mopt_pwm {npbr}

Threshold selection for the PWM frontier estimator

Description

This function implements the optimal smoothing parameter coefm involved in the probability-weighted moment frontier estimator of Daouia, Florens and Simar (2012).

Usage

mopt_pwm(xtab, ytab, x, a=2, rho, wind.coef=0.1)

Arguments

xtab

a numeric vector containing the observed inputs x_1,\ldots,x_n.

ytab

a numeric vector of the same length as xtab containing the observed outputs y_1,\ldots,y_n.

x

a numeric vector of evaluation points in which the estimator is to be computed.

a

a smoothing parameter (integer) larger than or equal to 2 (2 by default).

rho

a numeric vector of the same length as x or a scalar, which determines the values of rho.

wind.coef

a scalar coefficient to be selected in the interval (0,1].

Details

This is an implementation of an automated selection of the parameter coefm involved in the probability-weighted moment (PWM) estimator \tilde\varphi_{pwm}(x) [see dfs_pwm]. It is an adaptation of the experimental method kopt_momt_pick by Daouia et al. (2010). The idea is to select first (for each x) a grid of values for the parameter coefm given by c = 1, \cdots, \min(10,[\sqrt{N_x}]), where N_x=\sum_{i=1}^n1_{\{x_i\le x\}}, and then select the c where the variation of the results is the smallest. To achieve this, we compute the standard deviations of \tilde\varphi_{pwm}(x) over a “window” of size wind.coef \times \min(10,[\sqrt{N_x}]), where the coefficient wind.coef should be selected in the interval (0,1] in such a way to avoid numerical instabilities. The default option wind.coef=0.1 corresponds to having a window large enough to cover around 10\% of the possible values of c in the selected range of values for coefm. The value of c where the standard deviation is minimal defines the desired coefm.

Value

Returns a numeric vector with the same length as x.

Author(s)

Abdelaati Daouia and Thibault Laurent.

References

Daouia, A., Florens, J.-P. and Simar, L. (2010). Frontier estimation and extreme value theory. Bernoulli, 16, 1039-1063.

See Also

dfs_pwm, kopt_momt_pick.

Examples

data("post")
x.post<- seq(post$xinput[100],max(post$xinput), 
 length.out=100) 
## Not run: 
# When rho[x] is known and equal to 2:
best_cm.1<- mopt_pwm(post$xinput, post$yprod, 
 x.post, a=2, rho=2)

## End(Not run)