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

Article type: Research Article

Authors: P. Dibal, Nicholas^{a; *} | Dallah, Hamadu^b

Affiliations: [a] Department of Mathematical Sciences, University of Maiduguri, Maiduguri, Nigeria | [b] Department of Actuarial Science, University of Lagos, Lagos, Nigeria

Correspondence: [*] Corresponding author: Nicholas P. Dibal, Department of Mathematical Sciences, University of Maiduguri, Nigeria. Tel.: +234 8065558591; E-mail: pndibal@unimaid.edu.ng.

Abstract: 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.

Keywords: Stratification, contamination, high breakdown point, ordinary least squares

DOI: 10.3233/MAS-210523

Journal: Model Assisted Statistics and Applications, vol. 16, no. 2, pp. 109-115, 2021