Results 1  10
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16
Asymptotic equivalence of density estimation and Gaussian white noise
 Ann. Statist
, 1996
"... Signal recovery in Gaussian white noise with variance tending to zero has served for some time as a representative model for nonparametric curve estimation, having all the essential traits in a pure form. The equivalence has mostly been stated informally, but an approximation in the sense of Le Cam’ ..."
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Cited by 121 (5 self)
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Signal recovery in Gaussian white noise with variance tending to zero has served for some time as a representative model for nonparametric curve estimation, having all the essential traits in a pure form. The equivalence has mostly been stated informally, but an approximation in the sense of Le Cam’s deficiency distance ∆ would make it precise. The models are then asymptotically equivalent for all purposes of statistical decision with bounded loss. In nonparametrics, a first result of this kind has recently been established for Gaussian regression (Brown and Low, 1993). We consider the analogous problem for the experiment given by n i. i. d. observations having density f on the unit interval. Our basic result concerns the parameter space of densities which are in a Hölder ball with exponent α> 12 and which are uniformly bounded away from zero. We show that an i. i. d. sample of size n with density f is globally asymptotically equivalent to a white noise experiment with drift f1/2 and variance 14n −1. This represents a nonparametric analog of Le Cam’s heteroscedastic Gaussian approximation in the finite dimensional case.
The Bayesian Foundations of Solution Concepts of Games,” Working
 University of Chicago
, 1986
"... We transform a noncooperative game into a Bayesian decision problem for each player where the uncertainty faced by a player is the strategy choices of the other players, the priors of other players on the choice of other players, the priors over priors, and so on. We provide a complete characterizat ..."
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Cited by 109 (0 self)
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We transform a noncooperative game into a Bayesian decision problem for each player where the uncertainty faced by a player is the strategy choices of the other players, the priors of other players on the choice of other players, the priors over priors, and so on. We provide a complete characterization between the extent of knowledge about the rationality of players and their ability to successively eliminate strategies which are not best responses. This paper therefore provides the informational foundations of iteratively undominated strategies and rationalizable strategic behavior (B.D. Bernheim, Economefrica 52 (1984) 10071028; D. Pearce, Economefrica 52 (1984), 10291050). Sufficient conditions are also found for Nash equilibrium behavior and a result akin to R. J. Aumann (Econometrica 55 (1987) l18) on correlated equilibria, is derived with different hypotheses. Journal of
PORTFOLIO CHOICE AND RISK ATTITUDES: AN EXPERIMENT
"... Using financial incentives, we study how portfolio choice (how much to invest in a risky asset) depends on three wellknown behavioral phenomena: ambiguity aversion, the illusion of control, and myopic loss aversion. We find evidence that these phenomena are present and test how the level of investm ..."
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Cited by 35 (7 self)
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Using financial incentives, we study how portfolio choice (how much to invest in a risky asset) depends on three wellknown behavioral phenomena: ambiguity aversion, the illusion of control, and myopic loss aversion. We find evidence that these phenomena are present and test how the level of investment is affected by these motivations; at the same time, we investigate whether participants are willing to explicitly pay a small sum of money to indulge preferences for less ambiguity, more control, or more frequent feedback/opportunities to choose the investment level. First, the observed preference for ‘‘control’ ’ did not affect investment behavior and in fact disappeared when participants were asked to actually pay to gain more control. Second, while people were indeed willing to pay for less ambiguity, the level of ambiguity did not influence investment levels. Finally, participants were willing to pay to have more frequent feedback opportunities to change their portfolio, even though prior research has shown that people invest less in risky assets (and earn less) in this case. (JEL B49, C91, D81, G11, G19) I.
Axiomatic foundations of multiplier preferences
, 2007
"... This paper axiomatizes the robust control criterion of multiplier preferences introduced by Hansen and Sargent (2001). The axiomatization relates multiplier preferences to other classes of preferences studied in decision theory. Some properties of multiplier preferences are generalized to the broade ..."
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Cited by 33 (3 self)
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This paper axiomatizes the robust control criterion of multiplier preferences introduced by Hansen and Sargent (2001). The axiomatization relates multiplier preferences to other classes of preferences studied in decision theory. Some properties of multiplier preferences are generalized to the broader class of variational preferences, recently introduced by Maccheroni, Marinacci and Rustichini (2006). The paper also establishes a link between the parameters of the multiplier criterion and the observable behavior of the agent. This link enables measurement of the parameters on the basis of observable choice data and provides a useful tool for applications. I am indebted to my advisor Eddie Dekel for his continuous guidance, support, and encouragement. I am grateful to Peter Klibanoff and Marciano Siniscalchi for many discussions which resulted in significant improvements of the paper. I would also like to thank Jeff Ely and Todd Sarver for helpful comments and suggestions. This project started after a very stimulating conversation with Tom Sargent and was further shaped by conversations with Lars Hansen. All errors are my own.
A Bayesian approach to testing portfolio efficiency
 Journal of Financial Economics
, 1987
"... This paper develops a Bayesian test of portfolio efficiency ~ and derives a computationally convenient posteriorodds ratio. The analysis indicates that stgniticance levels higher than the traditional 0.05 level are recommended for many test situations. in an example from the literature. the classi ..."
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Cited by 25 (2 self)
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This paper develops a Bayesian test of portfolio efficiency ~ and derives a computationally convenient posteriorodds ratio. The analysis indicates that stgniticance levels higher than the traditional 0.05 level are recommended for many test situations. in an example from the literature. the classical test fails to rgect with pvalue 0.082. yet the odds are nearly two to one against efficiency under apparently reasonable assumptions. Procedures for testing approximate efficiency and for aggregating subperiod results are also considered. 1.
Sparse Brain Network Recovery under Compressed Sensing
, 2010
"... Partial correlation is a useful connectivity measure for brain networks, especially, when it is needed to remove the confounding effects in highly correlated networks. Since it is difficult to estimate the exact partial correlation under the smalln largep situation, a sparseness constraint is gene ..."
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Cited by 8 (4 self)
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Partial correlation is a useful connectivity measure for brain networks, especially, when it is needed to remove the confounding effects in highly correlated networks. Since it is difficult to estimate the exact partial correlation under the smalln largep situation, a sparseness constraint is generally introduced. In this paper, we consider the sparse linear regression model with a l1norm penalty, a.k.a., least absolute shrinkage and selection operator (LASSO), for estimating sparse brain connectivity. LASSO is a wellknown decoding algorithm in the compressed sensing (CS). The CS theory states that LASSO can reconstruct the exact sparse signal even from a small set of noisy measurements. We briefly show that the penalized linear regression for partial correlation estimation is related with CS. It opens a new possibility that the proposed framework can be used for a sparse brain network recovery. As an illustration, we construct sparse brain networks of 97 regions of interest (ROIs) obtained from FDGPET data for the autism spectrum disorder (ASD) children and the pediatric control (PedCon) subjects. As a model validation, we check their reproducibilities by leaveoneout cross validation and compare the clustered structures derived from the brain networks of ASD and PedCon. Keywords: Brain Connectivity, Compressed Sensing, Partial Correlation, LASSO. 1
Amino Acids as Gustatory Stimuli in the Rat
"... ABSTRACT Neural activity in intact chorda tympani nerve of rats was studied with an electronic summator. Neural activity increased when amino acid solutions 0.01 ~ or above passed over the tongue. Response magnitude, at concentrations close to solubility limits for the amino acids tested, was: DLmet ..."
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Cited by 1 (0 self)
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ABSTRACT Neural activity in intact chorda tympani nerve of rats was studied with an electronic summator. Neural activity increased when amino acid solutions 0.01 ~ or above passed over the tongue. Response magnitude, at concentrations close to solubility limits for the amino acids tested, was: DLmethionine < DLtryptophan < DLValine ~ Dralanine ( glycine ~ 0.1 NaC1. Maximum response magnitudes to I ~ D, and 1.2 M DLalanine, and 1.5 glycine developed in 1 to 3 minutes. Following such stimulation, a 63 per cent reduction in response to 0.1 M NaC1 occurred 60 minutes after the first stimulation (medians). The depression was still present 20 hours later. Responses to glycine and alanine were not depressed. Amino acids vs. water preferences were investigated. With ascending concentration sequences, rats selected low
The Effect of Exchange Rates on Statistical Decisions
, 2011
"... Statistical decision theory, whether based on Bayesian principles or other concepts such as minimax or admissibility, relies on the idea of minimizing expected loss or maximizing expected utility. Loss and utility functions are generally treated as unitless numerical measures of how costly or valuab ..."
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Statistical decision theory, whether based on Bayesian principles or other concepts such as minimax or admissibility, relies on the idea of minimizing expected loss or maximizing expected utility. Loss and utility functions are generally treated as unitless numerical measures of how costly or valuable are the various consequences of potential decisions. In this paper, we address directly the issue of the units in which loss and utility are settled and the implications that those units have on the rankings of potential decisions. The simplest example is to imagine that the loss will be paid in units of some currency. If there are multiple currencies available for paying the loss, one must take explicit account of which currency is used as well as the exchange rates between the various available currencies. KEY WORDS: Currency; numeraire; scoring rule; statedependence; utility. 1.
Preparatory and Bridging Courses in Statistics
"... In this paper we look at preparatory and bridging courses in statistics at the inferface between secondary and tertiary education. We include discussion about similar mathematics courses which contain a probability and statistics component. Preparatory and bridging courses are defined to be those th ..."
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In this paper we look at preparatory and bridging courses in statistics at the inferface between secondary and tertiary education. We include discussion about similar mathematics courses which contain a probability and statistics component. Preparatory and bridging courses are defined to be those that fill a gap between
Frequent Inactivation of PTEN in Prostate Cancer Cell Lines and Xenografts1
, 2013
"... Loss of chromosome lOq is a frequently observed genetic defect in prostate cancer. Recently, the PTEN/MMAC1 tumor suppressor gene was identified and mapped to chromosome 10q23.3. We studied PTEN struc ture and expression in 4 in vitro cell lines and 11 in vivo xenografts derived from six primary and ..."
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Loss of chromosome lOq is a frequently observed genetic defect in prostate cancer. Recently, the PTEN/MMAC1 tumor suppressor gene was identified and mapped to chromosome 10q23.3. We studied PTEN struc ture and expression in 4 in vitro cell lines and 11 in vivo xenografts derived from six primary and nine metastatic human prostate cancers. DNA samples were allelotyped for eight polymorphic markers within and sur rounding the PTEN gene. Additionally, the nine PTEN exons were tested for deletions. In five samples (PC3, PC133, PCEW, PC295, and PC324), homozygous deletions of the PTEN gene or parts of the gene were de tected. PC295 contained a small homozygous deletion encompassing PTEN exon 5. In two DNAs (PC82 and PC346), nonsense mutations were found, and in two (LNCaP and PC374), frameshift mutations were found. Missense mutations were not detected. PTEN mRNA expression was clearly observed in all cell lines and xenografts without large homozygous