waldConfidenceInterval_ir_stageOne: Stage one IR-Wald confidence interval
In twostageTE: Two-Stage Threshold Estimation

Description Usage Arguments Value Author(s) Examples

View source: R/waldConfidenceInterval_ir_stageOne.R

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

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

`explanatory`	Explanatory sample points
`response`	Observed responses at the explanatory sample points
`Y_0`	Threshold of interest
`level`	Desired confidence level

`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

Shawn Mankad

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))
  }