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http://hdl.handle.net/2451/14771
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| Title: | Three Sides of Smoothing: Categorical Data Smoothing, Nonparametric
Regression, and Density Estimation |
| Authors: | Simonoff, Jeffrey S. |
| Keywords: | Kernel estimator
Local likelihood estimator
Local polynomial estimator
Maximum penalized likelihood estimator
Poisson regression |
| Issue Date: | 1997 |
| Publisher: | Stern School of Business, New York University |
| Series/Report no.: | SOR-97-3 |
| Abstract: | The past forty years have seen a great deal of research into the
construction and properties of nonparametric estimates of smooth
functions. This research has focused primarily on two sides of the
smoothing problem: nonparametric regression and density estimation.
Theoretical results for these two situations are similar, and
multivariate density estimation was an early justification for the
Nadaraya-Watson kernel regression estimator. A third, less
well-explored, strand of applications of smoothing is to the estimation
of probabilities in categorical data. In this paper the position of
categorical data smoothing as a bridge between nonparametric regression
and density estimation is explored. Nonparametric regression provides a
paradigm for the construction of effective categorical smoothing
estimates, and use of an appropriate likelihood function yields cell
probability estimates with many desirable properties. Such estimates can
be used to construct regression estimates when one or more of the
categorical variables are viewed as response variables. They also lead
naturally to the construction of well-behaved density estimates using
local or penalized likelihood estimation, which can then be used in a
regression context. Several real data sets are used to illustrate these points. |
| URI: | http://hdl.handle.net/2451/14771 |
| Appears in Collections: | IOMS: Statistics Working Papers
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