159 research outputs found
Generalized bootstrap for estimating equations
We introduce a generalized bootstrap technique for estimators obtained by
solving estimating equations. Some special cases of this generalized bootstrap
are the classical bootstrap of Efron, the delete-d jackknife and variations of
the Bayesian bootstrap. The use of the proposed technique is discussed in some
examples. Distributional consistency of the method is established and an
asymptotic representation of the resampling variance estimator is obtained.Comment: Published at http://dx.doi.org/10.1214/009053604000000904 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Bulk behaviour of Schur-Hadamard products of symmetric random matrices
We develop a general method for establishing the existence of the Limiting
Spectral Distributions (LSD) of Schur-Hadamard products of independent
symmetric patterned random matrices. We apply this method to show that the LSDs
of Schur-Hadamard products of some common patterned matrices exist and identify
the limits. In particular, the Schur-Hadamard product of independent Toeplitz
and Hankel matrices has the semi-circular LSD. We also prove an invariance
theorem that may be used to find the LSD in many examples.Comment: 27 pages, 1 figure; to appear, Random Matrices: Theory and
Applications. This is the final version, incorporating referee comment
A Dynamic Mechanism and Surplus Extraction Under Ambiguity
In the standard independent private values (IPV)model, each bidder’s beliefs about the values of any other bidder is represented by a unique prior. In this paper we relax this assumption and study the question of auction design in an IPV setting characterized by ambiguity: bidders have an imprecise knowledge of the distribution of values of others, and are faced with a set of priors. We also assume that their preferences exhibit ambiguity aversion; in particular, they are represented by the epsilon-contamination model. We show that a simple variation of a discrete Dutch auction can extract almost all surplus. This contrasts with optimal auctions under IPV without ambiguity as well as with optimal static auctions with ambiguity - in all of these, types other than the lowest participating type obtain a positive surplus. An important point of departure is that the modified Dutch mechanism we consider is dynamic rather than static, establishing that under ambiguity aversion – even when the setting is IPV in all other respects – a dynamic mechanism can have additional bite over its static counterparts.Ambiguity Aversion; Epsilon Contamination; Modified Dutch Auction; Dynamic Mechanism; Surplus Extraction
Bulk behaviour of skew-symmetric patterned random matrices
Limiting Spectral Distributions (LSD) of real symmetric patterned matrices
have been well-studied. In this article, we consider
skew-symmetric/anti-symmetric patterned random matrices and establish the LSDs
of several common matrices. For the skew-symmetric Wigner, skew-symmetric
Toeplitz and the skew-symmetric Circulant, the LSDs (on the imaginary axis) are
the same as those in the symmetric cases. For the skew-symmetric Hankel and the
skew-symmetric Reverse Circulant however, we obtain new LSDs. We also show the
existence of the LSDs for the triangular versions of these matrices.
We then introduce a related modification of the symmetric matrices by
changing the sign of the lower triangle part of the matrices. In this case, the
modified Wigner, modified Hankel and the modified Reverse Circulants have the
same LSDs as their usual symmetric counterparts while new LSDs are obtained for
the modified Toeplitz and the modified Symmetric Circulant.Comment: 21 pages, 2 figure
Multicolor urn models with reducible replacement matrices
Consider the multicolored urn model where, after every draw, balls of the
different colors are added to the urn in a proportion determined by a given
stochastic replacement matrix. We consider some special replacement matrices
which are not irreducible. For three- and four-color urns, we derive the
asymptotic behavior of linear combinations of the number of balls. In
particular, we show that certain linear combinations of the balls of different
colors have limiting distributions which are variance mixtures of normal
distributions. We also obtain almost sure limits in certain cases in contrast
to the corresponding irreducible cases, where only weak limits are known.Comment: Published in at http://dx.doi.org/10.3150/08-BEJ150 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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