Nonparametric Estimation of Continuously Parametrized Families of Probability Density Functions—Computational Aspects
We consider a rather general problem of nonparametric estimation of an uncountable set of probability density functions (p.d.f.’s) of the form: <inline-formula> <math display="inline"> <semantics> <mrow> <mi>f</mi> <mo>(</mo> <mi>x</...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-07-01
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| Series: | Algorithms |
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| Online Access: | https://www.mdpi.com/1999-4893/13/7/164 |
| _version_ | 1797563020898992128 |
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| author | Wojciech Rafajłowicz |
| author_facet | Wojciech Rafajłowicz |
| author_sort | Wojciech Rafajłowicz |
| collection | DOAJ |
| description | We consider a rather general problem of nonparametric estimation of an uncountable set of probability density functions (p.d.f.’s) of the form: <inline-formula> <math display="inline"> <semantics> <mrow> <mi>f</mi> <mo>(</mo> <mi>x</mi> <mo>;</mo> <mspace width="0.166667em"></mspace> <mi>r</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>, where <i>r</i> is a non-random real variable and ranges from <inline-formula> <math display="inline"> <semantics> <msub> <mi>R</mi> <mn>1</mn> </msub> </semantics> </math> </inline-formula> to <inline-formula> <math display="inline"> <semantics> <msub> <mi>R</mi> <mn>2</mn> </msub> </semantics> </math> </inline-formula>. We put emphasis on the algorithmic aspects of this problem, since they are crucial for exploratory analysis of big data that are needed for the estimation. A specialized learning algorithm, based on the 2D FFT, is proposed and tested on observations that allow for estimate p.d.f.’s of a jet engine temperatures as a function of its rotation speed. We also derive theoretical results concerning the convergence of the estimation procedure that contains hints on selecting parameters of the estimation algorithm. |
| first_indexed | 2024-03-10T18:36:37Z |
| format | Article |
| id | doaj.art-845c6da7eda44aa78e2dcbe4a02cd8c7 |
| institution | Directory Open Access Journal |
| issn | 1999-4893 |
| language | English |
| last_indexed | 2024-03-10T18:36:37Z |
| publishDate | 2020-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Algorithms |
| spelling | doaj.art-845c6da7eda44aa78e2dcbe4a02cd8c72023-11-20T06:13:38ZengMDPI AGAlgorithms1999-48932020-07-0113716410.3390/a13070164Nonparametric Estimation of Continuously Parametrized Families of Probability Density Functions—Computational AspectsWojciech Rafajłowicz0Department of Computer Engineering, Wroclaw University of Science and Technology, Wyb Wyspianskiego 27, 50 370 Wroclaw, PolandWe consider a rather general problem of nonparametric estimation of an uncountable set of probability density functions (p.d.f.’s) of the form: <inline-formula> <math display="inline"> <semantics> <mrow> <mi>f</mi> <mo>(</mo> <mi>x</mi> <mo>;</mo> <mspace width="0.166667em"></mspace> <mi>r</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>, where <i>r</i> is a non-random real variable and ranges from <inline-formula> <math display="inline"> <semantics> <msub> <mi>R</mi> <mn>1</mn> </msub> </semantics> </math> </inline-formula> to <inline-formula> <math display="inline"> <semantics> <msub> <mi>R</mi> <mn>2</mn> </msub> </semantics> </math> </inline-formula>. We put emphasis on the algorithmic aspects of this problem, since they are crucial for exploratory analysis of big data that are needed for the estimation. A specialized learning algorithm, based on the 2D FFT, is proposed and tested on observations that allow for estimate p.d.f.’s of a jet engine temperatures as a function of its rotation speed. We also derive theoretical results concerning the convergence of the estimation procedure that contains hints on selecting parameters of the estimation algorithm.https://www.mdpi.com/1999-4893/13/7/164nonparametric estimationFFTfamily of probability density functions |
| spellingShingle | Wojciech Rafajłowicz Nonparametric Estimation of Continuously Parametrized Families of Probability Density Functions—Computational Aspects Algorithms nonparametric estimation FFT family of probability density functions |
| title | Nonparametric Estimation of Continuously Parametrized Families of Probability Density Functions—Computational Aspects |
| title_full | Nonparametric Estimation of Continuously Parametrized Families of Probability Density Functions—Computational Aspects |
| title_fullStr | Nonparametric Estimation of Continuously Parametrized Families of Probability Density Functions—Computational Aspects |
| title_full_unstemmed | Nonparametric Estimation of Continuously Parametrized Families of Probability Density Functions—Computational Aspects |
| title_short | Nonparametric Estimation of Continuously Parametrized Families of Probability Density Functions—Computational Aspects |
| title_sort | nonparametric estimation of continuously parametrized families of probability density functions computational aspects |
| topic | nonparametric estimation FFT family of probability density functions |
| url | https://www.mdpi.com/1999-4893/13/7/164 |
| work_keys_str_mv | AT wojciechrafajłowicz nonparametricestimationofcontinuouslyparametrizedfamiliesofprobabilitydensityfunctionscomputationalaspects |