8,400 research outputs found
Simultaneous Selection of Optimal Bandwidths for the Sharp Regression Discontinuity Estimator
A new bandwidth selection rule that uses different bandwidths for the local
linear regression estimators on the left and the right of the cut-off point is
proposed for the sharp regression discontinuity estimator of the mean program
impact at the cut-off point. The asymptotic mean squared error of the estimator
using the proposed bandwidth selection rule is shown to be smaller than other
bandwidth selection rules proposed in the literature. An extensive simulation
study shows that the proposed method's performances for the sample sizes 500,
2000, and 5000 closely match the theoretical predictions
Automatic bandwidth selection for circular density estimation
Given angular data Ξ1,âŠ,Ξn[0,2Ï) a common objective is to estimate the density. In case that a kernel estimator is used, bandwidth selection is crucial to the performance. A âplug-in ruleâ for the bandwidth, which is based on the concentration of a reference density, namely, the von Mises distribution is obtained. It is seen that this is equivalent to the usual Euclidean plug-in rule in the case where the concentration becomes large. In case that the concentration parameter is unknown, alternative methods are explored which are intended to be robust to departures from the reference density. Simulations indicate that âwrapped estimatorsâ can perform well in this context. The methods are applied to a real bivariate dataset concerning protein structure
Bandwidth Selection in Nonparametric Kernel Testing
We propose a sound approach to bandwidth selection in nonparametric kernel testing. The main idea is to find an Edgeworth expansion of the asymptotic distribution of the test concerned. Due to the involvement of a kernel bandwidth in the leading term of the Edgeworth expansion, we are able to establish closedĂâform expressions to explicitly represent the leading terms of both the size and power functions and then determine how the bandwidth should be chosen according to certain requirements for both the size and power functions. For example, when a significance level is given, we can choose the bandwidth such that the power function is maximized while the size function is controlled by the significance level. Both asymptotic theory and methodology are established. In addition, we develop an easy implementation procedure for the practical realization of the established methodology and illustrate this on two simulated examples and a real data example.choice of bandwidth parameter, Edgeworth expansion, nonparametric kernel testing, power function, size function
Bandwidth selection for nonparametric kernel testing
We propose a sound approach to bandwidth selection in nonparametric kernel testing. The main idea is to find an Edgeworth expansion of the asymptotic distribution of the test concerned. Due to the involvement of a kernel bandwidth in the leading term of the Edgeworth expansion, we are able to establish closed-form expressions to explicitly represent the leading terms of both the size and power functions and then determine how the bandwidth should be chosen according to certain requirements for both the size and power functions. For example, when a significance level is given, we can choose the bandwidth such that the power function is maximized while the size function is controlled by the significance level. Both asymptotic theory and methodology are established. In addition, we develop an easy implementation procedure for the practical realization of the established methodology and illustrate this on two simulated examples and a real data example.Choice of bandwidth parameter; Edgeworth expansion; nonparametric kernel testing; power function; size function
Bandwidth selection for smooth backfitting in additive models
The smooth backfitting introduced by Mammen, Linton and Nielsen [Ann.
Statist. 27 (1999) 1443-1490] is a promising technique to fit additive
regression models and is known to achieve the oracle efficiency bound. In this
paper, we propose and discuss three fully automated bandwidth selection methods
for smooth backfitting in additive models. The first one is a penalized least
squares approach which is based on higher-order stochastic expansions for the
residual sums of squares of the smooth backfitting estimates. The other two are
plug-in bandwidth selectors which rely on approximations of the average squared
errors and whose utility is restricted to local linear fitting. The large
sample properties of these bandwidth selection methods are given. Their finite
sample properties are also compared through simulation experiments.Comment: Published at http://dx.doi.org/10.1214/009053605000000101 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Numerical performance of Penalized Comparison to Overfitting for multivariate kernel density estimation
Kernel density estimation is a well known method involving a smoothing
parameter (the bandwidth) that needs to be tuned by the user. Although this
method has been widely used the bandwidth selection remains a challenging issue
in terms of balancing algorithmic performance and statistical relevance. The
purpose of this paper is to compare a recently developped bandwidth selection
method for kernel density estimation to those which are commonly used by now
(at least those which are implemented in the R-package). This new method is
called Penalized Comparison to Overfitting (PCO). It has been proposed by some
of the authors of this paper in a previous work devoted to its statistical
relevance from a purely theoretical perspective. It is compared here to other
usual bandwidth selection methods for univariate and also multivariate kernel
density estimation on the basis of intensive simulation studies. In particular,
cross-validation and plug-in criteria are numerically investigated and compared
to PCO. The take home message is that PCO can outperform the classical methods
without algorithmic additionnal cost
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