We consider a single-product revenue management problem with an inventory constraint and unknown, noisy, demand function. The objective of the firm is to dynamically adjust the prices to maximize total expected revenue. We restrict our scope to the nonparametric approach where we only assume some common regularity conditions on the demand function instead of a specific functional form. We propose a family of pricing heuristics that successfully balance the tradeoff between exploration and exploitation. The idea is to generalize the classic bisection search method to a problem that is affected both by stochastic noise and an inventory constraint. Our algorithm extends the bisection method to produce a sequence of pricing intervals that converge to the optimal static price with high probability. Using regret (the revenue loss compared to the deterministic pricing problem for a clairvoyant) as the performance metric, we show that one of our heuristics exactly matches the theoretical asymptotic lower bound that has been previously shown to hold for any feasible pricing heuristic. Although the results are presented in the context of revenue management problems, our analysis of the bisection technique for stochastic optimization with learning can be potentially applied to other application areas.
{"title":"Near-Optimal Bisection Search for Nonparametric Dynamic Pricing with Inventory Constraint","authors":"Y. Lei, Stefanus Jasin, Amitabh Sinha","doi":"10.2139/ssrn.2509425","DOIUrl":"https://doi.org/10.2139/ssrn.2509425","url":null,"abstract":"We consider a single-product revenue management problem with an inventory constraint and unknown, noisy, demand function. The objective of the firm is to dynamically adjust the prices to maximize total expected revenue. We restrict our scope to the nonparametric approach where we only assume some common regularity conditions on the demand function instead of a specific functional form. We propose a family of pricing heuristics that successfully balance the tradeoff between exploration and exploitation. The idea is to generalize the classic bisection search method to a problem that is affected both by stochastic noise and an inventory constraint. Our algorithm extends the bisection method to produce a sequence of pricing intervals that converge to the optimal static price with high probability. Using regret (the revenue loss compared to the deterministic pricing problem for a clairvoyant) as the performance metric, we show that one of our heuristics exactly matches the theoretical asymptotic lower bound that has been previously shown to hold for any feasible pricing heuristic. Although the results are presented in the context of revenue management problems, our analysis of the bisection technique for stochastic optimization with learning can be potentially applied to other application areas.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73213361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the asymptotic refinements of a fully nonparametric bootstrap approach for quasi-likelihood ratio type tests of nonlinear restrictions. This bootstrap method applies to extremum estimators, such as quasi-maximum likelihood and generalized method of moments estimators. Unlike existing parametric bootstrap procedures for quasi-likelihood ratio type tests, this boot-strap approach does not require any specific parametric assumption on the data distribution, and constructs the bootstrap samples in a fully nonparametric way. We derive the higher order improvements of the nonparametric bootstrap compared to procedures based on standard first-order asymptotic theory. In particular, we show that the magnitude of these improvements is the same as those of the parametric bootstrap procedures currently proposed in the literature. Monte Carlo simulations confirm the reliability and accuracy of the nonparametric bootstrap approach.
{"title":"Asymptotic Refinements of a Fully Nonparametric Bootstrap for Quasi-Likelihood Ratio Tests of Extremum Estimators","authors":"Lorenzo Camponovo","doi":"10.2139/ssrn.2442389","DOIUrl":"https://doi.org/10.2139/ssrn.2442389","url":null,"abstract":"We study the asymptotic refinements of a fully nonparametric bootstrap approach for quasi-likelihood ratio type tests of nonlinear restrictions. This bootstrap method applies to extremum estimators, such as quasi-maximum likelihood and generalized method of moments estimators. Unlike existing parametric bootstrap procedures for quasi-likelihood ratio type tests, this boot-strap approach does not require any specific parametric assumption on the data distribution, and constructs the bootstrap samples in a fully nonparametric way. We derive the higher order improvements of the nonparametric bootstrap compared to procedures based on standard first-order asymptotic theory. In particular, we show that the magnitude of these improvements is the same as those of the parametric bootstrap procedures currently proposed in the literature. Monte Carlo simulations confirm the reliability and accuracy of the nonparametric bootstrap approach.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81867780","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper proposes bootstrap methods for the realized bipower variation and the Barndorff-Nielsen and Shephard (2006a) test for jumps. These results enable inference for the realized bipower variation in the presence of jumps in prices. Both the i.i.d and the WILD bootstrap are shown to outperform results obtained through the asymptotic theory. To detect jumps in the presence of microstructure noise, we propose a procedure that averages test results across multiple sampling frequencies. This method considerably improves jump detection, by generating a higher level of power than the asymptotic test, unaccompanied by a simultaneous increase in size.
本文提出了实现双功率变化的自举方法和跳跃的Barndorff-Nielsen and Shephard (2006a)检验。这些结果使我们能够推断在价格跳跃的情况下实现的双功率变化。结果表明，i.i.d和WILD bootstrap都优于渐近理论。为了检测微观结构噪声存在下的跳变，我们提出了一个在多个采样频率上平均测试结果的程序。这种方法通过产生比渐近检验更高的功率水平，而不伴随着尺寸的同时增加，大大改进了跳跃检测。
{"title":"Bootstrap Methods for the Realized Bipower Variation and for Jump Testing","authors":"Ana-Maria H. Dumitru","doi":"10.2139/ssrn.2201083","DOIUrl":"https://doi.org/10.2139/ssrn.2201083","url":null,"abstract":"This paper proposes bootstrap methods for the realized bipower variation and the Barndorff-Nielsen and Shephard (2006a) test for jumps. These results enable inference for the realized bipower variation in the presence of jumps in prices. Both the i.i.d and the WILD bootstrap are shown to outperform results obtained through the asymptotic theory. To detect jumps in the presence of microstructure noise, we propose a procedure that averages test results across multiple sampling frequencies. This method considerably improves jump detection, by generating a higher level of power than the asymptotic test, unaccompanied by a simultaneous increase in size.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82118761","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We develop quantile regression models in order to derive risk margin and to evaluate capital in non-life insurance applications. By utilizing the entire range of conditional quantile functions, especially higher quantile levels, we detail how quantile regression is capable of providing an accurate estimation of risk margin and an overview of implied capital based on the historical volatility of a general insurers loss portfolio. Two modelling frameworks are considered based around parametric and nonparametric quantile regression models which we develop specifically in this insurance setting. In the parametric quantile regression framework, several models including the flexible generalized beta distribution family, asymmetric Laplace (AL) distribution and power Pareto distribution are considered under a Bayesian regression framework. The Bayesian posterior quantile regression models in each case are studied via Markov chain Monte Carlo (MCMC) sampling strategies. In the nonparametric quantile regression framework, that we contrast to the parametric Bayesian models, we adopted an AL distribution as a proxy and together with the parametric AL model, we expressed the solution as a scale mixture of uniform distributions to facilitate implementation. The models are extended to adopt dynamic mean, variance and skewness and applied to analyze two real loss reserve data sets to perform inference and discuss interesting features of quantile regression for risk margin calculations.
{"title":"Risk Margin Quantile Function via Parametric and Non-Parametric Bayesian Quantile Regression","authors":"A. Dong, J. Chan, G. Peters","doi":"10.2139/ssrn.2394063","DOIUrl":"https://doi.org/10.2139/ssrn.2394063","url":null,"abstract":"We develop quantile regression models in order to derive risk margin and to evaluate capital in non-life insurance applications. By utilizing the entire range of conditional quantile functions, especially higher quantile levels, we detail how quantile regression is capable of providing an accurate estimation of risk margin and an overview of implied capital based on the historical volatility of a general insurers loss portfolio. Two modelling frameworks are considered based around parametric and nonparametric quantile regression models which we develop specifically in this insurance setting. In the parametric quantile regression framework, several models including the flexible generalized beta distribution family, asymmetric Laplace (AL) distribution and power Pareto distribution are considered under a Bayesian regression framework. The Bayesian posterior quantile regression models in each case are studied via Markov chain Monte Carlo (MCMC) sampling strategies. In the nonparametric quantile regression framework, that we contrast to the parametric Bayesian models, we adopted an AL distribution as a proxy and together with the parametric AL model, we expressed the solution as a scale mixture of uniform distributions to facilitate implementation. The models are extended to adopt dynamic mean, variance and skewness and applied to analyze two real loss reserve data sets to perform inference and discuss interesting features of quantile regression for risk margin calculations.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82110840","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper studies a general class of nonlinear varying coefficient time series models with possible nonstationarity in both the regressors and the varying coffiecient components. The model accommodates a cointegrating structure and allows for endogeneity with contemporaneous correlation among the regressors, the varying coefficient drivers, and the residuals. This framework allows for a mixture of stationary and non-stationary data and is well suited to a variety of models that are commonly used in applied econometric work. Nonparametric and semiparametric estimation methods are proposed to estimate the varying coefficient functions. The analytical findings reveal some important differences, including convergence rates, that can arise in the conduct of semiparametric regression with nonstationary data. The results include some new asymptotic theory for nonlinear functionals of nonstationary and stationary time series that are of wider interest and applicability and subsume much earlier research on such systems. The finite sample properties of the proposed econometric methods are analyzed in simulations. An empirical illustration examines nonlinear dependencies in aggregate consumption function behavior in the US over the period 1960-2009.
{"title":"Functional Coefficient Nonstationary Regression","authors":"Jiti Gao, P. Phillips","doi":"10.2139/ssrn.2303991","DOIUrl":"https://doi.org/10.2139/ssrn.2303991","url":null,"abstract":"This paper studies a general class of nonlinear varying coefficient time series models with possible nonstationarity in both the regressors and the varying coffiecient components. The model accommodates a cointegrating structure and allows for endogeneity with contemporaneous correlation among the regressors, the varying coefficient drivers, and the residuals. This framework allows for a mixture of stationary and non-stationary data and is well suited to a variety of models that are commonly used in applied econometric work. Nonparametric and semiparametric estimation methods are proposed to estimate the varying coefficient functions. The analytical findings reveal some important differences, including convergence rates, that can arise in the conduct of semiparametric regression with nonstationary data. The results include some new asymptotic theory for nonlinear functionals of nonstationary and stationary time series that are of wider interest and applicability and subsume much earlier research on such systems. The finite sample properties of the proposed econometric methods are analyzed in simulations. An empirical illustration examines nonlinear dependencies in aggregate consumption function behavior in the US over the period 1960-2009.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80830486","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The so-called leverage hypothesis is that negative shocks to prices/returns aect volatility more than equal positive shocks. Whether this is attributable to changing nancial leverage is still subject to dispute but the terminology is in wide use. There are many tests of the leverage hypothesis using discrete time data. These typically involve tting of a general parametric or semiparametric model to conditional volatility and then testing the implied restrictions on parameters or curves. We propose an alternative way of testing this hypothesis using realized volatility as an alternative direct nonparametric measure. Our null hypothesis is of conditional distributional dominance and so is much stronger than the usual hypotheses considered previously. We implement our test on a number of stock return datasets using intraday data over a long span. We nd powerful evidence in favour of our hypothesis.
{"title":"A Nonparametric Test of a Strong Leverage Hypothesis","authors":"O. Linton, Yoon-Jae Whang, Yu-Min Yen","doi":"10.2139/ssrn.2145341","DOIUrl":"https://doi.org/10.2139/ssrn.2145341","url":null,"abstract":"The so-called leverage hypothesis is that negative shocks to prices/returns aect volatility more than equal positive shocks. Whether this is attributable to changing nancial leverage is still subject to dispute but the terminology is in wide use. There are many tests of the leverage hypothesis using discrete time data. These typically involve tting of a general parametric or semiparametric model to conditional volatility and then testing the implied restrictions on parameters or curves. We propose an alternative way of testing this hypothesis using realized volatility as an alternative direct nonparametric measure. Our null hypothesis is of conditional distributional dominance and so is much stronger than the usual hypotheses considered previously. We implement our test on a number of stock return datasets using intraday data over a long span. We nd powerful evidence in favour of our hypothesis.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82132316","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper proposes a simple, fast and direct nonparametric test to verify if a sample is drawn from a distribution with a finite first moment. The method can also be applied to test for the existence of finite moments of another order by taking the sample to the corresponding power. The test is based on the difference in the asymptotic behaviour of the arithmetic mean between cases when the underlying probability function either has or does not have a finite first moment. Test consistency is proved; then, test performance is illustrated with Monte-Carlo simulations and a practical application for the S&P500 index.
{"title":"A Simple Nonparametric Test for the Existence of Finite Moments","authors":"Igor Fedotenkov","doi":"10.2139/ssrn.2202269","DOIUrl":"https://doi.org/10.2139/ssrn.2202269","url":null,"abstract":"This paper proposes a simple, fast and direct nonparametric test to verify if a sample is drawn from a distribution with a finite first moment. The method can also be applied to test for the existence of finite moments of another order by taking the sample to the corresponding power. The test is based on the difference in the asymptotic behaviour of the arithmetic mean between cases when the underlying probability function either has or does not have a finite first moment. Test consistency is proved; then, test performance is illustrated with Monte-Carlo simulations and a practical application for the S&P500 index.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79254570","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2013-02-16DOI: 10.1016/J.FRL.2012.11.002
Godfrey Smith
{"title":"Simulated Testing of Nonparametric Measure Changes for Hedging European Options","authors":"Godfrey Smith","doi":"10.1016/J.FRL.2012.11.002","DOIUrl":"https://doi.org/10.1016/J.FRL.2012.11.002","url":null,"abstract":"","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91000294","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Determining whether a data set contains one or more outliers is a challenge commonly faced in applied statistics. This paper introduces a distribution-free test for multiple outliers in data drawn from an unknown data generating process. Besides, a sequential algorithm is proposed in order to identify the outlying observations in the sample. Our methodology relies on a two-stage nonparametric bootstrap procedure. Monte Carlo experiments show that the proposed test has good asymptotic properties, even for relatively small samples and heavy tailed distributions. The new outlier detection test could be instrumental in a wide range of statistical applications. The empirical performance of the test is illustrated by means of two examples in the fields of aeronautics and macroeconomics.
{"title":"A Distribution-Free Test for Outliers","authors":"B. Candelon, N. Metiu","doi":"10.2139/ssrn.2796894","DOIUrl":"https://doi.org/10.2139/ssrn.2796894","url":null,"abstract":"Determining whether a data set contains one or more outliers is a challenge commonly faced in applied statistics. This paper introduces a distribution-free test for multiple outliers in data drawn from an unknown data generating process. Besides, a sequential algorithm is proposed in order to identify the outlying observations in the sample. Our methodology relies on a two-stage nonparametric bootstrap procedure. Monte Carlo experiments show that the proposed test has good asymptotic properties, even for relatively small samples and heavy tailed distributions. The new outlier detection test could be instrumental in a wide range of statistical applications. The empirical performance of the test is illustrated by means of two examples in the fields of aeronautics and macroeconomics.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84908268","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Bayesian partially identified models have received a growing attention in recent years in the econometric literature, due to their broad applications in empirical studies. Classical Bayesian approach in this literature has been assuming a parametric model, by specifying an ad-hoc parametric likelihood function. However, econometric models usually only identify a set of moment inequalities, and therefore assuming a known likelihood function suffers from the risk of misspecification, and may result in inconsistent estimations of the identified set. On the other hand, moment-condition based likelihoods such as the limited information and exponential tilted empirical likelihood, though guarantee the consistency, lack of probabilistic interpretations. We propose a semi-parametric Bayesian partially identified model, by placing a nonparametric prior on the unknown likelihood function. Our approach thus only requires a set of moment conditions but still possesses a pure Bayesian interpretation. We study the posterior of the support function, which is essential when the object of interest is the identified set. The support function also enables us to construct two-sided Bayesian credible sets (BCS) for the identified set. It is found that, while the BCS of the partially identified parameter is too narrow from the frequentist point of view, that of the identified set has asymptotically correct coverage probability in the frequentist sense. Moreover, we establish the posterior consistency for both the structural parameter and its identified set. We also develop the posterior concentration theory for the support function, and prove the semi-parametric Bernstein von Mises theorem. Finally, the proposed method is applied to analyze a financial asset pricing problem.
由于贝叶斯部分识别模型在实证研究中的广泛应用，近年来在计量经济学文献中受到越来越多的关注。本文献中的经典贝叶斯方法通过指定一个特别的参数似然函数来假设一个参数模型。然而，计量经济模型通常只识别一组矩不等式，因此假设一个已知的似然函数存在规范错误的风险，并可能导致对识别集的估计不一致。另一方面，基于矩条件的似然，如有限信息和指数倾斜的经验似然，虽然保证了一致性，但缺乏概率解释。我们通过在未知似然函数上放置非参数先验，提出了一个半参数贝叶斯部分识别模型。因此，我们的方法只需要一组力矩条件，但仍然具有纯贝叶斯解释。我们研究支持函数的后验，当感兴趣的对象是识别集时，这是必不可少的。该支持函数还使我们能够为识别集构造双面贝叶斯可信集(BCS)。发现部分辨识参数的BCS从频域角度看过于狭窄，而辨识集的BCS在频域意义上具有渐近正确的覆盖概率。此外，我们还建立了结构参数及其识别集的后验一致性。我们还发展了支持函数的后验集中理论，并证明了半参数Bernstein von Mises定理。最后，将该方法应用于一个金融资产定价问题的分析。
{"title":"Semi-Parametric Bayesian Partially Identified Models Based on Support Function","authors":"Yuan Liao, Anna Simoni","doi":"10.2139/ssrn.2189030","DOIUrl":"https://doi.org/10.2139/ssrn.2189030","url":null,"abstract":"Bayesian partially identified models have received a growing attention in recent years in the econometric literature, due to their broad applications in empirical studies. Classical Bayesian approach in this literature has been assuming a parametric model, by specifying an ad-hoc parametric likelihood function. However, econometric models usually only identify a set of moment inequalities, and therefore assuming a known likelihood function suffers from the risk of misspecification, and may result in inconsistent estimations of the identified set. On the other hand, moment-condition based likelihoods such as the limited information and exponential tilted empirical likelihood, though guarantee the consistency, lack of probabilistic interpretations. We propose a semi-parametric Bayesian partially identified model, by placing a nonparametric prior on the unknown likelihood function. Our approach thus only requires a set of moment conditions but still possesses a pure Bayesian interpretation. We study the posterior of the support function, which is essential when the object of interest is the identified set. The support function also enables us to construct two-sided Bayesian credible sets (BCS) for the identified set. It is found that, while the BCS of the partially identified parameter is too narrow from the frequentist point of view, that of the identified set has asymptotically correct coverage probability in the frequentist sense. Moreover, we establish the posterior consistency for both the structural parameter and its identified set. We also develop the posterior concentration theory for the support function, and prove the semi-parametric Bernstein von Mises theorem. Finally, the proposed method is applied to analyze a financial asset pricing problem.","PeriodicalId":11744,"journal":{"name":"ERN: Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2012-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86805641","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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