1,534 research outputs found
Estimation of nonlinear models with Berkson measurement errors
This paper is concerned with general nonlinear regression models where the
predictor variables are subject to Berkson-type measurement errors. The
measurement errors are assumed to have a general parametric distribution, which
is not necessarily normal. In addition, the distribution of the random error in
the regression equation is nonparametric. A minimum distance estimator is
proposed, which is based on the first two conditional moments of the response
variable given the observed predictor variables. To overcome the possible
computational difficulty of minimizing an objective function which involves
multiple integrals, a simulation-based estimator is constructed. Consistency
and asymptotic normality for both estimators are derived under fairly general
regularity conditions.Comment: Published at http://dx.doi.org/10.1214/009053604000000670 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Three Dimensional Strongly Symmetric Circulant Tensors
In this paper, we give a necessary and sufficient condition for an even order
three dimensional strongly symmetric circulant tensor to be positive
semi-definite. In some cases, we show that this condition is also sufficient
for this tensor to be sum-of-squares. Numerical tests indicate that this is
also true in the other cases
Positive Semi-Definiteness and Sum-of-Squares Property of Fourth Order Four Dimensional Hankel Tensors
A positive semi-definite (PSD) tensor which is not a sum-of-squares (SOS)
tensor is called a PSD non-SOS (PNS) tensor. Is there a fourth order four
dimensional PNS Hankel tensor? Until now, this question is still an open
problem. Its answer has both theoretical and practical meanings. We assume that
the generating vector of the Hankel tensor is symmetric. Under this
assumption, we may fix the fifth element of at . We show that
there are two surfaces and with the elements of as variables, such that , is SOS if and only if
, and is PSD if and only if , where is the
first element of . If for a point , then there are no fourth order four dimensional PNS Hankel tensors
with symmetric generating vectors for such . Then, we
call such a point PNS-free. We show that a -degree planar closed convex
cone, a segment, a ray and an additional point are PNS-free. Numerical tests
check various grid points, and find that they are also PNS-free
- β¦