MISE = R(K)/(nh) + h^4 mu2^2 R(f'')/4. The two terms pull in
opposite directions, and the balance caps the attainable rate at
n^{-4/5} – strictly worse than the parametric n^{-1}, and the
ceiling that higher-order kernels and gamma kernels try to beat.
Usage
morie_fauzi_mise(n, h = NULL, R_K = NULL, mu2_K = 1, R_f2 = 1, sigma = 1)
Arguments
- n
sample size.
- h
bandwidth; the optimiser if NULL.
- R_K
int K^2; the Gaussian value if NULL.
- mu2_K
int u^2 K(u) du.
- R_f2
int f''^2.
- sigma
retained for signature parity with the Python module.
Value
list: mise, variance_part, bias_part, h, h_optimal,
mise_optimal, rate_exponent, parametric_rate_exponent,
bandwidth_rate, ceiling_note, n, method.
References
Fauzi and Maesono (2023), Ch. 1.
Examples
morie_fauzi_mise(1000)$h_optimal
#> [1] 0.1950199
