11,590 research outputs found
Mixture of Regression Models with Single-Index
In this article, we propose a class of semiparametric mixture regression
models with single-index. We argue that many recently proposed
semiparametric/nonparametric mixture regression models can be considered
special cases of the proposed model. However, unlike existing semiparametric
mixture regression models, the new pro- posed model can easily incorporate
multivariate predictors into the nonparametric components. Backfitting
estimates and the corresponding algorithms have been proposed for to achieve
the optimal convergence rate for both the parameters and the nonparametric
functions. We show that nonparametric functions can be esti- mated with the
same asymptotic accuracy as if the parameters were known and the index
parameters can be estimated with the traditional parametric root n convergence
rate. Simulation studies and an application of NBA data have been conducted to
demonstrate the finite sample performance of the proposed models.Comment: 28 pages, 2 figure
Nonparametric and Varying Coefficient Modal Regression
In this article, we propose a new nonparametric data analysis tool, which we
call nonparametric modal regression, to investigate the relationship among
interested variables based on estimating the mode of the conditional density of
a response variable Y given predictors X. The nonparametric modal regression is
distinguished from the conventional nonparametric regression in that, instead
of the conditional average or median, it uses the "most likely" conditional
values to measures the center. Better prediction performance and robustness are
two important characteristics of nonparametric modal regression compared to
traditional nonparametric mean regression and nonparametric median regression.
We propose to use local polynomial regression to estimate the nonparametric
modal regression. The asymptotic properties of the resulting estimator are
investigated. To broaden the applicability of the nonparametric modal
regression to high dimensional data or functional/longitudinal data, we further
develop a nonparametric varying coefficient modal regression. A Monte Carlo
simulation study and an analysis of health care expenditure data demonstrate
some superior performance of the proposed nonparametric modal regression model
to the traditional nonparametric mean regression and nonparametric median
regression in terms of the prediction performance.Comment: 33 page
Rankin-Cohen brackets and formal quantization
In this paper, we use the theory of deformation quantization to understand
Connes' and Moscovici's results \cite{cm:deformation}. We use Fedosov's method
of deformation quantization of symplectic manifolds to reconstruct Zagier's
deformation \cite{z:deformation} of modular forms, and relate this deformation
to the Weyl-Moyal product. We also show that the projective structure
introduced by Connes and Moscovici is equivalent to the existence of certain
geometric data in the case of foliation groupoids. Using the methods developed
by the second author \cite{t1:def-gpd}, we reconstruct a universal deformation
formula of the Hopf algebra \calh_1 associated to codimension one foliations.
In the end, we prove that the first Rankin-Cohen bracket defines a
noncommutative Poisson structure for an arbitrary \calh_1 action.Comment: 21 pages, minor changes and typos correcte
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