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You searched for subject:( Hill estimators). Showing records 1 – 2 of 2 total matches.

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University of Ottawa

1. Loukrati, Hicham. Tail Empirical Processes: Limit Theorems and Bootstrap Techniques, with Applications to Risk Measures .

Degree: 2018, University of Ottawa

Au cours des dernières années, des changements importants dans le domaine des assurances et des finances attirent de plus en plus l’attention sur la nécessité d’élaborer un cadre normalisé pour la mesure des risques. Récemment, il y a eu un intérêt croissant de la part des experts en assurance sur l’utilisation de l’espérance conditionnelle des pertes (CTE) parce qu’elle partage des propriétés considérées comme souhaitables et applicables dans diverses situations. En particulier, il répond aux exigences d’une mesure de risque “cohérente”, selon Artzner [2]. Cette thèse représente des contributions à l’inférence statistique en développant des outils, basés sur la convergence des intégrales fonctionnelles, pour l’estimation de la CTE qui présentent un intérêt considérable pour la science actuarielle. Tout d’abord, nous développons un outil permettant l’estimation de la moyenne conditionnelle E[X|X > x], ensuite nous construisons des estimateurs de la CTE, développons la théorie asymptotique nécessaire pour ces estimateurs, puis utilisons la théorie pour construire des intervalles de confiance. Pour la première fois, l’approche de bootstrap non paramétrique est explorée dans cette thèse en développant des nouveaux résultats applicables à la valeur à risque (VaR) et à la CTE. Des études de simulation illustrent la performance de la technique de bootstrap.

Subjects/Keywords: Extremes; Conditional tail expectation; Regularly varying tail; Hill estimator; Bootstrap; Harmonic moment estimators; T-Hill estimator; Value-at-Risk; Tail empirical distribution function

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Loukrati, H. (2018). Tail Empirical Processes: Limit Theorems and Bootstrap Techniques, with Applications to Risk Measures . (Thesis). University of Ottawa. Retrieved from http://hdl.handle.net/10393/37594

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Loukrati, Hicham. “Tail Empirical Processes: Limit Theorems and Bootstrap Techniques, with Applications to Risk Measures .” 2018. Thesis, University of Ottawa. Accessed August 09, 2020. http://hdl.handle.net/10393/37594.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Loukrati, Hicham. “Tail Empirical Processes: Limit Theorems and Bootstrap Techniques, with Applications to Risk Measures .” 2018. Web. 09 Aug 2020.

Vancouver:

Loukrati H. Tail Empirical Processes: Limit Theorems and Bootstrap Techniques, with Applications to Risk Measures . [Internet] [Thesis]. University of Ottawa; 2018. [cited 2020 Aug 09]. Available from: http://hdl.handle.net/10393/37594.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Loukrati H. Tail Empirical Processes: Limit Theorems and Bootstrap Techniques, with Applications to Risk Measures . [Thesis]. University of Ottawa; 2018. Available from: http://hdl.handle.net/10393/37594

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

2. Wang, Tiandong. Heavy Tail Phenomena in in Preferential Attachment Networks .

Degree: 2019, Cornell University

Preferential attachment is widely used to model the power-law behavior of degree distributions in social networks. In this thesis, we study three aspects of a directed preferential attachment model. First, we consider fitting this network model under different data scenarios. We propose both parametric and semi-parametric estimation procedures and compare the corresponding estimating results. Second, we see from empirical studies that statistical estimates of the marginal tail exponent of the power-law degree distribution often use the Hill estimator, even though no theoretical justification has been given. Hence, we study the convergence of the joint empirical measure for in- and out-degrees and prove the consistency of the Hill estimator for the preferential attachment model. Finally, we consider a widely adopted threshold selection procedure when estimating the power-law index in practice and examine the asymptotic behavior of the selected threshold as well as the corresponding power-law index given. Advisors/Committee Members: Jarrow, Robert A. (committeeMember), Wells, Martin Timothy (committeeMember).

Subjects/Keywords: Statistics; Estimation; Hill estimators; multivariate heavy tail statistics; power laws; preferential attachment; Operations research

…the consistency of the two marginal Hill estimators. This allows us to reformulate known… …Convergence of the joint empirical measure . Consistency of the Hill Estimator… …of the Hill estimator vs. k, the RMSE of α̂n,kn∗ is indicated by the dashed red line… …indicated by the dashed red line; right: RMSE of the Hill estimator vs. k, the RMSE of α̂n,kn∗ is… …estimated using an extreme value theory method relying on the Hill estimator. Such Hill estimates… 

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Wang, T. (2019). Heavy Tail Phenomena in in Preferential Attachment Networks . (Thesis). Cornell University. Retrieved from http://hdl.handle.net/1813/67567

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Wang, Tiandong. “Heavy Tail Phenomena in in Preferential Attachment Networks .” 2019. Thesis, Cornell University. Accessed August 09, 2020. http://hdl.handle.net/1813/67567.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Wang, Tiandong. “Heavy Tail Phenomena in in Preferential Attachment Networks .” 2019. Web. 09 Aug 2020.

Vancouver:

Wang T. Heavy Tail Phenomena in in Preferential Attachment Networks . [Internet] [Thesis]. Cornell University; 2019. [cited 2020 Aug 09]. Available from: http://hdl.handle.net/1813/67567.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Wang T. Heavy Tail Phenomena in in Preferential Attachment Networks . [Thesis]. Cornell University; 2019. Available from: http://hdl.handle.net/1813/67567

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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