Comparison of Estimators of Equity Return Standard Deviation Using Pitman Closeness Criterion and Control Charting Applications

Alan, Chow; Dane, Lahtinen Kyre; Kelsey, Edwards

doi:10.2478/sbe-2020-0001

Cited by 1 publication

(1 citation statement)

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“…In subsection III-C, we illustrate our method by a numerical example where we apply the procedure on a simulated sample. In subsection III-D, we compare our estimators to other common estimators by their bias, mean square error, and Pitman closeness criterion explained in [15], [16] and [17].…”

Section: Introductionmentioning

confidence: 99%

Asymptotically Unbiased Estimation of Mean and Standard Deviation in the Presence of Outlying Errors

Joudah

Abbas

2020

IEEE Access

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In this work, we develop a new method for estimating the mean and standard deviation of normally distributed populations when errors exist in the sample. Our estimators are asymptotically unbiased if all errors are outlying errors (i.e. all errors lie outside a region defined by the parameters of normal distribution). However, the proposed method requires having an upper bound for the percentage of errors in the sample. The proposed method is compared with the already existing and commonly used estimators in terms of bias, mean square error, and Pitman closeness criterion. The proposed method is found to be superior to the others when the sample size is not too small. A simulation study is designed to test the performance of our estimators when most but not all errors are outlying errors. The findings of the simulation study also indicate the superiority of the proposed method when the sample size is moderately large. As an application, we use our method in Phase I of designing a control chart to improve its performance. We apply the method on a dataset where the robustness of our proposed method is tested (and compared with the other estimators) against the presence of outlying errors in Phase I data. In the findings of the application, we notice that our estimators were the only ones that identified out of control data points in Phase II when Phase I samples are contaminated with the outliers.

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Section: Introductionmentioning

confidence: 99%