civil Engineers. Collected Journals  
The hyperellipsoid is centered on the estimated values of the ambiguity parameters with semiaxes equal to the square root of the eigenvalues of the covariance matrix.  ...  Once the most likely integer values of the ambiguity parameters are obtained, they are considered as constraint parameters and another least-squares adjustment with functional constraint is to be performed  ... 

Estimation of parameters of a harmonic chirp model

Rhythm Grover, Debasis Kundu, Amit Mitra
2021 IET Signal Processing  
We propose two methods of estimation: the least squares estimation method and the approximate least squares estimation method.  ...  We establish the asymptotic properties of the least squares estimators as well as the approximate least squares estimators of the parameters of this model under the assumption of stationary errors.  ...  parameter α°ALSE, approximate least squares estimator; RMSE, root mean square error GROVER ET AL  ... 
doi:10.1049/sil2.12038 fatcat:fw7u3xf4kjaffarndhvmlo63hi

Hyperspectral imagery: clutter adaptation in anomaly detection

S.M. Schweizer, J.M.F. Moura
2000 IEEE Transactions on Information Theory  
., the estimation of the Gauss-Markov random field parameters. We develop three methods: maximum-likelihood; least squares; and approximate maximum-likelihood.  ...  Finally, we test extensively with real hyperspectral imagery the adaptive anomaly detector incorporating either the least squares or the approximate maximum-likelihood estimators.  ...  As observed with the synthesized data, the approximate-ML and least squares methods perform nearly identically.  ... 
doi:10.1109/18.857796 fatcat:7tbbp2x2brbjnhjj6qeulo6rii

The Robustness of LISREL Estimates in Structural Equation Models with Categorical Variables

Corinna A. Ethington
1987 Journal of Experimental Education  
This study examined the effect of type of correlation matrix on the robustness of LISREL maximum likelihood and unweighted least squares structural parameter estimates for models with categorical manifest  ...  Moreover, the degree of bias was consistent for both the maximum likelihood and unweighted least squares estimates.  ...  With the exception of Case 3, the analysis of mixed matrices produced average estimates that more closely approximated the model parameters.  ... 
doi:10.1080/00220973.1987.10806438 fatcat:z4hx4ijjtnbzvmnyveqbktmrfa

Regularized Nonlinear Least Trimmed Squares Estimator in the Presence of Multicollinearity and Outliers

George Kemboi Kirui Keitany
2018 American Journal of Theoretical and Applied Statistics  
This study proposes a regularized robust Nonlinear Least Trimmed squares estimator that relies on an Elastic net penalty in nonlinear regression.  ...  Regularization parameter selection was done using a robust cross-validation criterion and estimation through Newton Raphson iteration algorthm for the oprimal model coefficients.  ...  Amongst these methods are Huber's M-estimators, MM-estimators, Least Trimmed Squares, Least Median Squares estimators.  ... 
doi:10.11648/j.ajtas.20180704.14 fatcat:gh2imz7ftrhy7iykgytrogjjd4

Parameter identification methods for metamodeling simulations

Don Caughlin
1996 Proceedings of the 28th conference on Winter simulation - WSC '96  
This paper presents methods that support new procedures that expanded the set of available metamodel representations beyond the traditional least squares formulation and added the capability to use dynamical  ...  A metamodel is a mathematical approximation of the system relationships defined by a high fidelity model or simulation.  ...  An exact fit involves interpolation; an approximate fit uses least squares (minimum mean square error) approximation.  ... 
doi:10.1145/256562.256805 fatcat:dhkiapeksbeyzf7ojvkt3qdd5m

Improved estimation of the slope parameter in a linear ultrastructural model when measurement errors are not necessarily normal

Anil K. Srivastava, Shalabh
1997 Journal of Econometrics  
Assuming knowledge of the variance of the measurement errors associated with explanatory variable, a consistent class of the slope parameter has been considered and large-sample asymptotic properties have  ...  ., the functional and the structural, of the measurement error model under one roof.  ...  Introduction It is well known that the classical least squares theory provides the best linear and unbiased estimate for the slope parameter in a linear regression relationship when observations are recorded  ... 
doi:10.1016/s0304-4076(96)01822-2 fatcat:hor5sqrtyvgw7k6furetikdouq

Accuracy of atomic positions in the zunyite structure

W. B. Kamb
1960 Acta Crystallographica  
The accuracy of positional parameters in the refined zunyite structure is estimated by four different statistical methods, includin~ a comparison of two entirely independent refinements of the structure  ...  The estimates show tolerable agreement, but disagree as to the importance of Fo measurement error in affecting the parameter error.  ...  The least-squares estimate agrees tolerably with the estimate from a comparison of the hkO and hhl refinements.  ... 
doi:10.1107/s0365110x60000042 fatcat:ev5wmkx6rne4hlcz4hzl66uoym

Page 2792 of Mathematical Reviews Vol. , Issue 86f [page]

1986 Mathematical Reviews  
Author summary: “The least-squares state estimation problem is considered for continuous-time systems with state-dependent observation noise.  ...  Takeuchi, Yoshiki; Akashi, Hajime 86f:93095 Least-squares state estimation of systems with state-dependent observation noise. Automatica—J. IFAC 21 (1985), no. 3, 303-313.  ... 

Improved estimation of the slope parameter in a linear ultrastructural model when measurement errors are not necessarily normal

Anil K. Srivastava, Shalabh
1997 Journal of Econometrics  
Assuming knowledge of the variance of the measurement errors associated with explanatory variable, a consistent class of the slope parameter has been considered and large-sample asymptotic properties have  ...  ., the functional and the structural, of the measurement error model under one roof.  ...  Introduction It is well known that the classical least squares theory provides the best linear and unbiased estimate for the slope parameter in a linear regression relationship when observations are recorded  ... 
doi:10.1016/s0304-4076(97)80007-3 fatcat:6cv5hxc3engulgjze632nrmosq
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