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Nonparametric Probability Density Function Estimation Using the Padé Approximation.

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Titel: Nonparametric Probability Density Function Estimation Using the Padé Approximation.
Autoren: Aghamiri, Hamid Reza1 (AUTHOR), Hosseini, S. Abolfazl2 (AUTHOR), Green, James R.1,3 (AUTHOR), Oommen, B. John1,3 (AUTHOR) oommen@scs.carleton.ca
Quelle: Algorithms. Feb2025, Vol. 18 Issue 2, p88. 22p.
Schlagwörter: *PROBABILITY density function, *NONPARAMETRIC estimation, *SIGNAL processing, *SAMPLE size (Statistics), *ENGINEERING
Abstract: Estimating the Probability Density Function (PDF) of observed data is crucial as a problem in its own right, and also for diverse engineering applications. This paper utilizes two powerful mathematical tools, the concept of moments and the relatively little-known Padé approximation to achieve this. On the one hand, moments encapsulate crucial information that is central to both the "time-" and "frequency-"domain representations of the data. On the other hand, the Padé approximation provides an effective means of obtaining a convergent series from the data. In this paper, we invoke these established tools to estimate the PDF. As far as we know, the theoretical results that we have proven, and the experimental results that confirm them, are novel and rather pioneering. The method we propose is nonparametric. It leverages the concept of using the moments of the sample data—drawn from the unknown PDF that we aim to estimate—to reconstruct the original PDF. This is achieved through the application of the Padé approximation. Apart from the theoretical analysis, we have also experimentally evaluated the validity and efficiency of our scheme. The Padé approximation is asymmetric. The most unique facet of our work is that we have utilized this asymmetry to our advantage by working with two mirrored versions of the data to obtain two different versions of the PDF. We have then effectively "superimposed" them to yield the final composite PDF. We are not aware of any other research that utilizes such a composite strategy, in any signal processing domain. To evaluate the performance of the proposed method, we have employed synthetic samples obtained from various well-known distributions, including mixture densities. The accuracy of the proposed method has also been compared with that gleaned by several State-Of-The-Art (SOTA) approaches. The results that we have obtained underscore the robustness and effectiveness of our method, particularly in scenarios where the sample sizes are considerably reduced. Thus, this research confirms how the SOTA of estimating nonparametric PDFs can be enhanced by the Padé approximation, offering notable advantages over existing methods in terms of accuracy when faced with limited data. [ABSTRACT FROM AUTHOR]
Datenbank: Academic Search Index
Beschreibung
Abstract:Estimating the Probability Density Function (PDF) of observed data is crucial as a problem in its own right, and also for diverse engineering applications. This paper utilizes two powerful mathematical tools, the concept of moments and the relatively little-known Padé approximation to achieve this. On the one hand, moments encapsulate crucial information that is central to both the "time-" and "frequency-"domain representations of the data. On the other hand, the Padé approximation provides an effective means of obtaining a convergent series from the data. In this paper, we invoke these established tools to estimate the PDF. As far as we know, the theoretical results that we have proven, and the experimental results that confirm them, are novel and rather pioneering. The method we propose is nonparametric. It leverages the concept of using the moments of the sample data—drawn from the unknown PDF that we aim to estimate—to reconstruct the original PDF. This is achieved through the application of the Padé approximation. Apart from the theoretical analysis, we have also experimentally evaluated the validity and efficiency of our scheme. The Padé approximation is asymmetric. The most unique facet of our work is that we have utilized this asymmetry to our advantage by working with two mirrored versions of the data to obtain two different versions of the PDF. We have then effectively "superimposed" them to yield the final composite PDF. We are not aware of any other research that utilizes such a composite strategy, in any signal processing domain. To evaluate the performance of the proposed method, we have employed synthetic samples obtained from various well-known distributions, including mixture densities. The accuracy of the proposed method has also been compared with that gleaned by several State-Of-The-Art (SOTA) approaches. The results that we have obtained underscore the robustness and effectiveness of our method, particularly in scenarios where the sample sizes are considerably reduced. Thus, this research confirms how the SOTA of estimating nonparametric PDFs can be enhanced by the Padé approximation, offering notable advantages over existing methods in terms of accuracy when faced with limited data. [ABSTRACT FROM AUTHOR]
ISSN:19994893
DOI:10.3390/a18020088