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About 10,000 papers for “robust estimation”

Robust estimation

Anders Milhøj · Research at the University of Copenhagen (University of Copenhagen) · 2000

Cited by 0

Robust Estimation

2012

This chapter discusses different methods for robust estimation, with particular emphasis on the robust estimation of regressions. Robust statistics addresses the problem of making estimates that are insensitive to small changes in the basic assumptions of the statistical models employed. The notion of robust statistics carries over to statistical modeling. Statistical models such as regression models are theoretically elegant but not robust. Identifying robust estimators of regressions is a difficult problem, in fact, different choices of estimators, robust or not, might lead to radically different estimates of slopes and intercepts. An estimator is said to be resistant if it is insensitive to changes in one single observation. An indifference curve or indifference functions allows one to understand what happens if we add a new observation to a large sample. Different strategies for robust estimation of covariances include robust estimation of pairwise covariances and robust estimation of elliptic distributions.

Cited by 0

Robust frequency estimation

S.G. Oh, R.L. Kashyap · International Conference on Acoustics, Speech, and Signal Processing · 2003

A robust estimation method for frequencies of received signals is investigated. The received signals are represented as the sum of sinusoidal signals and an additive noise process. The additive noise is assumed to be a mixture of a Gaussian and an outlier process. The influence function of a robust estimate is derived for time-varying (sinusoidal) signals. The variance of the robust estimate is also derived, using the influence function, and found to be close to both the Cramer-Rao lower bounds, one of which is computed under the perfect Gaussian assumption and the other under the contaminated Gaussian assumption. It is proved that the robust estimate possesses high-resolution properties even when outliers exist.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Cited by 2

Unified robust estimation

Zhu Wang · Australian & New Zealand Journal of Statistics · 2024

Summary Robust estimation is primarily concerned with providing reliable parameter estimates in the presence of outliers. Numerous robust loss functions have been proposed in regression and classification, along with various computing algorithms. In modern penalised generalised linear models (GLMs), however, there is limited research on robust estimation that can provide weights to determine the outlier status of the observations. This article proposes a unified framework based on a large family of loss functions, a composite of concave and convex functions (CC‐family). Properties of the CC‐family are investigated, and CC‐estimation is innovatively conducted via the iteratively reweighted convex optimisation (IRCO), which is a generalisation of the iteratively reweighted least squares in robust linear regression. For robust GLM, the IRCO becomes the iteratively reweighted GLM. The unified framework contains penalised estimation and robust support vector machine (SVM) and is demonstrated with a variety of data applications.

Cited by 1

Joint robust estimation

Xiang Li, Jun S. Liu, Qiang Sun et al. · ArXiv.org · 2025

We introduce a joint robust estimation method for three parametric statistical models with heavy-tailed data: mean estimation, linear regression, and L2-penalized linear regression, where both the trend parameters and the error variance are unknown. Our approach is based on solving two coupled Catoni-type equations, one for estimating the trend parameters and the other for estimating the error variance. Notably, this joint estimation strategy cannot be obtained by minimizing a single loss function involving both the trend and variance parameters. The method offers four key advantages: (i) the length of the resulting (1 - epsilon) confidence interval scales as (log(1/epsilon))^{1/2}, matching the order achieved by classical estimators for sub-Gaussian data; (ii) it is tuning-free, eliminating the need for separate variance estimation; (iii) it allows flexible selection of Catoni-type functions tailored to the data; and (iv) it delivers strong performance for high-variance data, thanks to the explicit inclusion of the variance term in the denominators of both equations. We establish the consistency and asymptotic efficiency of the proposed joint robust estimators using new analytical techniques. The coupled equations are inherently complex, which makes the theoretical analysis of their solutions challenging. To address this, we employ the Poincare-Miranda theorem to show that the solutions lie within geometric regions, such as cylinders or cones, centered around the true parameter values. This methodology is of independent interest and extends to other statistical problems.

Cited by 0Open access

Robust Bayesian Estimation

Ahmed Saadoon Mannaa · IntechOpen eBooks · 2022

Bayes methods in statistical inference are one of the important methods, and most of the research and messages tend to use the Bayes method in the estimation process. The regular Bayes method does not meet this problem, so in this thesis it is possible to verify the existence of prior data conflict by modeling the parameters of the prior distribution and then comparing the standard deviation of the prior distribution with the standard deviation of the posterior distribution, if the value of the standard deviation of the prior distribution is greater than the deviation. The standard distribution for the posterior distribution, it means that there is a problem of prior data conflict. Then we used an approach to solve this problem through a set of prior distributions called this approach by the robust Bayesian method, to identify the behavior of the estimators, two types of failure models were used, the first Weibull distribution to match it with continuous data. The second is a (Binomial) distribution to match the discrete data, the regular Bayes method is compared with the robust Bayesian method by using integrated mean square error (IMSE). In the Weibull distribution, the scale parameter (θ) and the survival function were estimated for two simulation experiments, the first was in the case of prior data unconflict the second was in the case of prior data conflict, so the simulation results showed that the robust Bayes method is the best by using the comparison criterion integrated mean square error (IMSE). On the practical side, real data were collected from Al-Manathira Hospital of the Najaf Health Department for the deaths of heart attack patients for 2018, the time of admission of the patient to the hospital until death was recorded, which is the time Exit where a sample of (15) patients was collected and the test of goodness of fit showed that the data follow a Weibull distribution with two parameters, the robust Bayes method was used to estimate the scale parameter and the survival function. As for the Binomial distribution, the parameter (P) and survival function were estimated for two experiments from the first simulation, which was in the case of prior data unconflict, as for the second experiment, it was in the case of prior data conflict. The simulation results showed that the robust Bayes method is the best by using the comparison criterion (IMSE). On the practical side, real data were collected from Yarmouk Teaching Hospital on breast cancer patients’ mortality from 2010 to 2017, and the test of goodness of fit showed that the data follow a Binomial distribution, the robust Bayes method was used to estimate the parameter (P) and survival function.

Cited by 0Open access

Robust Dynamic Estimation

Olivier Rubel, P. A. Naik · Marketing Science · 2017

Managing marketing resources over time requires dynamic model estimation, which necessitates specifying some parametric or nonparametric probability distribution. When the data generating process differs from the assumed distribution, the resulting model is misspecified. To hedge against such a misspecification risk, the extant theory recommends using the sandwich estimator. This approach, however, only corrects the variance of estimated parameters, but not their values. Consequently, the sandwich estimator does not affect any managerial outcomes such as marketing budgeting and allocation decisions. To overcome this drawback, we present the minimax framework that does not necessitate distributional assumptions to estimate dynamic models. Applying minimax control theory, we derive an optimal robust filter, illustrate its application to a unique advertising data set from the Canadian Blood Services, and contribute several novel findings. We discover the compensatory effect: Advertising effectiveness increases and the carryover effect decreases as robustness increases. We also find that the robust filter uniformly outperforms the Kalman filter on the out-of-sample predictions. Furthermore, we uncover the existence of a profit-volatility trade-off, similar to the returns-risk trade-off in finance, whereby the volatility of profit stream decreases at the expense of reduced total profit as robustness increases. Finally, we prove that, unlike for-profit companies, managers of nonprofit organizations should optimally allocate budgets opposite the advertising-to-sales ratio heuristic; that is, advertise more (less) when sales are low (high). Data and the web appendix are available at https://doi.org/10.1287/mksc.2016.1010 .

Cited by 9

Robust shadow estimation

Chen, Senrui, Yu, Wenjun, Zeng, Pei et al. · arXiv (Cornell University) · 2020

Efficiently estimating properties of large and strongly coupled quantum systems is a central focus in many-body physics and quantum information theory. While quantum computers promise speedups for many such tasks, near-term devices are prone to noise that will generally reduce the accuracy of such estimates. Here we show how to mitigate errors in the shadow estimation protocol recently proposed by Huang, Kueng, and Preskill. By adding an experimentally friendly calibration stage to the standard shadow estimation scheme, our robust shadow estimation algorithm can obtain an unbiased estimate of the classical shadow of a quantum system and hence extract many useful properties in a sample-efficient and noise-resilient manner given only minimal assumptions on the experimental conditions. We give rigorous bounds on the sample complexity of our protocol and demonstrate its performance with several numerical experiments.

Cited by 0Open access

Robust Covariance Estimation

Ilias Diakonikolas, Daniel M. Kane · Cambridge University Press eBooks · 2023

A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.

Cited by 1

Robust Bayesian Estimation

Ahmed Saadoon · RePEc: Research Papers in Economics

Bayes methods in statistical inference are one of the important methods, and most of the research and messages tend to use the Bayes method in the estimation process. The regular Bayes method does not meet this problem, so in this thesis it is possible to verify the existence of prior data conflict by modeling the parameters of the prior distribution and then comparing the standard deviation of the prior distribution with the standard deviation of the posterior distribution, if the value of the standard deviation of the prior distribution is greater than the deviation. The standard distribution for the posterior distribution, it means that there is a problem of prior data conflict. Then we used an approach to solve this problem through a set of prior distributions called this approach by the robust Bayesian method, to identify the behavior of the estimators, two types of failure models were used, the first Weibull distribution to match it with continuous data. The second is a (Binomial) distribution to match the discrete data, the regular Bayes method is compared with the robust Bayesian method by using integrated mean square error (IMSE). In the Weibull distribution, the scale parameter (?) and the survival function were estimated for two simulation experiments, the first was in the case of prior data unconflict the second was in the case of prior data conflict, so the simulation results showed that the robust Bayes method is the best by using the comparison criterion integrated mean square error (IMSE). On the practical side, real data were collected from Al-Manathira Hospital of the Najaf Health Department for the deaths of heart attack patients for 2018, the time of admission of the patient to the hospital until death was recorded, which is the time Exit where a sample of (15) patients was collected and the test of goodness of fit showed that the data follow a Weibull distribution with two parameters, the robust Bayes method was used to estimate the scale parameter and the survival function. As for the Binomial distribution, the parameter (P) and survival function were estimated for two experiments from the first simulation, which was in the case of prior data unconflict, as for the second experiment, it was in the case of prior data conflict. The simulation results showed that the robust Bayes method is the best by using the comparison criterion (IMSE). On the practical side, real data were collected from Yarmouk Teaching Hospital on breast cancer patients' mortality from 2010 to 2017, and the test of goodness of fit showed that the data follow a Binomial distribution, the robust Bayes method was used to estimate the parameter (P) and survival function.

Cited by 0