Description Usage Arguments Value Author(s) References Examples
View source: R/waldConfidenceInterval_ir_stageTwo.R
This is an internal function not meant to be called directly. IR-Wald confidence interval that can be called at the second stage of a multistage procedure
1 2 | waldConfidenceInterval_ir_stageTwo(explanatory, response,
Y_0, gamma1, C_1, n1, level = NA)
|
explanatory |
Explanatory sample points |
response |
Observed responses at the explanatory sample points |
Y_0 |
Threshold of interest |
gamma1 |
Constant that is used in the first stage confidence interval |
C_1 |
Constant that is used in the first stage confidence interval |
n1 |
Sample size of the first stage |
level |
Desired confidence level |
estimate |
Point estimate for d_0 |
lower |
Lower bound of the confidence interval |
upper |
upper bound of the confidence interval |
sigmaSq |
Estimate of variance |
deriv_d0 |
Estimate of the derivative at d_0 |
Shawn Mankad
Tang R, Banerjee M, Michailidis G, Mankad S (2013). 'Two-Stage Plans for Estimating a Threshold Value of a Regression Function.' http://arxiv.org/abs/1304.4637
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 | 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=runif(75,oneStage_IR$L1 ,oneStage_IR$U1)
Y2=X2^2+rnorm(n=length(X2), sd=0.1)
twoStage_IR_IR = stageTwoAnalysis(oneStage_IR, X2, Y2, type="IR-wald", 0.95)
## The function is currently defined as
function (explanatory, response, Y_0, gamma1, C_1, n1, level = NA)
{
if (is.na(level)) {
level = 0.95
}
alpha = 1 - level
chernoff_realizations <- NULL; rm(chernoff_realizations);
data("chernoff_realizations", envir =environment())
ind = min(which(chernoff_realizations$DF - (1-alpha/2) >= 0))
q = chernoff_realizations$xcoor[ind]
n = length(response)
fit = threshold_estimate_ir(explanatory, response, Y_0)
phi_0 = C_1 * n1 * (n^(-1))
sigmaSq = estimateSigmaSq(explanatory, response)$sigmaSq
deriv_d0 = estimateDeriv(explanatory, response, fit$threshold_estimate_explanatory,
sigmaSq)
C_di = (4 * sigmaSq/(deriv_d0^2))^(1/3)
n = length(explanatory)
p = gamma1/(1 + gamma1)
C_di2 = C_di * (C_1/((1 - p) * p^(gamma1) * phi_0))
band = n^(-1 * (1 + gamma1)/3) * C_di2 * q
return(list(estimate = fit$threshold_estimate_explanatory,
lower = max(min(explanatory), fit$threshold_estimate_explanatory -
band), upper = min(max(explanatory), fit$threshold_estimate_explanatory +
band), sigmaSq = sigmaSq, deriv_d0 = deriv_d0))
}
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