Single index models are a special type of nonlinear regression
model that are partially linear and play an important role in
fields that employ multidimensional regression models. A wavelet
series is thought of as a good approximation to any function in
the space. There are two ways to represent the function: one
in which all wavelet coefficients are used in the series, and
another that allows for shrinkage rules. We propose posterior
inference for the two wavelet representations of the function.
To implement posterior inference, we define a hierarchial
(mixture) prior model on the scaling(wavelet) coefficients. Since
from the two representations a non-zero coefficient has
information about the features of the function at a certain scale
and location, a prior model for the coefficient should depend on
its resolution level. In wavelet shrinkage rules we use
"pseudo-priors" for a zero coefficient.
In single index models a direction theta affects estimates of
the function. Transforming theta to a spherical polar coordinate
is a convenient way of imposing the constraint. The posterior distribution of the direction is
unknown and we employ a Metropolis algorithm and an independence
sampler, which require a proposal distribution. A normal
distribution is proposed as the proposal distribution for the
direction. We introduce ways to choose its mode (mean) using the
independence sampler.
For Monte Carlo simulations and real data we compare performances
of the Metropolis algorithm and independence samplers for the
direction and two functions: the cosine function is represented
only by the smooth part in the wavelet series and the Doppler
function is represented by both smooth and detail parts of the
series.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/304 |
| Date | 30 September 2004 |
| Creators | Park, Chun Gun |
| Contributors | Hart, Jeffrey D., Vannucci, Marina |
| Publisher | Texas A&M University |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Dissertation, text |
| Format | 2948849 bytes, 127193 bytes, electronic, application/pdf, text/plain, born digital |
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