cutoff.edgeworth: Critical value based on Edgeworth expansion of the size...

In L2DensityGoFtest: Density Goodness-of-Fit Test

Critical value based on Edgeworth expansion of the size function for the density goodness-of-fit test \hat{S}_n(h) of Bagkavos, Patil and Wood (2021)

Description

Implements the critical value for the density goodness-of-fit test S.n, approximating via an Edgeworth expansion the size function of the test statistic S.n.

Usage

cutoff.edgeworth(xin, dist, kfun, p1, p2, sig.lev)

Arguments

xin	A vector of data points - the available sample.
dist	The null distribution.
kfun	The kernel to use in the density estimates used in the bandwidth expression.
p1	Parameter 1 (vector or object) for the null distribution.
p2	Parameter 2 (vector or object) for the null distribution.
sig.lev	Significance level of the hypothesis test.

Details

Implements the critical value for the density goodness-of-fit test S.n, approximating via an Edgeworth expansion the size function of the test statistic S.n, given by

l_α = z_α + d_0 √{h} + d_2(n √{h})^{-1}

where z_α is the 1-α quantile of the normal distribution and d_0 = d_1 - C_{ H_0} and

d_j = (z_α^2 - 1)c_j, j=1,2

with

c_1 = \frac{4K^{(3)}(0)μ_2^3 ν_3}{3σ^3}, \; c_2 = \frac{μ_3^2K^2(0)}{σ^3}, \; μ_i =\int K^i(x)\,dx, i=1,….

and

C_{H_0} = 2≤ft (E f_0'( θ_0) \right )^2 Δ^{-1}, \; ν_i = E ≤ft \{f^{i}(x)\right \} = \int f^{i+1}(x)\,dx, i=1,…

This critical value is the density function equivalent to the critical value estimate obtained in the closely relatated regression setting in Gao and Gijbels (2008) and is suitable for finite sample implementations of the test.

Value

A scalar, the estimate of the critical value at the given significance level.

Author(s)

Dimitrios Bagkavos

R implementation and documentation: Dimitrios Bagkavos <[e-mail]>

References

Gao and Gijbels, Bandwidth selection in nonparametric kernel testing, pp. 1584-1594, JASA (2008)

See Also

cutoff.asymptotic, cutoff.bootstrap

L2DensityGoFtest documentation built on Feb. 16, 2023, 9:24 p.m.