Asymptotic normality of the deconvolution estimator — morie_deconv

\([n h_n/b_n]^{1/2}(\hat f_U(u) - f_U(u) - \mathrm{bias}) \to_D N(0, \sigma^2)\). The normalising factor carries \(b_n\), a deconvolution-specific inflation absent from ordinary kernel estimation – it encodes the price of dividing by a vanishing characteristic function. The bias is SUBTRACTED, not assumed away: undersmoothing is what makes it negligible, and if it is not, the interval is centred wrongly. Mirrors morie.fn.hrzdcnm.

Usage

morie_deconv_normality(fn_u, f_u, n, h, b, bias = 0, sigma = 1)

Arguments

fn_u: estimate at the evaluation point.
f_u: truth at the evaluation point.
n: sample size.
h: bandwidth, positive.
b: deconvolution inflation factor, positive.
bias: asymptotic bias.
sigma: limiting standard deviation, positive.

Value

list: z, scaling, p_two_sided, bias_subtracted, method.

References

Horowitz, Ch. 5, Sec. 5.1.3.

Examples

morie_deconv_normality(0.41, 0.399, 1000, 0.2, 2)$z
#> [1] 0.11