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NSYSU

1.
Huang, Jun-Hua.
Quasi-Fejer-*monotonicity* and its applications.

Degree: Master, Applied Mathematics, 2011, NSYSU

URL: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0705111-104240

Iterative methods are extensively used to solve linear and nonlinear problems arising from both pure and applied sciences, and in particular, in fixed point theory and optimization. An iterative method which is used to find a fixed point of an operator or an optimal solution to an optimization problem generates a sequence in an iterative manner. We are in a hope that
this sequence can converge to a solution of the problem under investigation. It is therefore quite naturally to require that the distance of this sequence to the solution set of the problem under investigation be decreasing from iteration to iteration. This is the idea of Fejer-monotonicity. In this paper, We consider quasi-Fejer monotone sequences; that is, we consider Fejer monotone sequences together with errors. Properties of quasi-Fejer monotone sequences are investigated, weak and strong convergence of quasi-Fejer monotone sequences are obtained, and an application to the convex feasibility problem is included.
*Advisors/Committee Members: Lai-Jiu Lin (chair), Hong-Kun Xu (committee member), Yen-Cherng Lin (chair), Jen-Chih Yao (chair).*

Subjects/Keywords: Fejer monotonicity; quasi-Fejer monotonicity; strong convergence; quasi-nonexpansive operator; subgradient projector; inexact algorithm; nonexpansive operator; constraint disintegration method; weak convergence

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APA (6^{th} Edition):

Huang, J. (2011). Quasi-Fejer-monotonicity and its applications. (Thesis). NSYSU. Retrieved from http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0705111-104240

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Huang, Jun-Hua. “Quasi-Fejer-monotonicity and its applications.” 2011. Thesis, NSYSU. Accessed September 26, 2020. http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0705111-104240.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Huang, Jun-Hua. “Quasi-Fejer-monotonicity and its applications.” 2011. Web. 26 Sep 2020.

Vancouver:

Huang J. Quasi-Fejer-monotonicity and its applications. [Internet] [Thesis]. NSYSU; 2011. [cited 2020 Sep 26]. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0705111-104240.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Huang J. Quasi-Fejer-monotonicity and its applications. [Thesis]. NSYSU; 2011. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0705111-104240

Not specified: Masters Thesis or Doctoral Dissertation

University of Exeter

2. Hartmann, L. Perceived ambiguity, ambiguity attitude and strategic ambiguity in games.

Degree: PhD, 2019, University of Exeter

URL: http://hdl.handle.net/10871/35581

This thesis contributes to the theoretical work on decision and game theory when decision makers or players perceive ambiguity. The first article introduces a new axiomatic framework for ambiguity aversion and provides axiomatic characterizations for important preference classes that thus far had lacked characterizations. The second article introduces a new axiom called Weak Monotonicity which is shown to play a crucial role in the multiple prior model. It is shown that for many important preference classes, the assumption of monotonic preferences is a consequence of the other axioms and does not have to be assumed. The third article introduces an intuitive definition of perceived ambiguity in the multiple prior model. It is shown that the approach allows an application to games where players perceive strategic ambiguity. A very general equilibrium existence result is given. The modelling capabilities of the approach are highlighted through the analysis of examples. The fourth article applies the model from the previous article to a specific class of games with a lattice-structure. We perform comparative statics on perceived ambiguity and ambiguity attitude. We show that more optimism does not necessarily lead to higher equilibria when players have Alpha-Maxmin preferences. We present necessary and sufficient conditions on the structure of the prior sets for this comparative statics result to hold. The introductory chapter provides the basis of the four articles in this thesis. An overview of axiomatic decision theory, decision-making under ambiguity and ambiguous games is given. It introduces and discusses the most relevant results from the literature.

Subjects/Keywords: 330; Choquet Expected Utility; Balanced Capacities; Exact Capacities; Multiple Priors; Monotonicity; Weak Monotonicity; Maxmin Expected Utility; Subjective Expected Utility; Perceived Ambiguity; Ambiguity Attitude; Ambiguous Games; Alpha-Maxmin Preferences; Comparative Statics

Record Details Similar Records

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

APA (6^{th} Edition):

Hartmann, L. (2019). Perceived ambiguity, ambiguity attitude and strategic ambiguity in games. (Doctoral Dissertation). University of Exeter. Retrieved from http://hdl.handle.net/10871/35581

Chicago Manual of Style (16^{th} Edition):

Hartmann, L. “Perceived ambiguity, ambiguity attitude and strategic ambiguity in games.” 2019. Doctoral Dissertation, University of Exeter. Accessed September 26, 2020. http://hdl.handle.net/10871/35581.

MLA Handbook (7^{th} Edition):

Hartmann, L. “Perceived ambiguity, ambiguity attitude and strategic ambiguity in games.” 2019. Web. 26 Sep 2020.

Vancouver:

Hartmann L. Perceived ambiguity, ambiguity attitude and strategic ambiguity in games. [Internet] [Doctoral dissertation]. University of Exeter; 2019. [cited 2020 Sep 26]. Available from: http://hdl.handle.net/10871/35581.

Council of Science Editors:

Hartmann L. Perceived ambiguity, ambiguity attitude and strategic ambiguity in games. [Doctoral Dissertation]. University of Exeter; 2019. Available from: http://hdl.handle.net/10871/35581

Delft University of Technology

3.
Musta, E.
Smooth nonparametric estimation under *monotonicity* constraints.

Degree: 2019, Delft University of Technology

URL: http://resolver.tudelft.nl/uuid:35430f5f-daa8-49df-999f-bf97addd51ab ; urn:NBN:nl:ui:24-uuid:35430f5f-daa8-49df-999f-bf97addd51ab ; 35430f5f-daa8-49df-999f-bf97addd51ab ; 10.4233/uuid:35430f5f-daa8-49df-999f-bf97addd51ab ; urn:isbn:978-94-6384-012-5 ; urn:NBN:nl:ui:24-uuid:35430f5f-daa8-49df-999f-bf97addd51ab ; http://resolver.tudelft.nl/uuid:35430f5f-daa8-49df-999f-bf97addd51ab

In this thesis we address the problem of estimating a curve of interest (which might be a probability density, a failure rate or a regression function) under monotonicity constraints. The main concern is investigating large sample distributional properties of smooth isotonic estimators, which have a faster rate of convergence and a nicer graphical representation compared to standard isotonic estimators such as the constrained nonparametric maximum likelihood and the Grenander-type estimator. In the first part, we focus on the pointwise behavior of estimators for the hazard rate in the right censoring and Cox regression models, while the second part is dedicated to global errors of estimators in a general setup, which includes estimation of a probability density, a failure rate, or a regression function. We provide central limit theorems and assess the finite sample performance of the estimators by means of simulation studies for constructing confidence intervals and goodness of fit tests.
*Advisors/Committee Members: Jongbloed, G., Lopuhaa, H.P., Delft University of Technology.*

Subjects/Keywords: Isotonic estimation; Kernel smoothing; Nonparametric estimation; Maximum likelihood estimation; Grenander-type estimator; Cox regression model; global errors; confidence intervals; testing monotonicity; central limit theorem; Weak convergence

Record Details Similar Records

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

APA (6^{th} Edition):

Musta, E. (2019). Smooth nonparametric estimation under monotonicity constraints. (Doctoral Dissertation). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:35430f5f-daa8-49df-999f-bf97addd51ab ; urn:NBN:nl:ui:24-uuid:35430f5f-daa8-49df-999f-bf97addd51ab ; 35430f5f-daa8-49df-999f-bf97addd51ab ; 10.4233/uuid:35430f5f-daa8-49df-999f-bf97addd51ab ; urn:isbn:978-94-6384-012-5 ; urn:NBN:nl:ui:24-uuid:35430f5f-daa8-49df-999f-bf97addd51ab ; http://resolver.tudelft.nl/uuid:35430f5f-daa8-49df-999f-bf97addd51ab

Chicago Manual of Style (16^{th} Edition):

Musta, E. “Smooth nonparametric estimation under monotonicity constraints.” 2019. Doctoral Dissertation, Delft University of Technology. Accessed September 26, 2020. http://resolver.tudelft.nl/uuid:35430f5f-daa8-49df-999f-bf97addd51ab ; urn:NBN:nl:ui:24-uuid:35430f5f-daa8-49df-999f-bf97addd51ab ; 35430f5f-daa8-49df-999f-bf97addd51ab ; 10.4233/uuid:35430f5f-daa8-49df-999f-bf97addd51ab ; urn:isbn:978-94-6384-012-5 ; urn:NBN:nl:ui:24-uuid:35430f5f-daa8-49df-999f-bf97addd51ab ; http://resolver.tudelft.nl/uuid:35430f5f-daa8-49df-999f-bf97addd51ab.

MLA Handbook (7^{th} Edition):

Musta, E. “Smooth nonparametric estimation under monotonicity constraints.” 2019. Web. 26 Sep 2020.

Vancouver:

Musta E. Smooth nonparametric estimation under monotonicity constraints. [Internet] [Doctoral dissertation]. Delft University of Technology; 2019. [cited 2020 Sep 26]. Available from: http://resolver.tudelft.nl/uuid:35430f5f-daa8-49df-999f-bf97addd51ab ; urn:NBN:nl:ui:24-uuid:35430f5f-daa8-49df-999f-bf97addd51ab ; 35430f5f-daa8-49df-999f-bf97addd51ab ; 10.4233/uuid:35430f5f-daa8-49df-999f-bf97addd51ab ; urn:isbn:978-94-6384-012-5 ; urn:NBN:nl:ui:24-uuid:35430f5f-daa8-49df-999f-bf97addd51ab ; http://resolver.tudelft.nl/uuid:35430f5f-daa8-49df-999f-bf97addd51ab.

Council of Science Editors:

Musta E. Smooth nonparametric estimation under monotonicity constraints. [Doctoral Dissertation]. Delft University of Technology; 2019. Available from: http://resolver.tudelft.nl/uuid:35430f5f-daa8-49df-999f-bf97addd51ab ; urn:NBN:nl:ui:24-uuid:35430f5f-daa8-49df-999f-bf97addd51ab ; 35430f5f-daa8-49df-999f-bf97addd51ab ; 10.4233/uuid:35430f5f-daa8-49df-999f-bf97addd51ab ; urn:isbn:978-94-6384-012-5 ; urn:NBN:nl:ui:24-uuid:35430f5f-daa8-49df-999f-bf97addd51ab ; http://resolver.tudelft.nl/uuid:35430f5f-daa8-49df-999f-bf97addd51ab