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Finite-Sample Maximum Likelihood Estimation of Location [article]

Shivam Gupta, Jasper C.H. Lee, Eric Price, Paul Valiant
2022 arXiv   pre-print
We consider 1-dimensional location estimation, where we estimate a parameter λ from n samples λ + η_i, with each η_i drawn i.i.d. from a known distribution f.  ...  For fixed f the maximum-likelihood estimate (MLE) is well-known to be optimal in the limit as n →∞: it is asymptotically normal with variance matching the Cramér-Rao lower bound of 1/nℐ, where ℐ is the  ...  The goal of this paper is to establish a finite-sample and high probability theory for the location estimation problem, in both the algorithmic bound and the estimation lower bound.  ... 
arXiv:2206.02348v2 fatcat:glekopqwofdcljh5j37jrwbjsq

Vessel wall differences between middle cerebral artery and basilar artery plaques on magnetic resonance imaging

Peng-Peng Niu, Yao Yu, Hong-Wei Zhou, Yang Liu, Yun Luo, Zhen-Ni Guo, Hang Jin, Yi Yang
2016 Scientific Reports  
Estimates of the final model for eccentricity index. Supplementary Table S6. Estimates of null model for plaque range. Supplementary Table S7. Estimates of the final model for plaque range.  ...  Estimates of null model for remodeling ratio. Supplementary Table S2. Estimates of the final model for remodeling ratio. Supplementary Table S3.  ...  Estimates of null model for remodeling ratio.The restricted maximum likelihood estimation was used.  ... 
doi:10.1038/srep38534 pmid:27917937 pmcid:PMC5137109 fatcat:j4hyq5tubvfgfjhn63eokgimme

On the existence of maximum likelihood estimates for presence-only data

Trevor J. Hefley, Mevin B. Hooten, David Warton
2015 Methods in Ecology and Evolution  
We found that when habitat preferences are strong or the number of presence-only locations is small, by chance, maximum likelihood coefficient estimates for the Poisson point process model may not exist  ...  In data sets where the maximum likelihood estimates do not exist, penalized likelihood and Bayesian methods will produce coefficient estimates, but these are sensitive to the choice of estimation procedure  ...  Acknowledgements We thank the citizens who reported sightings of whooping cranes and the United States Fish and Wildlife Service for maintaining the location records.  ... 
doi:10.1111/2041-210x.12340 fatcat:hl7t6f4qtreadhgq5yba25e45q

Page 5375 of Mathematical Reviews Vol. , Issue 88j [page]

1988 Mathematical Reviews  
a better estimate of finite sample mean squared error.  ...  The finite-sample mean-squared error of the maximum likelihood estimator, however, is consid- erably greater than the asymptotic covariance matrix, and the estimator based on first derivatives provides  ... 

Page 588 of The Annals of Mathematical Statistics Vol. 29, Issue 2 [page]

1958 The Annals of Mathematical Statistics  
The (symmetrical) dou scale, where the sample median is the maximum likelihood estimator of location, could easily be shown to be such an example.  ...  The technique of proof used below was origina Vy ae vel yped to provide a simple example where the maximum likelihood estimate of location, though asymptotically efficient, was not of minimum variance  ... 

Correcting spatial Gaussian process parameter and prediction variance estimation under informative sampling [article]

Erin M. Schliep, Christopher K. Wikle, Ranadeep Daw
2021 arXiv   pre-print
Second, even with unbiased estimates of the spatial covariance parameters, since the kriging variance is a function of the observation locations, these estimates will vary based on the sample and overestimate  ...  In this work, we develop a weighted composite likelihood approach to improve spatial covariance parameter estimation under informative sampling designs.  ...  Acknowledgement The work of the authors was supported by the National Institute of Statistical Science.  ... 
arXiv:2108.12354v1 fatcat:ez2zjjm3qnerjekopbplsi746a

Page 5150 of Mathematical Reviews Vol. , Issue 81M [page]

1981 Mathematical Reviews  
The maximum of the pseudo-likelihood is located by maxi- mizing the individual log-likelihoods which have optima at 6,,- ++ ,6,, say.  ...  L.; Bouchon, B. 81m:62043 Minimum of h-divergence and maximum likelihood estimator. J. Inform. Optim. Sci. 1 (1980), no. 3, 296-307.  ... 

Page 5121 of Mathematical Reviews Vol. , Issue 87i [page]

1987 Mathematical Reviews  
usefulness in the case of different sample sizes (Japanese) (pp. 96-120); Nobuo Inagaki, On the weak conver- gence of progressively truncated maximum likelihood estimators (Japanese) (pp. 121-143); Sakutaro  ...  Asymptotic variances and covariances of the estimators are obtained as well as the efficiency of the estimator of the pa- rameter relative to its maximum likelihood estimate when one of the parameters  ... 

Page 12 of The American Statistician Vol. 3, Issue 4 [page]

1949 The American Statistician  
For any finite size sample no matter how large, say ten million, it has not been proved that maximum likelihood estimates necessarily have as small or smaller sampling variance than those of other statistics  ...  “The minimal variances that characterize maximum likeli- hood estimates, and efficient estimates in general, are asymptotic values of these variances, and do not refer to the variance for samples of finite  ... 

Questions and Answers

Frederick Mosteller, John W. Tukey
1949 American Statistician  
For any finite size sample no matter how large, say ten million, it has not been proved that maximum likelihood estimates necessarily have as small or smaller sampling variance than those of other statistics  ...  “The minimal variances that characterize maximum likeli- hood estimates, and efficient estimates in general, are asymptotic values of these variances, and do not refer to the variance for samples of finite  ... 
doi:10.2307/2681357 fatcat:tkysim7zjrdrzayhj5xm7hlimq

Questions and Answers

Frederick Mosteller, John W. Tukey
1949 American Statistician  
For any finite size sample no matter how large, say ten million, it has not been proved that maximum likelihood estimates necessarily have as small or smaller sampling variance than those of other statistics  ...  “The minimal variances that characterize maximum likeli- hood estimates, and efficient estimates in general, are asymptotic values of these variances, and do not refer to the variance for samples of finite  ... 
doi:10.1080/00031305.1949.10501602 fatcat:3z564kfqlje33mzgartzvrqh5e

A simple robust estimation for parameters of Cauchy distribution

Sándor Fegyverneki
2013 Miskolc Mathematical Notes  
A simulation study for finite sample size shows that the efficiency of these robust estimators is rather similar to the maximum likelihood ones.  ...  These estimators are simple, robust and consistent, but asymptotically less efficient than the maximum likelihood estimators which are not robust.  ...  The estimation of the parameters is a well discussed problem. Mostly, the location parameter and the scale parameter are estimated by the maximum likelihood (ML) estimators O and O ; respectively.  ... 
doi:10.18514/mmn.2013.830 fatcat:n4ehxccdqbatff5bioowcemxyu

Page 6178 of Mathematical Reviews Vol. , Issue 96j [page]

1996 Mathematical Reviews  
A small simulation study for fi- nite sample sizes shows that under Gp the finite efficiency of the minimum distance estimators is rather similar to the maximum likelihood ones.” 96j:62041 62F10 62F12  ...  The interest in this paper is to estimate the minimum and maximum of the unknown location parameters.  ... 

On Location and Scale Maximum Likelihood Estimators

A. K. Gupta, G. J. Szekely
1994 Proceedings of the American Mathematical Society  
The maximum likelihood estimators of location and scale parameters have the following undesirable properties: (i) they are not always consistent, and (ii) the asymptotic correlation of the MLE's of the  ...  "unrelated" location and scale parameters can be arbitrarily close to one.  ...  ON THE DEPENDENCE OF LOCATION AND SCALE MAXIMUM LIKELIHOOD ESTIMATORS Denote by 0 the range of MLE's (p., a) of (p, a).  ... 
doi:10.2307/2159900 fatcat:7djktqzkxzdc5pedwarosf7hjm

Page 1120 of Mathematical Reviews Vol. , Issue 85c [page]

1985 Mathematical Reviews  
Let 21,---,Z, be a sample of size n from a population with den- sity function f(z — @) depending on an unknown location pa- rameter 9 € R.  ...  Motivated by the maximum-likelihood method the following pro- cedure of estimating the unknown parameter 6 of the underly- 85c:62069 bution Pe, and let X = (z,--- . tions formed with P.  ... 
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