11,776 research outputs found
On Berry--Esseen bounds for non-instantaneous filters of linear processes
Let , where the are
i.i.d. with mean 0 and at least finite second moment, and the are assumed
to satisfy with . When ,
is usually called a long-range dependent or long-memory process. For a certain
class of Borel functions , , from
to , which includes indicator functions and
polynomials, the stationary sequence is
considered. By developing a finite orthogonal expansion of
, the Berry--Esseen type bounds for the normalized sum
are obtained when
obeys the central limit theorem with positive limiting variance.Comment: Published in at http://dx.doi.org/10.3150/07-BEJ112 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Statistical Properties of Microstructure Noise
We study the estimation of moments and joint moments of microstructure noise.
Estimators of arbitrary order of (joint) moments are provided, for which we
establish consistency as well as central limit theorems. In particular, we
provide estimators of auto-covariances and auto-correlations of the noise.
Simulation studies demonstrate excellent performance of our estimators even in
the presence of jumps and irregular observation times. Empirical studies reveal
(moderate) positive auto-correlation of the noise for the stocks tested
Sorting using complete subintervals and the maximum number of runs in a randomly evolving sequence
We study the space requirements of a sorting algorithm where only items that
at the end will be adjacent are kept together. This is equivalent to the
following combinatorial problem: Consider a string of fixed length n that
starts as a string of 0's, and then evolves by changing each 0 to 1, with then
changes done in random order. What is the maximal number of runs of 1's?
We give asymptotic results for the distribution and mean. It turns out that,
as in many problems involving a maximum, the maximum is asymptotically normal,
with fluctuations of order n^{1/2}, and to the first order well approximated by
the number of runs at the instance when the expectation is maximized, in this
case when half the elements have changed to 1; there is also a second order
term of order n^{1/3}.
We also treat some variations, including priority queues. The proofs use
methods originally developed for random graphs.Comment: 31 PAGE
Using a Laplace approximation to estimate the random coefficients logit model by non-linear least squares
Current methods of estimating the random coefficients logit model employ simulations of the distribution of the taste parameters through pseudo-random sequences. These methods suffer from difficulties in estimating correlations between parameters and computational limitations such as the curse of dimensionality. This paper provides a solution to these problems by approximating the integral expression of the expected choice probability using a multivariate extension of the Laplace approximation. Simulation results reveal that our method performs very well, both in terms of accuracy and computational time. This paper is a revised version of CWP01/06.
Monotonicity, asymptotic normality and vertex degrees in random graphs
We exploit a result by Nerman which shows that conditional limit theorems
hold when a certain monotonicity condition is satisfied. Our main result is an
application to vertex degrees in random graphs, where we obtain asymptotic
normality for the number of vertices with a given degree in the random graph
with a fixed number of edges from the corresponding result for the
random graph with independent edges. We also give some simple
applications to random allocations and to spacings. Finally, inspired by these
results, but logically independent of them, we investigate whether a one-sided
version of the Cram\'{e}r--Wold theorem holds. We show that such a version
holds under a weak supplementary condition, but not without it.Comment: Published in at http://dx.doi.org/10.3150/07-BEJ6103 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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