| Summary: | 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.
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