Compromised-Imputation and EWMA-Based Memory-Type Mean Estimators Using Quantile Regression
Survey sampling commonly faces the challenge of missing information, prompting the development of various imputation-based mean estimation methods to address this concern. Among these, ratio-type regression estimators have been devised to compute population parameters using only current sample data....
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-10-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/10/1888 |
| _version_ | 1797572188821258240 |
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| author | Mohammed Ahmed Alomair Usman Shahzad |
| author_facet | Mohammed Ahmed Alomair Usman Shahzad |
| author_sort | Mohammed Ahmed Alomair |
| collection | DOAJ |
| description | Survey sampling commonly faces the challenge of missing information, prompting the development of various imputation-based mean estimation methods to address this concern. Among these, ratio-type regression estimators have been devised to compute population parameters using only current sample data. However, recent pioneering research has revolutionized this approach by integrating both past and current sample information through the application of exponentially weighted moving averages (EWMA). This groundbreaking methodology has given rise to the creation of memory-type estimators tailored for surveys conducted over time. In this paper, we present novel imputation-based memory-type mean estimators that leverage EWMA and quantile regression to handle missing observations. For the performance assessment between traditional, adapted and proposed estimators, real-life time-scaled datasets related to the stock market and humidity are considered. Furthermore, we conduct a simulation study using an asymmetric dataset to further validate the effectiveness of the introduced estimators. The humidity data results show that the proposed estimators (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><msub><mi>p</mi><msub><mi>q</mi><mrow><mo>(</mo><mn>0.25</mn><mo>)</mo></mrow></msub></msub></msub></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><msub><mi>p</mi><msub><mi>q</mi><mrow><mo>(</mo><mn>0.45</mn><mo>)</mo></mrow></msub></msub></msub></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi>T</mi><mrow><msub><mi>p</mi><msub><mi>q</mi><mrow><mo>(</mo><mn>0.25</mn><mo>)</mo></mrow></msub></msub></mrow><msup><mrow></mrow><mo>′</mo></msup></msubsup></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi>T</mi><mrow><msub><mi>p</mi><msub><mi>q</mi><mrow><mo>(</mo><mn>0.45</mn><mo>)</mo></mrow></msub></msub></mrow><msup><mrow></mrow><mo>′</mo></msup></msubsup></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi>T</mi><mrow><msub><mi>p</mi><msub><mi>q</mi><mrow><mo>(</mo><mn>0.25</mn><mo>)</mo></mrow></msub></msub></mrow><msup><mrow></mrow><mrow><mo>″</mo></mrow></msup></msubsup></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi>T</mi><mrow><msub><mi>p</mi><msub><mi>q</mi><mrow><mo>(</mo><mn>0.45</mn><mo>)</mo></mrow></msub></msub></mrow><msup><mrow></mrow><mrow><mo>″</mo></mrow></msup></msubsup></semantics></math></inline-formula>) have the minimum MSE. The stock market data results show that the proposed estimators (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><msub><mi>p</mi><msub><mi>q</mi><mrow><mo>(</mo><mn>0.85</mn><mo>)</mo></mrow></msub></msub></msub></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi>T</mi><mrow><msub><mi>p</mi><msub><mi>q</mi><mrow><mo>(</mo><mn>0.85</mn><mo>)</mo></mrow></msub></msub></mrow><msup><mrow></mrow><mo>′</mo></msup></msubsup></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi>T</mi><mrow><msub><mi>p</mi><msub><mi>q</mi><mrow><mo>(</mo><mn>0.85</mn><mo>)</mo></mrow></msub></msub></mrow><msup><mrow></mrow><mrow><mo>″</mo></mrow></msup></msubsup></semantics></math></inline-formula>) also have the minimum MSE. Additionally, the simulation results demonstrate that the proposed estimators (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><msub><mi>p</mi><msub><mi>q</mi><mrow><mo>(</mo><mn>0.45</mn><mo>)</mo></mrow></msub></msub></msub></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi>T</mi><mrow><msub><mi>p</mi><msub><mi>q</mi><mrow><mo>(</mo><mn>0.45</mn><mo>)</mo></mrow></msub></msub></mrow><msup><mrow></mrow><mo>′</mo></msup></msubsup></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi>T</mi><mrow><msub><mi>p</mi><msub><mi>q</mi><mrow><mo>(</mo><mn>0.45</mn><mo>)</mo></mrow></msub></msub></mrow><msup><mrow></mrow><mrow><mo>″</mo></mrow></msup></msubsup></semantics></math></inline-formula>) have the minimum MSE when compared to traditional and adapted estimators. Therefore, in conclusion, the use of the proposed estimators is recommended over traditional and adapted ones. |
| first_indexed | 2024-03-10T20:51:47Z |
| format | Article |
| id | doaj.art-657087cc1b87454185e8f98b9bf239a2 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T20:51:47Z |
| publishDate | 2023-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-657087cc1b87454185e8f98b9bf239a22023-11-19T18:18:16ZengMDPI AGSymmetry2073-89942023-10-011510188810.3390/sym15101888Compromised-Imputation and EWMA-Based Memory-Type Mean Estimators Using Quantile RegressionMohammed Ahmed Alomair0Usman Shahzad1Department of Quantitative Methods, School of Business, King Faisal University, Al-Ahsa 31982, Saudi ArabiaDepartment of Mathematics and Statistics, International Islamic University, Islamabad 44000, PakistanSurvey sampling commonly faces the challenge of missing information, prompting the development of various imputation-based mean estimation methods to address this concern. Among these, ratio-type regression estimators have been devised to compute population parameters using only current sample data. However, recent pioneering research has revolutionized this approach by integrating both past and current sample information through the application of exponentially weighted moving averages (EWMA). This groundbreaking methodology has given rise to the creation of memory-type estimators tailored for surveys conducted over time. In this paper, we present novel imputation-based memory-type mean estimators that leverage EWMA and quantile regression to handle missing observations. For the performance assessment between traditional, adapted and proposed estimators, real-life time-scaled datasets related to the stock market and humidity are considered. Furthermore, we conduct a simulation study using an asymmetric dataset to further validate the effectiveness of the introduced estimators. The humidity data results show that the proposed estimators (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><msub><mi>p</mi><msub><mi>q</mi><mrow><mo>(</mo><mn>0.25</mn><mo>)</mo></mrow></msub></msub></msub></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><msub><mi>p</mi><msub><mi>q</mi><mrow><mo>(</mo><mn>0.45</mn><mo>)</mo></mrow></msub></msub></msub></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi>T</mi><mrow><msub><mi>p</mi><msub><mi>q</mi><mrow><mo>(</mo><mn>0.25</mn><mo>)</mo></mrow></msub></msub></mrow><msup><mrow></mrow><mo>′</mo></msup></msubsup></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi>T</mi><mrow><msub><mi>p</mi><msub><mi>q</mi><mrow><mo>(</mo><mn>0.45</mn><mo>)</mo></mrow></msub></msub></mrow><msup><mrow></mrow><mo>′</mo></msup></msubsup></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi>T</mi><mrow><msub><mi>p</mi><msub><mi>q</mi><mrow><mo>(</mo><mn>0.25</mn><mo>)</mo></mrow></msub></msub></mrow><msup><mrow></mrow><mrow><mo>″</mo></mrow></msup></msubsup></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi>T</mi><mrow><msub><mi>p</mi><msub><mi>q</mi><mrow><mo>(</mo><mn>0.45</mn><mo>)</mo></mrow></msub></msub></mrow><msup><mrow></mrow><mrow><mo>″</mo></mrow></msup></msubsup></semantics></math></inline-formula>) have the minimum MSE. The stock market data results show that the proposed estimators (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><msub><mi>p</mi><msub><mi>q</mi><mrow><mo>(</mo><mn>0.85</mn><mo>)</mo></mrow></msub></msub></msub></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi>T</mi><mrow><msub><mi>p</mi><msub><mi>q</mi><mrow><mo>(</mo><mn>0.85</mn><mo>)</mo></mrow></msub></msub></mrow><msup><mrow></mrow><mo>′</mo></msup></msubsup></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi>T</mi><mrow><msub><mi>p</mi><msub><mi>q</mi><mrow><mo>(</mo><mn>0.85</mn><mo>)</mo></mrow></msub></msub></mrow><msup><mrow></mrow><mrow><mo>″</mo></mrow></msup></msubsup></semantics></math></inline-formula>) also have the minimum MSE. Additionally, the simulation results demonstrate that the proposed estimators (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><msub><mi>p</mi><msub><mi>q</mi><mrow><mo>(</mo><mn>0.45</mn><mo>)</mo></mrow></msub></msub></msub></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi>T</mi><mrow><msub><mi>p</mi><msub><mi>q</mi><mrow><mo>(</mo><mn>0.45</mn><mo>)</mo></mrow></msub></msub></mrow><msup><mrow></mrow><mo>′</mo></msup></msubsup></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi>T</mi><mrow><msub><mi>p</mi><msub><mi>q</mi><mrow><mo>(</mo><mn>0.45</mn><mo>)</mo></mrow></msub></msub></mrow><msup><mrow></mrow><mrow><mo>″</mo></mrow></msup></msubsup></semantics></math></inline-formula>) have the minimum MSE when compared to traditional and adapted estimators. Therefore, in conclusion, the use of the proposed estimators is recommended over traditional and adapted ones.https://www.mdpi.com/2073-8994/15/10/1888missing informationimputation methodsquantile regressionEWMAmean square error |
| spellingShingle | Mohammed Ahmed Alomair Usman Shahzad Compromised-Imputation and EWMA-Based Memory-Type Mean Estimators Using Quantile Regression Symmetry missing information imputation methods quantile regression EWMA mean square error |
| title | Compromised-Imputation and EWMA-Based Memory-Type Mean Estimators Using Quantile Regression |
| title_full | Compromised-Imputation and EWMA-Based Memory-Type Mean Estimators Using Quantile Regression |
| title_fullStr | Compromised-Imputation and EWMA-Based Memory-Type Mean Estimators Using Quantile Regression |
| title_full_unstemmed | Compromised-Imputation and EWMA-Based Memory-Type Mean Estimators Using Quantile Regression |
| title_short | Compromised-Imputation and EWMA-Based Memory-Type Mean Estimators Using Quantile Regression |
| title_sort | compromised imputation and ewma based memory type mean estimators using quantile regression |
| topic | missing information imputation methods quantile regression EWMA mean square error |
| url | https://www.mdpi.com/2073-8994/15/10/1888 |
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