estimate_fixed_pi0: Estimate a constant functional proportion
In StoreyLab/fFDR: Functional FDR for multiple hypothesis testing

Description Usage Arguments Details Value

Estimate the constant functional proportion pi0(z) when it is independent of the informative variabe z

estimate_fixed_pi0(
  p,
  z0,
  lambda = seq(0, 0.9, 0.05),
  tau = seq(0, 0.9, 0.05),
  pi0.method = "smoother",
  lambda.df = 3,
  tau.df = 3
)

`p`	A vector of p-values
`z0`	A vector of observations from the informative variable, of the same length as `p`
`lambda`	Choices of the tuning parameter "lambda" (for the p-value) used to estimate pi0(z)
`tau`	Choices of the tuning parameter "tau" (for the informative variable) used to estiamte pi0(z)
`pi0.method`	The method used to estimate pi0(z), being either "smoother" (default) or "bootstrap". The method depends on the tuning parameters "lambda" and "tau"
`lambda.df`	Degrees of freedom for smoother in argument "lambda"
`tau.df`	Degrees of freedom for smoother in argument "tau"

Assume the random variable z0 may affect the power of a statistical test (that induces the p-values) or the likelihood of a true null hypothesis. The m observations z0_i, i=1,...,m of z0 are quantile transformed into z_i, i=1,...,m such that z_i = rank(z0_i) / m, where rank(z0_i) is the rank of z0_i among z0_i, i=1,...,m. Consequently, z_i, i=1,...,m are approximately uniformly distributed on the interval [0,1]. When z_i, i=1,...,m are regarded as observations from the random variable z, then z is approximately uniformly distributed on [0,1]. Namely, z0 has been quantile transformed into z, and they are equivalent. Further, z or z0 is referred to as the informative variable.

Estimate of pi0(z)

StoreyLab/fFDR documentation built on March 8, 2021, 10:14 p.m.