7,455 research outputs found
Sieve-based confidence intervals and bands for L\'{e}vy densities
The estimation of the L\'{e}vy density, the infinite-dimensional parameter
controlling the jump dynamics of a L\'{e}vy process, is considered here under a
discrete-sampling scheme. In this setting, the jumps are latent variables, the
statistical properties of which can be assessed when the frequency and time
horizon of observations increase to infinity at suitable rates. Nonparametric
estimators for the L\'{e}vy density based on Grenander's method of sieves was
proposed in Figueroa-L\'{o}pez [IMS Lecture Notes 57 (2009) 117--146]. In this
paper, central limit theorems for these sieve estimators, both pointwise and
uniform on an interval away from the origin, are obtained, leading to pointwise
confidence intervals and bands for the L\'{e}vy density. In the pointwise case,
our estimators converge to the L\'{e}vy density at a rate that is arbitrarily
close to the rate of the minimax risk of estimation on smooth L\'{e}vy
densities. In the case of uniform bands and discrete regular sampling, our
results are consistent with the case of density estimation, achieving a rate of
order arbitrarily close to , where is the
number of observations. The convergence rates are valid, provided that is
smooth enough and that the time horizon and the dimension of the sieve
are appropriately chosen in terms of .Comment: Published in at http://dx.doi.org/10.3150/10-BEJ286 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
CONSUMER PREFERENCES FOR NON-CONVENTIONALLY GROWN PRODUCE
This study examines the potential for marketing fresh fruits and vegetables with labels indicating enhanced food and/or environmental safety attributes as compared to conventional produce. Four labels were investigated: Organic, Certified Organic, Certified Pesticide Residue-Free, and Grown with IPM. Results confirm findings of other surveys relating to concerns about pesticide residues. Seventy-one percent (71%) of respondents stated they believed that pesticide residues in food present a serious or moderate health hazard to consumers. In addition, 74% believed that pesticides pose a serious or moderate hazard to the environment, and 64% felt there was a serious or moderate hazard to farm workers. Results indicate there is a positive information effect for likelihood of purchasing for all of the labels, and this effect is statistically significant for all of the labels except for Certified Pesticide Residue-Free. The magnitude of the information effect for the Grown with IPM label was considerably higher than for the other labels, suggesting that there might be substantial payoffs for informing consumers about this label.Consumer/Household Economics,
Small-time asymptotics of stopped L\'evy bridges and simulation schemes with controlled bias
We characterize the small-time asymptotic behavior of the exit probability of
a L\'evy process out of a two-sided interval and of the law of its overshoot,
conditionally on the terminal value of the process. The asymptotic expansions
are given in the form of a first-order term and a precise computable error
bound. As an important application of these formulas, we develop a novel
adaptive discretization scheme for the Monte Carlo computation of functionals
of killed L\'evy processes with controlled bias. The considered functionals
appear in several domains of mathematical finance (e.g., structural credit risk
models, pricing of barrier options, and contingent convertible bonds) as well
as in natural sciences. The proposed algorithm works by adding discretization
points sampled from the L\'evy bridge density to the skeleton of the process
until the overall error for a given trajectory becomes smaller than the maximum
tolerance given by the user.Comment: Published in at http://dx.doi.org/10.3150/13-BEJ517 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
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