284,726 research outputs found
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
Computationally Efficient Nonparametric Importance Sampling
The variance reduction established by importance sampling strongly depends on
the choice of the importance sampling distribution. A good choice is often hard
to achieve especially for high-dimensional integration problems. Nonparametric
estimation of the optimal importance sampling distribution (known as
nonparametric importance sampling) is a reasonable alternative to parametric
approaches.In this article nonparametric variants of both the self-normalized
and the unnormalized importance sampling estimator are proposed and
investigated. A common critique on nonparametric importance sampling is the
increased computational burden compared to parametric methods. We solve this
problem to a large degree by utilizing the linear blend frequency polygon
estimator instead of a kernel estimator. Mean square error convergence
properties are investigated leading to recommendations for the efficient
application of nonparametric importance sampling. Particularly, we show that
nonparametric importance sampling asymptotically attains optimal importance
sampling variance. The efficiency of nonparametric importance sampling
algorithms heavily relies on the computational efficiency of the employed
nonparametric estimator. The linear blend frequency polygon outperforms kernel
estimators in terms of certain criteria such as efficient sampling and
evaluation. Furthermore, it is compatible with the inversion method for sample
generation. This allows to combine our algorithms with other variance reduction
techniques such as stratified sampling. Empirical evidence for the usefulness
of the suggested algorithms is obtained by means of three benchmark integration
problems. As an application we estimate the distribution of the queue length of
a spam filter queueing system based on real data.Comment: 29 pages, 7 figure
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Nonparametric regression analysis
textNonparametric regression uses nonparametric and flexible methods in analyzing complex data with unknown regression relationships by imposing minimum assumptions on the regression function. The theory and applications of nonparametric regression methods with an emphasis on kernel regression, smoothing spines and Gaussian process regression are reviewed in this report. Two datasets are analyzed to demonstrate and compare the three nonparametric regression models in R.Statistic
Sparse Additive Models
We present a new class of methods for high-dimensional nonparametric
regression and classification called sparse additive models (SpAM). Our methods
combine ideas from sparse linear modeling and additive nonparametric
regression. We derive an algorithm for fitting the models that is practical and
effective even when the number of covariates is larger than the sample size.
SpAM is closely related to the COSSO model of Lin and Zhang (2006), but
decouples smoothing and sparsity, enabling the use of arbitrary nonparametric
smoothers. An analysis of the theoretical properties of SpAM is given. We also
study a greedy estimator that is a nonparametric version of forward stepwise
regression. Empirical results on synthetic and real data are presented, showing
that SpAM can be effective in fitting sparse nonparametric models in high
dimensional data
Pointwise universal consistency of nonparametric linear estimators
This paper presents sufficient conditions for pointwise universal consistency of nonparametric delta estimators. We show the applicability of these conditions for some classes of nonparametric estimators
Semi-parametric regression: Efficiency gains from modeling the nonparametric part
It is widely admitted that structured nonparametric modeling that circumvents
the curse of dimensionality is important in nonparametric estimation. In this
paper we show that the same holds for semi-parametric estimation. We argue that
estimation of the parametric component of a semi-parametric model can be
improved essentially when more structure is put into the nonparametric part of
the model. We illustrate this for the partially linear model, and investigate
efficiency gains when the nonparametric part of the model has an additive
structure. We present the semi-parametric Fisher information bound for
estimating the parametric part of the partially linear additive model and
provide semi-parametric efficient estimators for which we use a smooth
backfitting technique to deal with the additive nonparametric part. We also
present the finite sample performances of the proposed estimators and analyze
Boston housing data as an illustration.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ296 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
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