420 research outputs found
Semiparametrically efficient rank-based inference for shape II. Optimal R-estimation of shape
A class of R-estimators based on the concepts of multivariate signed ranks
and the optimal rank-based tests developed in Hallin and Paindaveine [Ann.
Statist. 34 (2006)] is proposed for the estimation of the shape matrix of an
elliptical distribution. These R-estimators are root-n consistent under any
radial density g, without any moment assumptions, and semiparametrically
efficient at some prespecified density f. When based on normal scores, they are
uniformly more efficient than the traditional normal-theory estimator based on
empirical covariance matrices (the asymptotic normality of which, moreover,
requires finite moments of order four), irrespective of the actual underlying
elliptical density. They rely on an original rank-based version of Le Cam's
one-step methodology which avoids the unpleasant nonparametric estimation of
cross-information quantities that is generally required in the context of
R-estimation. Although they are not strictly affine-equivariant, they are shown
to be equivariant in a weak asymptotic sense. Simulations confirm their
feasibility and excellent finite-sample performances.Comment: Published at http://dx.doi.org/10.1214/009053606000000948 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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Semiparametric estimation for a class of time-inhomogenous diffusion processes
Copyright @ 2009 Institute of Statistical Science, Academia SinicaWe develop two likelihood-based approaches to semiparametrically estimate a class of time-inhomogeneous diffusion processes: log penalized splines (P-splines) and the local log-linear method. Positive volatility is naturally embedded and this positivity is not guaranteed in most existing diffusion models. We investigate different smoothing parameter selections. Separate bandwidths are used for drift and volatility estimation. In the log P-splines approach, different smoothness for different time varying coefficients is feasible by assigning different penalty parameters. We also provide theorems for both approaches and report statistical inference results. Finally, we present a case study using the weekly three-month Treasury bill data from 1954 to 2004. We find that the log P-splines approach seems to capture the volatility dip in mid-1960s the best. We also present an application to calculate a financial market risk measure called Value at Risk (VaR) using statistical estimates from log P-splines
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