robust estimation of a location parameter

A comparison of robust methods and detection of outliers techniques when estimating a location parameter. Voxels that are prone to PVE are removed from this labeled set, following which robust location estimators with high breakdown points are used to estimate the mean and the covariance of each tissue class. The content of this chapter was presented at the IMS 1967 Annual Meeting as an invited paper titled ‘Robust estimation and robust parameter’ (mimeographed) in a session on robust estimation. Debapriya Sengupta. Recommended Citation. Normal distribution is used as special case form the family of symmetric stable dis-tributions to show the derivation of the asymptotic estimation of loca- Math. MathSciNet zbMATH CrossRef Google Scholar Fisher, R.A. (1922). in Bayesian Data Analysis (2004) consider a data set relating to speed-of-light measurements made by Simon Newcomb. Parameter Estimation for the Lognormal Distribution Brenda Faith Ginos Brigham Young University - Provo ... robust estimation ... due to the nature of its contribution in the density function, is a location parameter which determines where to shift the three-parameter density function along the X-axis. Robust estimation of a location parameter in the presence of asymmetry, Ann. Hajek. Key Difficulties: The problem is closely related to the rejection of out-lying observations, one purpose of which is robust estimation of location. The estimator depends on a tuning parameter which controls the degree of robustness. (1949) Note on the consistency of the M.L. A survey of sampling from contaminated distributions. Simultaneous robust estimates of location and scale parameters are derived from minimizing a minimum‐distance criterion function. This paper contains a new approach toward a theory of robust estimation; it treats in detail the asymptotic theory of estimating a location parameter for contaminated normal distributions, and exhibits estimators--intermediaries between sample mean and sample median--that are asymptotically most robust (in a sense to be specified) among all translation invariant estimators. Download. proposed a theory of robust estimation of a location parameter using M-estimates in a non-mixture context. We show that the sample median and the sample mean are obtained as limit cases. Sample mean and standard deviation are the classical estimators of the location and scale parameters of a statistical distribution. Asymptotically most powerful rank order tests. For example, in Figure 2 the 2D location of the right foot is inaccurate. In statistics, a location parameter of a probability distribution is a scalar- or vector-valued parameter, which determines the "location" or shift of the distribution.In the literature of location parameter estimation, the probability distributions with such parameter are found to be formally defined in one of the following equivalent ways: The trimmed mean is a robust estimate. 2 Robust mean estimation We consider the generalized location model (GLM), with samples X 1; ;X n with X i i.i.d.˘L 0. E. (1963). 318, pp. Statist., 4, 68–85. Introduction. Robust statistics are statistics with good performance for data drawn from a wide range of probability distributions, especially for distributions that are not normal.Robust statistical methods have been developed for many common problems, such as estimating location, scale, and regression parameters.One motivation is to produce statistical methods that are not unduly affected by outliers. $\begingroup$ @Peter Best kind of depends on a lot of things - what sort of treatment one seeks, for example. A Monte Carlo analysis investigates the finite sample properties of the estimator. Existing efforts using DRO typically ignore, or have serious difficulties in exploiting, the available information regarding the generative model (1). Shu, Ven-Shion, "Robust estimation of a location parameter in the presence of outliers" (1978). Abstract: In this paper, we investigate the noise benefits to maximum likelihood type estimators (M-estimator) for the robust estimation of a location parameter. For the general background, see Tukey (1960) (p. 448 ff.). This paper deals with the problem of estimating the location parameter of a two-parameter exponential distribution in case of contaminated data. 1Research Scholar, Department of Statistics, Bharathiar University, India, The outliers arise from gross errors or contamination from distributions with long tails. Introduction. © 2020 Elsevier B.V. All rights reserved. Mostly, the loca-tion parameter and the scale parameter ˙are estimated by the maximum likelihood (ML) estimators Oand ˙;O respectively. Partial reviews of previous work are given by Tukey (1960) and Gastwirth (1966). Tukey, J.W. Key Difficulties: Robust Estimation of Shape Parameters G.A. Examples of parameterized models to be fit to image data inclu de lines and ellipses, camera calibration models, image motion models, 3D pla-nar regions, 3D models, and human face models. Not affiliated Cite as, This paper contains a new approach toward a theory of robust estimation; it treats in detail the asymptotic theory of estimating a location parameter for contaminated normal distributions, and exhibits estimators—intermediaries between sample mean and sample median—that are asymptotically most robust (in a sense to be specified) among all translation invariant estimators. A robust Bayesian estimation of location parameter θ of symmetric stable distributions α ∈ (2, 1.5, 1, 0.5) used to estimate the location parameter θ for the posterior distribution. Ann. The problem of robust estimation of location has a long history and inten-sive recent activity. Over 10 million scientific documents at your fingertips. To set a general context, letX=fx ScienceDirect ® is a registered trademark of Elsevier B.V. ScienceDirect ® is a registered trademark of Elsevier B.V. A note on robust estimation of location. A note on robust estimation of location. Since in this case the sample minimum is an extremely unreliable estimator, robust alternatives are necessary. I also prefer to read many sources rather than one - including papers, talks, notes as well as books. Ap-plications of robust regression (Chen and Meer, 2003) are, for instance, line fitting (Wang and Suter, 2004), or camera motion estimation (Bouthemy et al., 1999). For exam-ple, estimation of a normal mean under bound restrictions has been studied by Casella and Strawderman (1981), Bickel (1981), and Moors (1981), and estimation of parameters un- estimators of a scale parameter, with the goal of easing the transition from what the student is familiar with to alternative ways of analyzing estimators. The estimation of the parameters is a well discussed problem. (1967). 353-389. Download preview PDF. estimate. We use cookies to help provide and enhance our service and tailor content and ads. 318, pp. A note on robust estimation of location. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Abstract—One of the purposes of the robust method of estimation is to reduce the influence of outliers in the data, on the estimates. Gelman et al. With symmetric heavy-tailed noise distributions, the asymptotic efficiency of the estimation can be enhanced by injecting extra noise into the M-estimators. (1962). Recently, Desgagne (2015) consider the robust parameter estimation based on the log-´ regularly varying function, and show the sufficient condition to obtain whole robustness against outliers for estimation of location and scale parameters. A. Rejection of outliers. The estimator depends on a tuning parameter which controls the degree of robustness. We consider the problem of robust mean and location estimation w.r.t. Alternatively, the robust statistics literature also consider the robustification of the MLE problem, for example, to estimate a robust location parameter [20]. The context of estimating the scale parameter of an exponential distribu-tion, rather than the location parameter for a … https://doi.org/10.1016/j.spl.2020.108812. training robust logistic regression classifiers [29,7]. Robust alternatives have been proposed, of which the median and the median absolute deviation are best known. However, using the minimum is a very crude heuristic. 145.239.82.134. Ann. Retrospective Theses and Dissertations. The basic idea is to incorporate the density power weight into conventional parameter estimation. We show that the deviation-optimal minimax subgaussian rate for con dence 1 is max r ‘(1=2S) p N;sup v2S 1=2v 2 log(1= ) N! any pseudo-norm of the form x 2R d!kxk S = sup v2 v;x where S is any symmetric subset of R . Suresh 2 + 1 Department of Information Technology, Anna University, India. model, and F is a member of D . Communications in Statistics - … Journal of the American Statistical Association: Vol. Robust estimation of a location parameter (1964) by P J Huber Venue: Ann. A common computational problem in vision is to esti-mate the parameters of a model from image data. (a) estimated 2D joint locations where the right foot location is inaccurate. (1967). Wald. Huber’s article “Robust Estimation of Location Parameter” was the first fundament of the theory of robust estimation, which introduced an elastic class of estimates, called M-estimates, which have become a very useful instrument, having established which properties they have (for instance consistency and asymptotic normality). Comparison of 3D pose estimation by minimizing L 1-norm vs L 2-norm penalty. IOWA STATE UNIVERSITY, PH.D., 1973 Universi^ Micrpnlms InOematiOnal 300 N ^EEBHOAD, ANNAHBOR.MMStoe . Estimates of location based on rank tests. A robust estimation technique (MLDE) is developed which uses minimum distance estimation in conjunction with maximum likelihood estimation (MLE). The data sets for that book can be found via the Classic data sets page, and the book's website contains more information on the data. Asymptotic minimax robust estimation of a location parameter as introduced by P. J. Huber is considered. J. Results indicate that efficiency can be preserved in finite samples by setting the tuning parameter to a low fraction of a (robust) estimate of the scale. The first type is based on a simple relation for the median. 3.1.1 L 1-norm Objective Function L Robust estimation of a location parameter with the integrated Hogg function. That has been developed and published as Bickel and Lehmann Descriptive statistics for nonparametric models. Hodges, J.L., Jr. and Lehmann. Shu, Ven-Shion, "Robust estimation of a location parameter in the presence of outliers" (1978). This technique is then applied to the four-parameter generalized Gamma distribution to obtain location, scale, shape, and power parameter … This paper deals with the problem of estimating the location parameter of a two-parameter exponential distribution in case of contaminated data. The content of this chapter was presented at the IMS 1967 Annual Meeting as an invited paper titled ‘Robust estimation and robust parameter’ (mimeographed) in a session on robust estimation. The additional location parameter helped a lot. Jones, J. Princen, J. Illingworth and J. Kittler Dept. The scale parameter, needed in M-estimation and linked to the scale parameter of the inliers residuals, is often set a priori or estimated by the Median Absolute Deviation. We study the properties of an M-estimator arising from the minimization of an integrated version of the quantile loss function.

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