Project Details
Description
This proposal concerns research and education on adaptive regression
when the random errors are dependent. Many procedures have been
(and will be) proposed for nonparametric regression based on
different assumptions. In applications, a difficulty a user often
faces is the choice of the best method for the data at
hand. This is specially the case for high-dimensional function
estimation, where to overcome the curse of dimensionality, various
parsimonious models such as projection pursuit, CART, neural nets,
additive models, MARS, etc. are proposed according to different
characterizations of the target function. A main interest in this
research is to construct adaptive estimators by combining a
collection of candidate procedures. The goal for the combined
procedure is to perform automatically as well as (or nearly as well
as) the best original procedure without knowing which one it is.
The random errors will be assumed to be generally dependent,
including both short- and long-range cases. The effects of
dependence on adaptation capability will be studied. It is
anticipated that theoretically proven and computationally feasible
algorithms will be proposed to combine regression procedures
targeted at various characteristics of the regression function and
different dependence structures for the random errors.
Function estimation is an important statistical tool that tries to
understand accurately the functional relationships between variables based on
data and it has applications in many disciplines for successfully
addressing scientific questions. In reality, observations are always
subject to random noise (error) from different sources. When the
random errors are dependent on each other, the dependence may
disguise the functional relationship of interest. Long-range
dependence refers to a situation where the errors are still highly
correlated even when they occur at times or locations that are far
away from each other. It is known that such a long-range dependence makes
the estimation of the target function much harder. In applications,
the degree of dependence between the errors is usually unknown,
which makes the function estimation problem even harder. In this
proposal, we intend to develop methods that adaptively handle
different degrees of dependence among the errors so that the
function of interest can be estimated optimally without knowing the
dependence structure of the errors. The research results and related
work by others on long-range dependent data will be brought to
students at various levels in several statistics
courses. Collaborations will be conducted with several professors at
Iowa State University and their students in atmospheric science,
electrical engineering, agronomy and possibly other fields to
appropriately address long-range dependence phenomena, which have
been encountered often and known to cause problems in data analysis
with the existing statistical methods.
Status | Finished |
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Effective start/end date | 12/15/04 → 5/31/07 |
Funding
- National Science Foundation: $81,226.00