R: Threshold estimate based on local linear approximation
threshold_estimate_locLinear
R Documentation
Threshold estimate based on local linear approximation
Description
The main idea for the procedure in Tang et al. (2011) is to utilize
a local linear approximation in the vicinity of the first stage estimate, and
to bootstrap this local approximation to obtain confidence intervals.
Observed responses at the explanatory sample points
Y_0
Threshold of interest
Details
This is an internal function not meant to be called directly.
It function uses a local linear approximation to form a point estimate.
Value
threshold_estimate_explanatory
Point estimate of d_0
threshold
Threshold of interest (equal to Y_0 input)
Author(s)
Shawn Mankad
References
Tang R, Banerjee M, Michailidis G (2011). 'A two-stage hybrid procedure
for estimating an inverse regression function.' The Annals of Statistics,
39, 956-989.
Examples
X=runif(25, 0,1)
Y=X^2+rnorm(n=length(X), sd=0.1)
oneStage_IR=stageOneAnalysis(X, Y, 0.25, type="IR-wald", 0.99)
X2 = c(rep(oneStage_IR$L1,37),rep(oneStage_IR$U1,38))
Y2=X2^2+rnorm(n=length(X2), sd=0.1)
stageTwoAnalysis(oneStage_IR, explanatory = X2, response = Y2,
type = "locLinear", level = 0.95)
## The function is currently defined as
function (explanatory, response, Y_0)
{
n = length(response)
if (sum(response < Y_0) == n) {
list(threshold_estimate_explanatory = max(explanatory),
threshold_estimate_response = max(response), threshold = Y_0,
Y_hat = max(response), index = n)
}
else if (sum(response >= Y_0) == n) {
list(threshold_estimate_explanatory = min(explanatory),
threshold_estimate_response = min(response), threshold = Y_0,
Y_hat = min(response), index = 1)
}
else {
beta = lm(response ~ explanatory)$coef
estim_x = (Y_0 - beta[1])/beta[2]
list(threshold_estimate_explanatory = estim_x, threshold = Y_0)
}
}