Comparison of high-breakdown-point estimators for image denoising

Observations on certain real-life cases include units that are incompatible with other data sets. Values that are extreme in nature do influence estimates obtained by conventional estimators. Robust estimators are therefore necessary for efficient estimation of parameters. This paper uses stratification with simple random sampling without replacement to optimize sample allocation in stratum for efficient parameter estimation as an alternative method of handling highly contaminated samples. Our proposed method stratifies the highly contaminated population into two non-overlapping sub-populations, and stratified samples of sizes 50, 200, and 500 was drawn. We estimate the model parameters form the contaminated sampled data using ordinary least squares under the proposed method, and using the two high breakdown point estimators; the Least Median of Squares and Least Trimmed Squares. Our findings shows that the proposed method did not perform well for low contamination levels (⩽ 30%) but outperformed Least Median of Squares and Least Trimmed Squares for higher contamination rates (⩾ 40%). This indicates that our proposed method compares well and compete favorably with the two high breakdown point estimators.

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ASYMPTOTIC THEORY FOR SOME HIGH BREAKDOWN POINT ESTIMATORS

Econometric Theory ◽

10.1017/s0266466602185070 ◽

2002 ◽

Vol 18 (5) ◽

pp. 1172-1196 ◽

Cited By ~ 18

Author(s):

Victoria Zinde-Walsh

Keyword(s):

Time Series ◽

Gaussian Process ◽

Wiener Process ◽

Asymptotic Theory ◽

Breakdown Point ◽

Generalized Derivative ◽

Limit Process ◽

High Breakdown Point ◽

Point Estimators ◽

Joint Limit

High breakdown point estimators in regression are robust against gross contamination in the regressors and also in the errors; the least median of squares (LMS) estimator has the additional property of packing the majority of the sample most tightly around the estimated regression hyperplane in terms of absolute deviations of the residuals and thus is helpful in identifying outliers. Asymptotics for a class of high breakdown point smoothed LMS estimators are derived here under a variety of conditions that allow for time series applications; joint limit processes for several smoothed estimators are examined. The limit process for the LMS estimator is represented via a generalized Gaussian process that defines the generalized derivative of the Wiener process.

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Robust Estimation of Variance Components with High Breakdown Point in the 1-Way Random Effect Model

Contributions to Statistics - Industrial Statistics ◽

10.1007/978-3-642-59268-3_5 ◽

1997 ◽

pp. 65-73 ◽

Cited By ~ 2

Author(s):

Steffen Uhlig

Keyword(s):

Robust Estimation ◽

Variance Components ◽

Random Effect ◽

Random Effect Model ◽

Breakdown Point ◽

High Breakdown Point ◽

Effect Model ◽

Estimation Of Variance

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About Regression Estimators with High Breakdown Point

Statistics ◽

10.1080/02331889808802657 ◽

1998 ◽

Vol 32 (2) ◽

pp. 111-129 ◽

Cited By ~ 29

Author(s):

D. L. Vandev ◽

N. M. Neykov*

Keyword(s):

Breakdown Point ◽

High Breakdown Point ◽

Regression Estimators

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GENERAL TRIMMED ESTIMATION: ROBUST APPROACH TO NONLINEAR AND LIMITED DEPENDENT VARIABLE MODELS

Econometric Theory ◽

10.1017/s0266466608080596 ◽

2008 ◽

Vol 24 (6) ◽

pp. 1500-1529 ◽

Cited By ~ 35

Author(s):

Pavel Čížek

Keyword(s):

Regression Models ◽

Breakdown Point ◽

Robust Estimators ◽

Linear Regression Models ◽

Mixing Conditions ◽

Least Trimmed Squares ◽

Limited Dependent Variable ◽

Data Contamination ◽

High Breakdown Point ◽

Regression Estimators

High-breakdown-point regression estimators protect against large errors and data contamination. We generalize the concept of trimming used by many of these robust estimators, such as the least trimmed squares and maximum trimmed likelihood, and propose a general trimmed estimator, which renders robust estimators applicable far beyond the standard (non)linear regression models. We derive here the consistency and asymptotic distribution of the proposed general trimmed estimator under mild β-mixing conditions and demonstrate its applicability in nonlinear regression and limited dependent variable models.

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