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17 pages, 646 KB

Open AccessArticle

A Smoothed Three-Part Redescending M-Estimator

by Alistair J. Martin and Brenton R. Clarke

Stats 2025, 8(2), 33; https://doi.org/10.3390/stats8020033 - 30 Apr 2025

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A smoothed M-estimator is derived from Hampel’s three-part redescending estimator for location and scale. The estimator is shown to be weakly continuous and Fréchet differentiable in the neighbourhood of the normal distribution. Asymptotic assessment is conducted at asymmetric contaminating distributions, where smoothing is shown to improve variance and change-of-variance sensitivity. Other robust metrics compared are largely unchanged, and therefore, the smoothed functions represent an improvement for asymmetric contamination near the rejection point with little downside. Full article

(This article belongs to the Section Statistical Methods)

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19 pages, 1101 KB

Open AccessArticle

Robust Särndal-Type Mean Estimators with Re-Descending Coefficients

by Khudhayr A. Rashedi, Alanazi Talal Abdulrahman, Tariq S. Alshammari, Khalid M. K. Alshammari, Usman Shahzad, Javid Shabbir, Tahir Mehmood and Ishfaq Ahmad

Axioms 2025, 14(4), 261; https://doi.org/10.3390/axioms14040261 - 29 Mar 2025

Cited by 2 | Viewed by 1017

Abstract

When extreme values or outliers occur in asymmetric datasets, conventional mean estimation methods suffer from low accuracy and reliability. This study introduces a novel class of robust Särndal-type mean estimators utilizing re-descending M-estimator coefficients. These estimators effectively combine the benefits of robust regression techniques and the integration of extreme values to improve mean estimation accuracy under simple random sampling. The proposed methodology leverages distinct re-descending coefficients from prior studies. Performance evaluation is conducted using three real-world datasets and three synthetically generated datasets containing outliers, with results indicating superior performance of the proposed estimators in terms of mean squared error (MSE) and percentage relative efficiency (PRE). Hence, the robustness, adaptability, and practical importance of these estimators are illustrated by these findings for survey sampling and more generally for data-intensive contexts. Full article

(This article belongs to the Section Mathematical Analysis)

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21 pages, 953 KB

Open AccessArticle

Sequential Mixed Cost-Based Multi-Sensor and Relative Dynamics Robust Fusion for Spacecraft Relative Navigation

by Shoupeng Li and Weiwei Liu

Remote Sens. 2024, 16(23), 4384; https://doi.org/10.3390/rs16234384 - 23 Nov 2024

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Abstract

The non-redescending convex functions degrade the filtering robustness, whereas the redescending non-convex functions improve filtering robustness, but they tend to converge towards local minima. This work investigates the properties of convex and non-convex cost functions from robustness and stability perspectives, respectively. To improve filtering robustness and stability to the high level of non-Gaussian noise, a sequential mixed convex and non-convex cost strategy is presented. To avoid the matrix singularity induced by applying the non-convex function, the M-estimation type Kalman filter is transformed into its information filtering form. Further, to address the problem of the estimation consistency in the iterated unscented Kalman filter, the iterated sigma point filtering framework is adopted using the statistical linear regression method. The simulation results show that, under different levels of heavy-tailed non-Gaussian noise, the mixed cost strategy can avoid the non-convex function-based filters falling into the local minimum, and further can improve the robustness of the convex function-based filter. Therefore, the mixed cost strategy provides a comprehensive improvement in the efficiency of the robust iterated filter. Full article

(This article belongs to the Topic Multi-Sensor Integrated Navigation Systems)

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16 pages, 36164 KB

Open AccessArticle

Enhancing Image Quality via Robust Noise Filtering Using Redescending M-Estimators

by Ángel Arturo Rendón-Castro, Dante Mújica-Vargas, Antonio Luna-Álvarez and Jean Marie Vianney Kinani

Entropy 2023, 25(8), 1176; https://doi.org/10.3390/e25081176 - 7 Aug 2023

Cited by 2 | Viewed by 2077

Abstract

In the field of image processing, noise represents an unwanted component that can occur during signal acquisition, transmission, and storage. In this paper, we introduce an efficient method that incorporates redescending M-estimators within the framework of Wiener estimation. The proposed approach effectively suppresses impulsive, additive, and multiplicative noise across varied densities. Our proposed filter operates on both grayscale and color images; it uses local information obtained from the Wiener filter and robust outlier rejection based on Insha and Hampel’s tripartite redescending influence functions. The effectiveness of the proposed method is verified through qualitative and quantitative results, using metrics such as PSNR, MAE, and SSIM. Full article

(This article belongs to the Special Issue Pattern Recognition and Data Clustering in Information Theory)

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