Confidence bands for monotone probabilities

Usage

calibration_bands(
  x,
  y,
  alpha = 0.05,
  method = "standard",
  digits = NULL,
  nc = FALSE
)

x: covariate.
y: response variable (in 0,1).
alpha: type one error probability (1 minus the confidence level).
method: "standard" for the original method proposed in the article, "round" for rounding the covariate, or "YB" for the bounds by Yang & Barber (2019).
digits: number of digits for method "round". Default is 2. Has no effect for the other methods.
nc: use non-crossing bands for method "standard" or "round". Has no effect for method "YB". Default is FALSE. See also "summary(...,iso_test=TRUE)" in this context. Crossings allow to reject the null hypothesis of monotonicity in the calibration curve.

An object of class calibrationband, which is a list containing the following entries:

`bands`	a tibble holding `x,lwr,upr` the lower and upper bound, for each value of `x`. The upper bound extends to the left and the lower bound to the right, that is, the upper bound for `x[i]<s<x[i+1]` is `upr[i+1]`, and the lower bound for `x[i]<s<x[i+1]` is `lwr[i]`.
`cal`	a tibble holding the areas/segments of calibration (`out=0`) and miscalibration (`out=1`).
`bins`	a tibble of the characteristics of the isotonic bins.
`cases`	tibble of all predictions and observations. In addition it holds the column `isoy`, which is the isotonic regression of `y` at points `x`.
`alpha`	the given type one error probability (1 minus the nominal coverage of the band).
`method`	the selected method for computing the band.
`nc`	the selected method for non-crossing.
`digits`	the given digits for method `"round"` (or `NULL` for method `"standard"`).
`time`	time to compute the upper and lower band.