twostageTE (version 1.3)

waldConfidenceInterval_ir_stageOne: Stage one IR-Wald confidence interval

Description

This is an internal function not meant to be called directly. Classical IR-Wald confidence interval that can be called at the first stage of a multistage procedure

Usage

waldConfidenceInterval_ir_stageOne(explanatory, response, Y_0, level = NA)

Arguments

explanatory

Explanatory sample points

response

Observed responses at the explanatory sample points

Y_0

Threshold of interest

level

Desired confidence level

Value

estimate

Point estimate for d_0

lower

Lower bound of the confidence interval

upper

upper bound of the confidence interval

C_1

Constant for computing the confidence interval -- required for second stage ir-wald analysis

sigmaSq

Estimate of variance

deriv_d0

Estimate of the derivative at d_0

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)

## The function is currently defined as
function (explanatory, response, Y_0, level = NA) 
{
    if (is.na(level)) {
        level = 0.95
    }
    alpha = 1 - level
    ## Import previously computed Chernoff quantiles, provided by Groeneboom and Wellner
    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)
    sigmaSq = estimateSigmaSq(explanatory, response)$sigmaSq
    deriv_d0 = estimateDeriv(explanatory, response, 
        fit$threshold_estimate_explanatory, sigmaSq) 
    g_d0 = 1/n

    n = length(explanatory)
    C_di = (4 * sigmaSq/(deriv_d0^2))^(1/3)
    band = n^(-1/3) * C_di * g_d0^(-1/3) * 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), C_1 = as.numeric(C_di * g_d0^(-1/3) * q), 
        sigmaSq = sigmaSq, deriv_d0 = deriv_d0))
  }