scholarly journals Highly Efficient Robust and Stable M-Estimates of Location

Mathematics ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 105
Author(s):  
Georgy Shevlyakov
Keyword(s):  
Asymptotic Efficiency ◽  
Evaluation Study ◽  
Comparative Performance ◽  
Normal Distributions ◽  
Gross Error ◽  
Double Exponential ◽  
Error Distributions ◽  
Heavy Tailed ◽  
M Estimate ◽  
M Estimates

This article is partially a review and partially a contribution. The classical two approaches to robustness, Huber’s minimax and Hampel’s based on influence functions, are reviewed with the accent on distribution classes of a non-neighborhood nature. Mainly, attention is paid to the minimax Huber’s M-estimates of location designed for the classes with bounded quantiles and Meshalkin-Shurygin’s stable M-estimates. The contribution is focused on the comparative performance evaluation study of these estimates, together with the classical robust M-estimates under the normal, double-exponential (Laplace), Cauchy, and contaminated normal (Tukey gross error) distributions. The obtained results are as follows: (i) under the normal, double-exponential, Cauchy, and heavily-contaminated normal distributions, the proposed robust minimax M-estimates outperform the classical Huber’s and Hampel’s M-estimates in asymptotic efficiency; (ii) in the case of heavy-tailed double-exponential and Cauchy distributions, the Meshalkin-Shurygin’s radical stable M-estimate also outperforms the classical robust M-estimates; (iii) for moderately contaminated normal, the classical robust estimates slightly outperform the proposed minimax M-estimates. Several directions of future works are enlisted.

scholarly journals Robust Mixture Modeling Based on Two-Piece Scale Mixtures of Normal Family

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 38 ◽  
Author(s):  
Mohsen Maleki ◽  
Javier Contreras-Reyes ◽  
Mohammad Mahmoudi
Keyword(s):  
Real Data ◽  
Finite Mixture ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Normal Distributions ◽  
Scale Mixtures ◽  
Robust Model ◽  
Heavy Tailed Distributions ◽  
The Family ◽  
Heavy Tailed

In this paper, we examine the finite mixture (FM) model with a flexible class of two-piece distributions based on the scale mixtures of normal (TP-SMN) family components. This family allows the development of a robust estimation of FM models. The TP-SMN is a rich class of distributions that covers symmetric/asymmetric and light/heavy tailed distributions. It represents an alternative family to the well-known scale mixtures of the skew normal (SMSN) family studied by Branco and Dey (2001). Also, the TP-SMN covers the SMN (normal, t, slash, and contaminated normal distributions) as the symmetric members and two-piece versions of them as asymmetric members. A key feature of this study is using a suitable hierarchical representation of the family to obtain maximum likelihood estimates of model parameters via an EM-type algorithm. The performances of the proposed robust model are demonstrated using simulated and real data, and then compared to other finite mixture of SMSN models.

A Comparison of Liquid Scintillation and Geiger–Müller Estimates of Primary Productivity in an in situ Experiment

1973 ◽  
Vol 30 (5) ◽  
pp. 708-711 ◽  
Author(s):  
F. J. Ward ◽  
Masami Nakanishi
Keyword(s):  
Light Intensity ◽  
Surface Area ◽  
Primary Productivity ◽  
Liquid Scintillation ◽  
Lake Biwa ◽  
In Situ Experiment ◽  
M Estimate ◽  
M Estimates ◽  
Loss Rates

For an in situ experiment conducted in Shiozu Bay, Lake Biwa, Japan, primary productivity estimates from liquid scintillation radioactivity counts of wet algae were generally higher than those from Geiger–Müller radioactivity counts of desiccated algae. Values at 0 m were similar, the G–M estimate at 0.5 m was 10% higher, but from 3 to 13 m the liquid scintillation values ranged from 11 to 33% higher than G–M estimates. The 20-m estimates were low and similar. Differences were caused primarily by 14C losses during desiccation prior to G–M counting. Increasing loss rates between 0.5 and 3.0 m may have been caused by decreasing light intensity. On the basis of surface area, the estimate from liquid scintillation data was 27% greater than that obtained from G–M data.

Post-That Washing Prior to Transplantation of Umbilical Cord Blood (UCB) That Were Depleted of Plasma but Not of Red Blood Cells.

Blood ◽  
2006 ◽  
Vol 108 (11) ◽  
pp. 5229-5229
Author(s):  
Robert Chow ◽  
Patrick Tan ◽  
Tang-Her Jaing ◽  
Joseph Rosenthal ◽  
Auayporn Nademanee ◽  
...  
Keyword(s):  
Median Time ◽  
Relapse Rate ◽  
Survival Data ◽  
Negative Impact ◽  
Chronic Gvhd ◽  
Cell Recovery ◽  
Hematopoietic Stem ◽  
Kaplan Meier ◽  
M Estimate ◽  
M Estimates

Abstract Washing after thawing of frozen UCB used for hematopoietic stem cell transplantation (HSCT) is widely practiced for the purpose of removal of the cryoprotectant DMSO and free hemoglobin from lysed red cells. An updated retrospective audited analysis was performed on the outcomes of 208 PD UCB used in 186 patients with known thaw conditions that have engraftment and/or survival data −106 washed (W) and 80 non-washed (NW). When the DMSO dose was kept under the recommended 1 g per kg of recipient weight, the only severe adverse reaction was a seizure and encephalopathy following infusion of a NW PD UCB that resolved without any sequelae. Total nucleated cell recovery after thawing as reported by transplant centers was higher for NW (median 89% vs. 75%). The Kaplan-Meier estimate of 3-month neutrophil (ANC500) engraftment were 91±4% for NW versus 88±4% for W with median time to neutrophil of 21 versus 24 days (p = 0.02). The K-M estimate for 6-month platelet 20K engraftment were 86±6% for NW and 78±5% for W with median time to engraftment at 46 days for NW and 55 days for W (p = 0.002). Acute grade III–IV GvHD were similar at 12% (NW) and 13% (W), but extensive chronic GvHD were 4% (NW) and 19% (W). 1-year TRM were 25±5% for NW and 34±5% for W (p=0.75), with relapse rate at 16±5% for NW and 28±5% for W (p=0.09). K-M estimates of 1-year OS were 63±6% versus 53±5% (p = 0.54), and for 1-year DFS were 62±6% versus 48±5% (p = 0.23) for NW and W respectively. To our knowledge, this was the largest transplant outcome study comparing no post-thaw wash versus wash for UCB, though the conclusions are confined to PD CBU. No clear benefits of post-thaw washing were seen for PD UCB. HSCT with NW PD UCB was at least as efficacious as that using W PD UCB with respect to GvHD, TRM, relapse rate, 1-year OS and DFS. Moreover, washing may have a negative impact on neutrophil and platelet engraftment of PD UCB.

Type I Error Rates and Power Estimates of Selected Parametric and Nonparametric Tests of Scale

1987 ◽  
Vol 12 (1) ◽  
pp. 45-61 ◽  
Author(s):  
Stephen F. Olejnik ◽  
James Algina
Keyword(s):  
Type I Error ◽  
Nonparametric Tests ◽  
Error Rates ◽  
Type I ◽  
Normal Distributions ◽  
Type I Error Rates ◽  
Heavy Tailed Distributions ◽  
The Mean ◽  
Heavy Tailed ◽  
Distribution Type

Estimated Type I error rates and power are reported for the Brown-Forsythe, O’Brien, Klotz, and Siegel-Tukey procedures. The effect of aligning the data, by using deviations from group means or group medians, is investigated for the latter two tests. Normal and non-normal distributions, equal and unequal sample-size combinations, and equal and unequal means are investigated for a two-group design. No test is robust and most powerful for all distributions, however, using O’Brien’s procedure will avoid the possibility of a liberal test and provide power almost as large as what would be provided by choosing the most powerful test for each distribution type. Using the Brown-Forsythe procedure with heavy-tailed distributions and O’Brien’s procedure for other distributions will increase power modestly and maintain robustness. Using the mean-aligned Klotz test or the unaligned Klotz test with appropriate distributions can increase power, but only at the risk of increased Type I error rates if the tests are not accurately matched to the distribution type.

scholarly journals Regularization Methods Based on the Lq-Likelihood for Linear Models with Heavy-Tailed Errors

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 1036
Author(s):  
Yoshihiro Hirose
Keyword(s):  
Linear Model ◽  
Power Function ◽  
Numerical Experiments ◽  
Linear Models ◽  
Regularization Methods ◽  
Penalized Least Squares ◽  
Normal Distributions ◽  
Normal Linear Model ◽  
Log Likelihood ◽  
Heavy Tailed

We propose regularization methods for linear models based on the Lq-likelihood, which is a generalization of the log-likelihood using a power function. Regularization methods are popular for the estimation in the normal linear model. However, heavy-tailed errors are also important in statistics and machine learning. We assume q-normal distributions as the errors in linear models. A q-normal distribution is heavy-tailed, which is defined using a power function, not the exponential function. We find that the proposed methods for linear models with q-normal errors coincide with the ordinary regularization methods that are applied to the normal linear model. The proposed methods can be computed using existing packages because they are penalized least squares methods. We examine the proposed methods using numerical experiments, showing that the methods perform well, even when the error is heavy-tailed. The numerical experiments also illustrate that our methods work well in model selection and generalization, especially when the error is slightly heavy-tailed.

Sparse Bayesian linear regression using generalized normal priors

2017 ◽  
Vol 15 (03) ◽  
pp. 1750021
Author(s):  
Hai Zhang ◽  
Puyu Wang ◽  
Qing Dong ◽  
Pu Wang
Keyword(s):  
Linear Regression ◽  
Predictor Variable ◽  
Real Data ◽  
Regression Coefficients ◽  
Bayesian Lasso ◽  
Normal Distributions ◽  
Regression Estimators ◽  
Bayesian Linear Regression ◽  
Heavy Tailed ◽  
Mixtures Of Normal Distributions

A sparse Bayesian linear regression model is proposed that generalizes the Bayesian Lasso to a class of Bayesian models with scale mixtures of normal distributions as priors for the regression coefficients. We assume a hierarchical Bayesian model with a binary indicator for whether a predictor variable is included in the model, a generalized normal prior distribution for the coefficients of the included variables, and a Student-t error model for robustness to heavy tailed noise. Our model out-performs other popular sparse regression estimators on synthetic and real data.

scholarly journals The Battle of the Video Codecs in the Healthcare Domain - A Comparative Performance Evaluation Study Leveraging VVC and AV1

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 11469-11481 ◽  
Author(s):  
Andreas S. Panayides ◽  
Marios S. Pattichis ◽  
Marios Pantziaris ◽  
Anthony G. Constantinides ◽  
Constantinos S. Pattichis
Keyword(s):  
Performance Evaluation ◽  
Evaluation Study ◽  
Comparative Performance ◽  
Video Codecs
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