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Approximate least squares parameter estimation with structured observations

2014
*
2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
*

We present an

doi:10.1109/icassp.2014.6854689
dblp:conf/icassp/YellepeddiP14
fatcat:shdkhygovfbytcjtkutk6twaqm
*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*. ...##
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The analysis of structural equation models by means of derivative free nonlinear least squares

1984
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Psychometrika
*

It is shown that the PAR Derivative-Free Nonlinear Regression program in BMDP can be used to fit

doi:10.1007/bf02302589
fatcat:ry5oxplytvbvbkceabq7sunxue
*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. ...##
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NONLINEAR REGRESSION FOR SPLIT PLOT EXPERIMENTS

1990
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Conference on Applied Statistics in Agriculture
*

The advantage of

doi:10.4148/2475-7772.1441
fatcat:u5fjq2dplbaqlct5nn3z2ieilm
*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 ». ...##
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Estimation of parameters in linear structural relationships: Sensitivity to the choice of the ratio of error variances

1984
*
Biometrika
*

Figures 2 and 3 compare the asymptotic mean

doi:10.1093/biomet/71.3.569
fatcat:6c6djp7sbrhujez7wgjbqp42ue
*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*. ...##
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Wavelet-Generalized Least Squares: A New BLU Estimator of Linear Regression Models with 1/f Errors

2002
*
NeuroImage
*

Here we introduce a novel method, called wavelet-generalized

doi:10.1006/nimg.2001.0955
pmid:11771991
fatcat:t35uetmaejhn3jc64wswbf6pcu
*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*...##
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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 ...##
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Estimation of parameters of a harmonic chirp model

2021
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IET Signal Processing
*

We propose two methods of

doi:10.1049/sil2.12038
fatcat:fw7u3xf4kjaffarndhvmlo63hi
*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 ...##
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Hyperspectral imagery: clutter adaptation in anomaly detection

2000
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IEEE Transactions on Information Theory
*

., the

doi:10.1109/18.857796
fatcat:7tbbp2x2brbjnhjj6qeulo6rii
*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. ...##
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The Robustness of LISREL Estimates in Structural Equation Models with Categorical Variables

1987
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Journal of Experimental Education
*

This study examined the effect of type of correlation matrix on the robustness of LISREL maximum likelihood and unweighted

doi:10.1080/00220973.1987.10806438
fatcat:z4hx4ijjtnbzvmnyveqbktmrfa
*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*. ...##
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Regularized Nonlinear Least Trimmed Squares Estimator in the Presence of Multicollinearity and Outliers

2018
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American Journal of Theoretical and Applied Statistics
*

This study proposes a regularized robust Nonlinear

doi:10.11648/j.ajtas.20180704.14
fatcat:gh2imz7ftrhy7iykgytrogjjd4
*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*. ...##
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Parameter identification methods for metamodeling simulations

1996
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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

doi:10.1145/256562.256805
fatcat:dhkiapeksbeyzf7ojvkt3qdd5m
*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*. ...##
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Improved estimation of the slope parameter in a linear ultrastructural model when measurement errors are not necessarily normal

1997
*
Journal of Econometrics
*

Assuming knowledge of the variance of the measurement errors associated

doi:10.1016/s0304-4076(96)01822-2
fatcat:hor5sqrtyvgw7k6furetikdouq
*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 ...##
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Accuracy of atomic positions in the zunyite structure

1960
*
Acta Crystallographica
*

The accuracy of positional

doi:10.1107/s0365110x60000042
fatcat:ev5wmkx6rne4hlcz4hzl66uoym
*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. ...##
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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. ...##
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Improved estimation of the slope parameter in a linear ultrastructural model when measurement errors are not necessarily normal

1997
*
Journal of Econometrics
*

Assuming knowledge of the variance of the measurement errors associated

doi:10.1016/s0304-4076(97)80007-3
fatcat:6cv5hxc3engulgjze632nrmosq
*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 ...
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