{"id":{"repo_id":"bologna","oai_identifier":"oai:amsdottorato.cib.unibo.it:1211"},"canonical_url":"https://search.dev.ndltd.org/etd/bologna/oai:amsdottorato.cib.unibo.it:1211","repository":{"repo_id":"bologna","name":"Università di Bologna","base_url":"https://amsdottorato.unibo.it/cgi/oai2"},"display":{"title":"Bayesian Analysis of Linear Inverse Problems with Applications in Economics and Finance","abstract":"In my PhD thesis I propose a Bayesian nonparametric estimation method for structural econometric models where the functional parameter of interest describes the economic agent's behavior. The structural parameter is characterized as the solution of a functional equation, or by using more technical words, as the solution of an inverse problem that can be either ill-posed or well-posed. From a Bayesian point of view, the parameter of interest is a random function and the solution to the inference problem is the posterior distribution of this parameter. A regular version of the posterior distribution in functional spaces is characterized. However, the infinite dimension of the considered spaces causes a problem of non continuity of the solution and then a problem of inconsistency, from a frequentist point of view, of the posterior distribution (i.e. problem of ill-posedness). The contribution of this essay is to propose new methods to deal with this problem of ill-posedness. The first one consists in adopting a Tikhonov regularization scheme in the construction of the posterior distribution so that I end up with a new object that I call regularized posterior distribution and that I guess it is solution of the inverse problem. The second approach consists in specifying a prior distribution on the parameter of interest of the g-prior type. Then, I detect a class of models for which the prior distribution is able to correct for the ill-posedness also in infinite dimensional problems. I study asymptotic properties of these proposed solutions and I prove that, under some regularity condition satisfied by the true value of the parameter of interest, they are consistent in a \"frequentist\" sense. Once I have set the general theory, I apply my bayesian nonparametric methodology to different estimation problems. First, I apply this estimator to deconvolution and to hazard rate, density and regression estimation. Then, I consider the estimation of an Instrumental Regression that is useful in micro-econometrics when we have to deal with problems of endogeneity. Finally, I develop an application in finance: I get the bayesian estimator for the equilibrium asset pricing functional by using the Euler equation defined in the Lucas'(1978) tree-type models.","abstract_html":"In my PhD thesis I propose a Bayesian nonparametric estimation method for structural econometric models where the functional parameter of interest describes the economic agent's behavior. The structural parameter is characterized as the solution of a functional equation, or by using more technical words, as the solution of an inverse problem that can be either ill-posed or well-posed. From a Bayesian point of view, the parameter of interest is a random function and the solution to the inference problem is the posterior distribution of this parameter. A regular version of the posterior distribution in functional spaces is characterized. However, the infinite dimension of the considered spaces causes a problem of non continuity of the solution and then a problem of inconsistency, from a frequentist point of view, of the posterior distribution (i.e. problem of ill-posedness). The contribution of this essay is to propose new methods to deal with this problem of ill-posedness. The first one consists in adopting a Tikhonov regularization scheme in the construction of the posterior distribution so that I end up with a new object that I call regularized posterior distribution and that I guess it is solution of the inverse problem. The second approach consists in specifying a prior distribution on the parameter of interest of the g-prior type. Then, I detect a class of models for which the prior distribution is able to correct for the ill-posedness also in infinite dimensional problems. I study asymptotic properties of these proposed solutions and I prove that, under some regularity condition satisfied by the true value of the parameter of interest, they are consistent in a "frequentist" sense. Once I have set the general theory, I apply my bayesian nonparametric methodology to different estimation problems. First, I apply this estimator to deconvolution and to hazard rate, density and regression estimation. Then, I consider the estimation of an Instrumental Regression that is useful in micro-econometrics when we have to deal with problems of endogeneity. Finally, I develop an application in finance: I get the bayesian estimator for the equilibrium asset pricing functional by using the Euler equation defined in the Lucas'(1978) tree-type models.","abstract_has_math":false,"creators":["Simoni, Anna <1980>"],"institution":"Alma Mater Studiorum - Università di Bologna","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Pastorello, Sergio"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2009,"date_issued":"2009-06-10","date_published":"2009-06-10","updated_at":"2026-07-24T01:12:10Z","subjects":["SECS-P/05 Econometria"],"languages":["it"],"rights":["info:eu-repo/semantics/openAccess"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["urn:nbn:it:unibo-1169"],"render_values":[{"text":"urn:nbn:it:unibo-1169","href":null,"code":true}]}]},"links":{"outbound_url":"https://doi.org/10.6092/unibo/amsdottorato/1211.","outbound_label":"DOI","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Pastorello, Sergio"]},{"key":"dc:creator","label":"Author","values":["Simoni, Anna <1980>"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2009-06-10"]},{"key":"dc:publisher","label":"Institution","values":["Alma Mater Studiorum - Università di Bologna"]},{"key":"dc:relation","label":"Dc Relation","values":["https://amsdottorato.unibo.it/id/eprint/1211/"]},{"key":"dc:type","label":"Dc Type","values":["Doctoral Thesis","PeerReviewed"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["SECS-P/05 Econometria"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["it"]},{"key":"dc:rights","label":"Dc Rights","values":["info:eu-repo/semantics/openAccess"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://amsdottorato.unibo.it/id/eprint/1211/1/Tesi_Anna_Simoni.pdf","urn:nbn:it:unibo-1169","Simoni, Anna (2009) Bayesian Analysis of Linear Inverse Problems with Applications in Economics and Finance, [Dissertation thesis], Alma Mater Studiorum Università di Bologna. Dottorato di ricerca in Economia , 20 Ciclo. DOI 10.6092/unibo/amsdottorato/1211."]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In my PhD thesis I propose a Bayesian nonparametric estimation method for structural econometric models where the functional parameter of interest describes the economic agent's behavior. The structural parameter is characterized as the solution of a functional equation, or by using more technical words, as the solution of an inverse problem that can be either ill-posed or well-posed. From a Bayesian point of view, the parameter of interest is a random function and the solution to the inference problem is the posterior distribution of this parameter. A regular version of the posterior distribution in functional spaces is characterized. However, the infinite dimension of the considered spaces causes a problem of non continuity of the solution and then a problem of inconsistency, from a frequentist point of view, of the posterior distribution (i.e. problem of ill-posedness). The contribution of this essay is to propose new methods to deal with this problem of ill-posedness. The first one consists in adopting a Tikhonov regularization scheme in the construction of the posterior distribution so that I end up with a new object that I call regularized posterior distribution and that I guess it is solution of the inverse problem. The second approach consists in specifying a prior distribution on the parameter of interest of the g-prior type. Then, I detect a class of models for which the prior distribution is able to correct for the ill-posedness also in infinite dimensional problems. I study asymptotic properties of these proposed solutions and I prove that, under some regularity condition satisfied by the true value of the parameter of interest, they are consistent in a \"frequentist\" sense. Once I have set the general theory, I apply my bayesian nonparametric methodology to different estimation problems. First, I apply this estimator to deconvolution and to hazard rate, density and regression estimation. Then, I consider the estimation of an Instrumental Regression that is useful in micro-econometrics when we have to deal with problems of endogeneity. Finally, I develop an application in finance: I get the bayesian estimator for the equilibrium asset pricing functional by using the Euler equation defined in the Lucas'(1978) tree-type models."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Bayesian Analysis of Linear Inverse Problems with Applications in Economics and Finance"]}]}],"canonical_facts":{"dc:contributor":["Pastorello, Sergio"],"dc:creator":["Simoni, Anna <1980>"],"dc:date":["2009-06-10"],"dc:description":["In my PhD thesis I propose a Bayesian nonparametric estimation method for structural econometric models where the functional parameter of interest describes the economic agent's behavior. The structural parameter is characterized as the solution of a functional equation, or by using more technical words, as the solution of an inverse problem that can be either ill-posed or well-posed. From a Bayesian point of view, the parameter of interest is a random function and the solution to the inference problem is the posterior distribution of this parameter. A regular version of the posterior distribution in functional spaces is characterized. However, the infinite dimension of the considered spaces causes a problem of non continuity of the solution and then a problem of inconsistency, from a frequentist point of view, of the posterior distribution (i.e. problem of ill-posedness). The contribution of this essay is to propose new methods to deal with this problem of ill-posedness. The first one consists in adopting a Tikhonov regularization scheme in the construction of the posterior distribution so that I end up with a new object that I call regularized posterior distribution and that I guess it is solution of the inverse problem. The second approach consists in specifying a prior distribution on the parameter of interest of the g-prior type. Then, I detect a class of models for which the prior distribution is able to correct for the ill-posedness also in infinite dimensional problems. I study asymptotic properties of these proposed solutions and I prove that, under some regularity condition satisfied by the true value of the parameter of interest, they are consistent in a \"frequentist\" sense. Once I have set the general theory, I apply my bayesian nonparametric methodology to different estimation problems. First, I apply this estimator to deconvolution and to hazard rate, density and regression estimation. Then, I consider the estimation of an Instrumental Regression that is useful in micro-econometrics when we have to deal with problems of endogeneity. Finally, I develop an application in finance: I get the bayesian estimator for the equilibrium asset pricing functional by using the Euler equation defined in the Lucas'(1978) tree-type models."],"dc:format":["application/pdf"],"dc:identifier":["https://amsdottorato.unibo.it/id/eprint/1211/1/Tesi_Anna_Simoni.pdf","urn:nbn:it:unibo-1169","Simoni, Anna (2009) Bayesian Analysis of Linear Inverse Problems with Applications in Economics and Finance, [Dissertation thesis], Alma Mater Studiorum Università di Bologna. Dottorato di ricerca in Economia , 20 Ciclo. DOI 10.6092/unibo/amsdottorato/1211."],"dc:language":["it"],"dc:publisher":["Alma Mater Studiorum - Università di Bologna"],"dc:relation":["https://amsdottorato.unibo.it/id/eprint/1211/"],"dc:rights":["info:eu-repo/semantics/openAccess"],"dc:subject":["SECS-P/05 Econometria"],"dc:title":["Bayesian Analysis of Linear Inverse Problems with Applications in Economics and Finance"],"dc:type":["Doctoral Thesis","PeerReviewed"]},"updated_at":"2026-07-24T01:12:10Z"}