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124
Performance Evaluation for Zero NetInvestment Strategies
, 2010
"... This paper introduces new nonparametric statistical methods to evaluate zerocost investment strategies. We focus on directional trading strategies, riskadjusted returns, and the investor’s decisions under uncertainty as the core of our analysis. By relying on classification tools with a long tradi ..."
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Cited by 29 (19 self)
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This paper introduces new nonparametric statistical methods to evaluate zerocost investment strategies. We focus on directional trading strategies, riskadjusted returns, and the investor’s decisions under uncertainty as the core of our analysis. By relying on classification tools with a long tradition in the sciences and biostatistics, we can provide a tighter connection between modelbased risk characteristics and the noarbitrage conditions for market efficiency. Moreover, we extend the methods to multicategorical settings, such as when the investor can sometimes take a neutral position. A variety of inferential procedures are provided, many of which are illustrated with applications to excess equity returns and to currency carry trades.
Asymptotically exact inference in conditional moment inequality models
, 2012
"... This paper derives the rate of convergence and asymptotic distribution for a class of KolmogorovSmirnov style test statistics for conditional moment inequality models for parameters on the boundary of the identified set under general conditions. In contrast to other moment inequality settings, the ..."
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Cited by 18 (0 self)
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This paper derives the rate of convergence and asymptotic distribution for a class of KolmogorovSmirnov style test statistics for conditional moment inequality models for parameters on the boundary of the identified set under general conditions. In contrast to other moment inequality settings, the rate of convergence is faster than rootn, and the asymptotic distribution depends entirely on nonbinding moments. The results require the development of new techniques that draw a connection between moment selection, irregular identification, bandwidth selection and nonstandard Mestimation. Using these results, I propose tests that are more powerful than existing approaches for choosing critical values for this test statistic. I quantify the power improvement by showing that the new tests can detect alternatives that converge to points on the identified set at a faster rate than those detected by existing approaches. A monte carlo study confirms that the tests and the asymptotic approximations they use perform well in finite samples. In an application to a regression of prescription drug expenditures on income with interval data from the Health and Retirement Study, confidence regions based on the new tests are substantially tighter than those based on existing methods.
Huang (2010): “Bootstrap Consistency for General Semiparametric MEstimation,”Annals of Statistics
"... Consider Mestimation in a semiparametric model that is characterized by a Euclidean parameter of interest and an infinitedimensional nuisance parameter. As a general purpose approach to statistical inferences, the bootstrap has found wide applications in semiparametric Mestimation and, because of ..."
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Cited by 16 (5 self)
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Consider Mestimation in a semiparametric model that is characterized by a Euclidean parameter of interest and an infinitedimensional nuisance parameter. As a general purpose approach to statistical inferences, the bootstrap has found wide applications in semiparametric Mestimation and, because of its simplicity, provides an attractive alternative to the inference approach based on the asymptotic distribution theory. The purpose of this paper is to provide theoretical justifications for the use of bootstrap as a semiparametric inferential tool. We show that, under general conditions, the bootstrap is asymptotically consistent in estimating the distribution of the Mestimate of Euclidean parameter; that is, the bootstrap distribution asymptotically imitates the distribution of the Mestimate. We also show that the bootstrap confidence set has the asymptotically correct coverage probability. These general conclusions hold, in particular, when the nuisance parameter is not estimable at rootn rate, and apply to a broad class of bootstrap methods with exchangeable bootstrap weights. This paper provides a first general theoretical study of the bootstrap in semiparametric models.
Change–Point Estimation Under Adaptive Sampling
, 2007
"... We consider the problem of locating a jump discontinuity (changepoint) in a smooth parametric regression model with a bounded covariate. It is assumed that one can sample the covariate at different values and measure the corresponding responses. Budget constraints dictate that a total of n such mea ..."
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Cited by 15 (7 self)
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We consider the problem of locating a jump discontinuity (changepoint) in a smooth parametric regression model with a bounded covariate. It is assumed that one can sample the covariate at different values and measure the corresponding responses. Budget constraints dictate that a total of n such measurements can be obtained. A multistage adaptive procedure is proposed, where at each stage an estimate of the change point is obtained and new points are sampled from its appropriately chosen neighborhood. It is shown that such procedures accelerate the rate of convergence of the least squares estimate of the changepoint. Further, the asymptotic distribution of the estimate is derived using empirical processes techniques. The improved efficiency of the procedure is demonstrated using real and synthetic data. This problem is primarily motivated by applications in engineering systems. Key words and phrases: adaptive sampling, change point estimation, multi–stage procedure, Skorokhod topology, two–stage procedure, zoomin. 1
HIGHER ORDER SEMIPARAMETRIC FREQUENTIST INFERENCE WITH THE PROFILE SAMPLER
 SUBMITTED TO THE ANNALS OF STATISTICS
, 2006
"... We consider higher order frequentist inference for the parametric component of a semiparametric model based on sampling from the posterior profile distribution. The first order validity of this procedure established by Lee, Kosorok and Fine (2005) is extended to second order validity in the setting ..."
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Cited by 12 (9 self)
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We consider higher order frequentist inference for the parametric component of a semiparametric model based on sampling from the posterior profile distribution. The first order validity of this procedure established by Lee, Kosorok and Fine (2005) is extended to second order validity in the setting where the infinite dimensional nuisance parameter achieves the parametric rate. Specifically, we obtain higher order estimates of the maximum profile likelihood estimator and of the efficient Fisher information. Moreover, we prove that an exact frequentist confidence interval for the parametric component at level alpha can be estimated by the alpha level credible set from the profile sampler with an error of order OP (n −1). As far as we are aware, these results are the first higher order frequentist results obtained for semiparametric estimation. A fully Bayesian interpretation is established under a certain data dependent prior. The theory is verified for three specific examples.
GENERAL FREQUENTIST PROPERTIES OF THE POSTERIOR PROFILE DISTRIBUTION
, 2008
"... In this paper, inference for the parametric component of a semiparametric model based on sampling from the posterior profile distribution is thoroughly investigated from the frequentist viewpoint. The higherorder validity of the profile sampler obtained in Cheng and Kosorok [Ann. Statist. 36 (2008) ..."
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Cited by 11 (5 self)
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In this paper, inference for the parametric component of a semiparametric model based on sampling from the posterior profile distribution is thoroughly investigated from the frequentist viewpoint. The higherorder validity of the profile sampler obtained in Cheng and Kosorok [Ann. Statist. 36 (2008)] is extended to semiparametric models in which the infinite dimensional nuisance parameter may not have a rootn convergence rate. This is a nontrivial extension because it requires a delicate analysis of the entropy of the semiparametric models involved. We find that the accuracy of inferences based on the profile sampler improves as the convergence rate of the nuisance parameter increases. Simulation studies are used to verify this theoretical result. We also establish that an exact frequentist confidence interval obtained by inverting the profile loglikelihood ratio can be estimated with higherorder accuracy by the credible set of the same type obtained from the posterior profile distribution. Our theory is verified for several specific examples.
Reinforcement learning algorithms for MDPs
, 2009
"... This article presents a survey of reinforcement learning algorithms for Markov Decision Processes (MDP). In the first half of the article, the problem of value estimation is considered. Here we start by describing the idea of bootstrapping and temporal difference learning. Next, we compare increment ..."
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Cited by 10 (0 self)
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This article presents a survey of reinforcement learning algorithms for Markov Decision Processes (MDP). In the first half of the article, the problem of value estimation is considered. Here we start by describing the idea of bootstrapping and temporal difference learning. Next, we compare incremental and batch algorithmic variants and discuss the impact of the choice of the function approximation method on the success of learning. In the second half, we describe methods that target the problem of learning to control an MDP. Here online and active learning are discussed first, followed by a description of direct and actorcritic methods.
Conditional density estimation by penalized likelihood model selection and applications. ArXiv 1103.2021
, 2011
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
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Cited by 10 (3 self)
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HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.