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Approximate maximum likelihood estimators for linear regression with design matrix uncertainty [article]

Richard J Clancy, Stephen Becker
<span title="2021-04-07">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
for regression problems under general uncertainty in the design matrix.  ...  To address difficulties encountered when dealing with distributions of sums of random variables, we rely on the saddle point method to estimate densities and form an approximate log-likelihood to maximize  ...  In this paper, we derive an approximate MLE for point estimation in linear regression problems with uncertainty in both the measurement vector and design matrix.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2104.03307v1">arXiv:2104.03307v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/j6gjh75ycbdz7fk45mqnzrtmqy">fatcat:j6gjh75ycbdz7fk45mqnzrtmqy</a> </span>
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Page 2604 of Mathematical Reviews Vol. , Issue 2001D [page]

<span title="">2001</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Maximum-likelihood estimation of C under normality uses the Eckart-Young theorem for reduced-rank matrix approximation in terms of a singular-value decomposition.  ...  Theobald (4-EDIN-S; Edinburgh) 2001d:62071 62512 62F10 62F12 Pourahmadi, Mohsen (1-NIL-S; De Kalb, IL) Maximum likelihood estimation of generalised linear models for multivariate normal covariance matrix  ... 
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Optimal robot excitation and identification

J. Swevers, C. Ganseman, D.B. Tukel, J. de Schutter, H. Van Brussel
<span title="">1997</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/e7nb2ustinavvlg2tmd7bwiy5m" style="color: black;">IEEE Transactions on Robotics and Automation</a> </i> &nbsp;
case of maximum-likelihood parameter estimation.  ...  It presents a new approach toward the design of optimal robot excitation trajectories, and formulates the maximum-likelihood estimation of dynamic robot model parameters.  ...  , for example a maximum-likelihood estimator.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/70.631234">doi:10.1109/70.631234</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/srn2m55kpjd4bidlczxyobh7pm">fatcat:srn2m55kpjd4bidlczxyobh7pm</a> </span>
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ProbABEL package for genome-wide association analysis of imputed data

Yurii S Aulchenko, Maksim V Struchalin, Cornelia M van Duijn
<span title="">2010</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/n5zrklrhlzhtdorf4rk4rmeo3i" style="color: black;">BMC Bioinformatics</a> </i> &nbsp;
Correct analysis of imputed data calls for the implementation of specific methods which take genotype imputation uncertainty into account.  ...  Over the last few years, genome-wide association (GWA) studies became a tool of choice for the identification of loci associated with complex traits.  ...  Balding and two anonymous reviewers for valuable suggestions and discussion.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1186/1471-2105-11-134">doi:10.1186/1471-2105-11-134</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/20233392">pmid:20233392</a> <a target="_blank" rel="external noopener" href="https://pubmed.ncbi.nlm.nih.gov/PMC2846909/">pmcid:PMC2846909</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/gdwfi3wj6vepbgjwq7nahc6hau">fatcat:gdwfi3wj6vepbgjwq7nahc6hau</a> </span>
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A Minimum Message Length Criterion for Robust Linear Regression [article]

Chi Kuen Wong, Enes Makalic, Daniel F. Schmidt
<span title="2018-02-20">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
A new criterion for variable selection and parameter estimation in Student-t regression is proposed.  ...  This paper applies the minimum message length principle to inference of linear regression models with Student-t errors.  ...  the maximum likelihood estimator.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1802.03141v2">arXiv:1802.03141v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7odq3ntptbfj3ioph7zgqr77bm">fatcat:7odq3ntptbfj3ioph7zgqr77bm</a> </span>
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Parameter estimation of complex mixed models based on meta-model approach

Pierre Barbillon, Célia Barthélémy, Adeline Samson
<span title="2016-06-22">2016</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ktmtypeyz5cs3j7f52np7ed2o4" style="color: black;">Statistics and computing</a> </i> &nbsp;
A control on the distance between the maximum likelihood estimates in this mixed meta-model and the maximum likelihood estimates obtained with the exact mixed model is guaranteed.  ...  The new source of uncertainty due to this approximation can be incorporated in the model which leads to what is called a mixed meta-model.  ...  When f is non linear with respect to ψ, the maximum likelihood estimator has no closed form.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s11222-016-9674-x">doi:10.1007/s11222-016-9674-x</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ysfkwlk7indvpd27stvfpjgfsm">fatcat:ysfkwlk7indvpd27stvfpjgfsm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20151010020952/https://hal.archives-ouvertes.fr/hal-01162351/file/versionpreprint.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/5f/3c/5f3c4d572b4b916dfe40ba45fec03a6b89776aff.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s11222-016-9674-x"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Parametric estimation of complex mixed models based on meta-model approach [article]

Pierre Barbillon, Célia Barthélémy
<span title="2015-06-10">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
A control on the distance between the maximum likelihood estimates in this mixed meta-model and the maximum likelihood estimates obtained with the exact mixed model is guaranteed.  ...  The new source of uncertainty due to this approximation can be incorporated in the model which leads to what is called a mixed meta-model.  ...  When f is non linear with respect to ψ, the maximum likelihood estimator has no closed form.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1506.03313v1">arXiv:1506.03313v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/afpbb2chqfbg5obayczkpgmhcq">fatcat:afpbb2chqfbg5obayczkpgmhcq</a> </span>
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Optimal Bayesian design applied to logistic regression experiments

Kathryn Chaloner, Kinley Larntz
<span title="">1989</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/rllg36he2jdbba4ztp4efgsxqq" style="color: black;">Journal of Statistical Planning and Inference</a> </i> &nbsp;
We derive a general theory for concave design critria for non-linear models and then apply the theory to logistic regression.  ...  A design for a situation where the best guess has substantial uncertainty attached to it is very different from a design for a situation where approximate values of the parameters are known.  ...  Acknowledgements We are grateful to the referees and our colleagues at the University of Minnesota for helpful suggestions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0378-3758(89)90004-9">doi:10.1016/0378-3758(89)90004-9</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/thrvfqadzraozaz4t4aava2lqm">fatcat:thrvfqadzraozaz4t4aava2lqm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170812050936/http://tangra.si.umich.edu/~radev/767w10/papers/Week13/ag/Chaloner%20and%20Lantz%201989%20-%20Optimal%20Bayesian%20design%20applied%20to%20logistic%20regression%20experiments.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/57/c5/57c5f3869365080f4133d1dd9ca5c84e90a281b5.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0378-3758(89)90004-9"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Functional Regression for State Prediction Using Linear PDE Models and Observations

N. C. Nguyen, H. Men, R. M. Freund, J. Peraire
<span title="">2016</span> <i title="Society for Industrial &amp; Applied Mathematics (SIAM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wbdvoluxebgjhn3wq3qsnldey4" style="color: black;">SIAM Journal on Scientific Computing</a> </i> &nbsp;
We next derive a linear regression model for the Gaussian functional by utilizing observations and adjoint states.  ...  We next derive a linear regression model for the Gaussian functional by utilizing observations and adjoint states.  ...  to log-maximum likelihood.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1137/14100275x">doi:10.1137/14100275x</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6ymworn2c5efvnovsuvlqm2nvy">fatcat:6ymworn2c5efvnovsuvlqm2nvy</a> </span>
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Page 8747 of Mathematical Reviews Vol. , Issue 2002K [page]

<span title="">2002</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
The paper deals with the maximum likelihood estimation problem under a mixed uncertainty, where the regression matrix is affected by deterministic, structured and norm-bounded uncertainty, while the measure  ...  A robust (with respect to the deter- ministic model uncertainty) maximum likelihood estimate in linear models is defined in a worst-case (with respect to the uncertainty) setting with relation to a lower  ... 
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Exact and approximate REML for heteroscedastic regression

G.K. Smyth, A.F. Huele, A.P. Verbyla
<span title="2001-10-01">2001</span> <i title="SAGE Publications"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/op52n4znkvcunjt7tmrdfcvdke" style="color: black;">Statistical Modelling</a> </i> &nbsp;
Exact REML for heteroscedastic linear models is compared with a number of approximate REML methods which have been proposed in the literature, especially with the methods proposed by Lee & Nelder (1998  ...  It is possible to obtain REML estimators by alternating between two generalized linear models but the final fitted generalized linear model objects will not return the correct standard errors for the variance  ...  It is possible to compute the maximum likelihood estimators for β and γ by alternately fitting a linear regression with responses y i and a gamma generalized linear model with responses d i .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1191/147108201128140">doi:10.1191/147108201128140</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xd7hwoubrrgfxffl2syttjtetu">fatcat:xd7hwoubrrgfxffl2syttjtetu</a> </span>
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Methods to account for uncertainties in exposure assessment in studies of environmental exposures

You Wu, F. Owen Hoffman, A. Iulian Apostoaei, Deukwoo Kwon, Brian A. Thomas, Racquel Glass, Lydia B. Zablotska
<span title="2019-04-08">2019</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2omnqwvuqbcizejqazxipnscry" style="color: black;">Environmental Health</a> </i> &nbsp;
We describe the four main statistical approaches to adjust for exposure estimation uncertainties (regression calibration, simulation-extrapolation, Monte Carlo maximum likelihood and Bayesian model averaging  ...  For exposures that are estimated independently between subjects and are more likely to introduce unshared errors, regression calibration and SIMEX methods are able to adequately account for exposure uncertainties  ...  A matrix form of the linear approximation of E(D tr | D est , X) could be found in [3] . For a multiplicative error model, the log transformation is used to convert it to an additive one.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1186/s12940-019-0468-4">doi:10.1186/s12940-019-0468-4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/uc2xar7h3jgxpophjs5liu2yua">fatcat:uc2xar7h3jgxpophjs5liu2yua</a> </span>
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NON LINEAR GENERALIZED ADDITIVE MODELS USING LIKELIHOOD ESTIMATIONS WITH LAPLACE AND NEWTON APPROXIMATIONS

Vinai George Biju
<span title="2020-07-26">2020</span> <i title="Journal of Mechanics of Continua and Mathematical Sciences"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/km45ab6gnrbt5o7ulvumvzqf34" style="color: black;">JOURNAL OF MECHANICS OF CONTINUA AND MATHEMATICAL SCIENCES</a> </i> &nbsp;
The AIC measure estimates for the penalized regression is yet to be worked on in the near future. VI. Acknowledgement  ...  The Model assortment through additional selection penalties and p-value estimates is proposed along with bivariate combination of input variables capturing different non-linear relationship.  ...  The authors would like to acknowledge Sapthagiri College of Engineering, Bangalore, VTU Research center for the support towards conduction of the research work.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.26782/jmcms.2020.07.00021">doi:10.26782/jmcms.2020.07.00021</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/oxcvixj3urdzxoag2dbmrsyzly">fatcat:oxcvixj3urdzxoag2dbmrsyzly</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20201105072442/https://www.journalimcms.org/wp-content/uploads/journal_download.php?postid=4974" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/43/92/43923e805a0c0d177488e0845e5d31ffdcc018fa.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.26782/jmcms.2020.07.00021"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Correction of Retransformation Bias in Nonlinear Predictions on Longitudinal Data with Generalized Linear Mixed Models

Liu X Freed MC
<span title="">2015</span> <i title="OMICS Publishing Group"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/pslllprjybgehpmmjuieptnl5u" style="color: black;">Journal of Biometrics &amp; Biostatistics</a> </i> &nbsp;
Generalized linear mixed models are generally applied to account for potential lack of independence inherent in longitudinally data.  ...  The results demonstrate that failure to retransform the random components in generalized linear mixed models results in severely biased nonlinear predictions, as well as much reduced standard error approximates  ...  likelihood or the restricted maximum likelihood estimate of β, and ˆi b is the prediction of b i .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4172/2155-6180.1000235">doi:10.4172/2155-6180.1000235</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6u4ihe7govcu5hgxw5gxlqbkdy">fatcat:6u4ihe7govcu5hgxw5gxlqbkdy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180724220333/https://www.omicsonline.org/open-access/correction-of-retransformation-bias-in-nonlinear-predictions-on-longitudinal-data-with-generalized-linear-mixed-models-2155-6180-1000235.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/dc/64/dc6496023a4131f2fe21f547ec30311712b0cb08.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4172/2155-6180.1000235"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Prediction in multilevel generalized linear models

Anders Skrondal, Sophia Rabe-Hesketh
<span title="">2009</span> <i title="Wiley"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/onhgxm6gxvhxnjuxe4r2p3tmoi" style="color: black;">Journal of the Royal Statistical Society: Series A (Statistics in Society)</a> </i> &nbsp;
For other multilevel generalized linear models we present approximations and suggest using parametric bootstrapping to obtain standard errors.  ...  Prediction of random effects is useful for instance in small area estimation and disease mapping, effectiveness studies and model diagnostics.  ...  We also thank the Research Council of Norway for a grant supporting our collaboration.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1111/j.1467-985x.2009.00587.x">doi:10.1111/j.1467-985x.2009.00587.x</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ln7pvh5wnve2rgrhiwp3fjumje">fatcat:ln7pvh5wnve2rgrhiwp3fjumje</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809231614/http://www.gllamm.org/JRSSApredict_09.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/93/a0/93a07176704b7679eb27c9459337beb06c3054ae.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1111/j.1467-985x.2009.00587.x"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>
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