Weak Convergence of the Conditional Set-Indexed Empirical Process for Missing at Random Functional Ergodic Data
This work examines the asymptotic characteristics of a conditional set-indexed empirical process composed of functional ergodic random variables with missing at random (MAR). This paper’s findings enlarge the previous advancements in functional data analysis through the use of empirical process meth...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-01-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/12/3/448 |
| _version_ | 1797318457390268416 |
|---|---|
| author | Salim Bouzebda Youssouf Souddi Fethi Madani |
| author_facet | Salim Bouzebda Youssouf Souddi Fethi Madani |
| author_sort | Salim Bouzebda |
| collection | DOAJ |
| description | This work examines the asymptotic characteristics of a conditional set-indexed empirical process composed of functional ergodic random variables with missing at random (MAR). This paper’s findings enlarge the previous advancements in functional data analysis through the use of empirical process methodologies. These results are shown under specific structural hypotheses regarding entropy and under appealing situations regarding the model. The regression operator’s asymptotic <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mn>1</mn><mo>−</mo><mi>α</mi><mo>)</mo></mrow></semantics></math></inline-formula>-confidence interval is provided for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0</mn><mo><</mo><mi>α</mi><mo><</mo><mn>1</mn></mrow></semantics></math></inline-formula> as an application. Additionally, we offer a classification example to demonstrate the practical importance of the methodology. |
| first_indexed | 2024-03-08T03:52:40Z |
| format | Article |
| id | doaj.art-5874ba4d59424900a32bb79b3af31a01 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-08T03:52:40Z |
| publishDate | 2024-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-5874ba4d59424900a32bb79b3af31a012024-02-09T15:18:23ZengMDPI AGMathematics2227-73902024-01-0112344810.3390/math12030448Weak Convergence of the Conditional Set-Indexed Empirical Process for Missing at Random Functional Ergodic DataSalim Bouzebda0Youssouf Souddi1Fethi Madani2Laboratoire de Mathématiques Appliquées de Compiègne (L.M.A.C.), Université de Technologie de Compiègne, 60200 Compiègne, FranceLaboratory of Stochastic Models, Statistics and Applications, University of Saida-Dr. Moulay Tahar, P.O. Box 138 EN-NASR, Saïda 20000, AlgeriaLaboratory of Stochastic Models, Statistics and Applications, University of Saida-Dr. Moulay Tahar, P.O. Box 138 EN-NASR, Saïda 20000, AlgeriaThis work examines the asymptotic characteristics of a conditional set-indexed empirical process composed of functional ergodic random variables with missing at random (MAR). This paper’s findings enlarge the previous advancements in functional data analysis through the use of empirical process methodologies. These results are shown under specific structural hypotheses regarding entropy and under appealing situations regarding the model. The regression operator’s asymptotic <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mn>1</mn><mo>−</mo><mi>α</mi><mo>)</mo></mrow></semantics></math></inline-formula>-confidence interval is provided for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0</mn><mo><</mo><mi>α</mi><mo><</mo><mn>1</mn></mrow></semantics></math></inline-formula> as an application. Additionally, we offer a classification example to demonstrate the practical importance of the methodology.https://www.mdpi.com/2227-7390/12/3/448conditional distributionsmall ball probabilitymissing at randomempirical processergodic functional datasemi-metric space |
| spellingShingle | Salim Bouzebda Youssouf Souddi Fethi Madani Weak Convergence of the Conditional Set-Indexed Empirical Process for Missing at Random Functional Ergodic Data Mathematics conditional distribution small ball probability missing at random empirical process ergodic functional data semi-metric space |
| title | Weak Convergence of the Conditional Set-Indexed Empirical Process for Missing at Random Functional Ergodic Data |
| title_full | Weak Convergence of the Conditional Set-Indexed Empirical Process for Missing at Random Functional Ergodic Data |
| title_fullStr | Weak Convergence of the Conditional Set-Indexed Empirical Process for Missing at Random Functional Ergodic Data |
| title_full_unstemmed | Weak Convergence of the Conditional Set-Indexed Empirical Process for Missing at Random Functional Ergodic Data |
| title_short | Weak Convergence of the Conditional Set-Indexed Empirical Process for Missing at Random Functional Ergodic Data |
| title_sort | weak convergence of the conditional set indexed empirical process for missing at random functional ergodic data |
| topic | conditional distribution small ball probability missing at random empirical process ergodic functional data semi-metric space |
| url | https://www.mdpi.com/2227-7390/12/3/448 |
| work_keys_str_mv | AT salimbouzebda weakconvergenceoftheconditionalsetindexedempiricalprocessformissingatrandomfunctionalergodicdata AT youssoufsouddi weakconvergenceoftheconditionalsetindexedempiricalprocessformissingatrandomfunctionalergodicdata AT fethimadani weakconvergenceoftheconditionalsetindexedempiricalprocessformissingatrandomfunctionalergodicdata |