| hopt.be {L2DensityGoFtest} | R Documentation |
Power-optimal bandwidth for the test statistic \hat{S}_n(h)
Description
Implements an optimal, with respect to Berry-Esseen bound, bandwidth for the density goodness-of-fit test \hat{S}_n(h) of Bagkavos, Patil and Wood (2021).
Usage
hopt.be(xin)
Arguments
xin |
A vector of data points - the available sample. |
Details
Implements the Berry-Esseen bound optimal bandwidth defined in (18), Bagkavos, Patil and Wood (2022), given by
h = n^{-1/2} \sqrt{\frac{\hat \nu_p R_4(K)}{\rho_\ast^2 \hat \nu_4 I_0(K)} },
where
\hat \nu_p = n^{-1} \sum_{j=1}^n \hat f(X_j; \hat h_a),
and \hat h_a is the density optimal bandwidth calculated by a reference to a prametric distribution, \rho_\star=1 and
R_4(K)=\int K^4(x)\,dx.
Value
The estimate of the Berry-Esseen optimal bandwidth.
Author(s)
Dimitrios Bagkavos
R implementation and documentation: Dimitrios Bagkavos <dimitrios.bagkavos@gmail.com>
References
Bagkavos, Patil and Wood: Nonparametric goodness-of-fit testing for a continuous multivariate parametric model, (2021), under review.