Stratified sampling in highly polluted data as an effective and reliable alternative to high breakdown point estimators

2021 ◽  
Vol 16 (2) ◽  
pp. 109-115
Author(s):  
Nicholas P. Dibal ◽  
Hamadu Dallah
Keyword(s):  
Real Life ◽  
Breakdown Point ◽  
Ordinary Least Squares ◽  
Efficient Estimation ◽  
Model Parameters ◽  
Sampled Data ◽  
Least Trimmed Squares ◽  
High Breakdown Point ◽  
Least Median Of Squares ◽  
Point Estimators

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.

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

2008 ◽  
Vol 24 (6) ◽  
pp. 1500-1529 ◽  
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.

scholarly journals ASYMPTOTIC THEORY FOR SOME HIGH BREAKDOWN POINT ESTIMATORS

2002 ◽  
Vol 18 (5) ◽  
pp. 1172-1196 ◽  
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.

scholarly journals Robustness and Sensitivity Tuning of the Kalman Filter for Speech Enhancement

Signals ◽  
2021 ◽  
Vol 2 (3) ◽  
pp. 434-455
Author(s):  
Sujan Kumar Roy ◽  
Kuldip K. Paliwal
Keyword(s):  
Kalman Filter ◽  
Speech Enhancement ◽  
Linear Prediction ◽  
Real Life ◽  
Model Parameters ◽  
Noise Variance ◽  
Noisy Speech ◽  
Kalman Gain ◽  
Whitening Filter ◽  
Prediction Coefficient

Inaccurate estimates of the linear prediction coefficient (LPC) and noise variance introduce bias in Kalman filter (KF) gain and degrade speech enhancement performance. The existing methods propose a tuning of the biased Kalman gain, particularly in stationary noise conditions. This paper introduces a tuning of the KF gain for speech enhancement in real-life noise conditions. First, we estimate noise from each noisy speech frame using a speech presence probability (SPP) method to compute the noise variance. Then, we construct a whitening filter (with its coefficients computed from the estimated noise) to pre-whiten each noisy speech frame prior to computing the speech LPC parameters. We then construct the KF with the estimated parameters, where the robustness metric offsets the bias in KF gain during speech absence of noisy speech to that of the sensitivity metric during speech presence to achieve better noise reduction. The noise variance and the speech model parameters are adopted as a speech activity detector. The reduced-biased Kalman gain enables the KF to minimize the noise effect significantly, yielding the enhanced speech. Objective and subjective scores on the NOIZEUS corpus demonstrate that the enhanced speech produced by the proposed method exhibits higher quality and intelligibility than some benchmark methods.

A robust possibilistic programming model for production-routing problem in a three-echelon supply chain

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mohammad Ali Beheshtinia ◽  
Narjes Salmabadi ◽  
Somaye Rahimi
Keyword(s):  
Supply Chain ◽  
Real Life ◽  
Model Parameters ◽  
Pickup And Delivery ◽  
Distribution Centers ◽  
Routing Problem ◽  
Remarkable Feature ◽  
Content Type ◽  
Proposed Model ◽  
Production Routing

Purpose This paper aims to provide an integrated production-routing model in a three-echelon supply chain containing a two-layer transportation system to minimize the total costs of production, transportation, inventory holding and expired drugs treatment. In the proposed problem, some specifications such as multisite manufacturing, simultaneous pickup and delivery and uncertainty in parameters are considered. Design/methodology/approach At first, a mathematical model has been proposed for the problem. Then, one possibilistic model and one robust possibilistic model equivalent to the initial model are provided regarding the uncertain nature of the model parameters and the inaccessibility of their probability function. Finally, the performance of the proposed model is evaluated using the real data collected from a pharmaceutical production center in Iran. The results reveal the proper performance of the proposed models. Findings The results obtained from applying the proposed model to a real-life production center indicated that the number of expired drugs has decreased because of using this model, also the costs of the system were reduced owing to integrating simultaneous drug pickup and delivery operations. Moreover, regarding the results of simulations, the robust possibilistic model had the best performance among the proposed models. Originality/value This research considers a two-layer vehicle routing in a production-routing problem with inventory planning. Moreover, multisite manufacturing, simultaneous pickup of the expired drugs and delivery of the drugs to the distribution centers are considered. Providing a robust possibilistic model for tackling the uncertainty in demand, costs, production capacity and drug expiration costs is considered as another remarkable feature of the proposed model.

Identification of ’Effective’ Linear Joints Using Coupling and Joint Identification Techniques

1998 ◽  
Vol 120 (2) ◽  
pp. 331-338 ◽  
Author(s):  
Y. Ren ◽  
C. F. Beards
Keyword(s):  
Dynamic Properties ◽  
Real Life ◽  
Model Parameters ◽  
Coupling Technique ◽  
Alternative Approach ◽  
Identification Technique ◽  
Joint Identification ◽  
Stiff Joint ◽  
Almost All ◽  
Identification Techniques

Almost all real-life structures are assembled from components connected by various types of joints. Unlike many other parts, the dynamic properties of a joint are difficult to model analytically. An alternative approach for establishing a theoretical model of a joint is to extract the model parameters from experimental data using joint identification techniques. The accuracy of the identification is significantly affected by the properties of the joints themselves. If a joint is stiff, its properties are often difficult to identify accurately. This is because the responses at both ends of the joint are linearly-dependent. To make things worse, the existence of a stiff joint can also affect the accuracy of identification of other effective joints (the term “effective joints” in this paper refers to those joints which otherwise can be identified accurately). This problem is tackled by coupling these stiff joints using a generalized coupling technique, and then the properties of the remaining joints are identified using a joint identification technique. The accuracy of the joint identification can usually be improved by using this approach. Both numerically simulated and experimental results are presented.

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