estimate_fixed_pi0: Estimate a constant functional proportion

Description Usage Arguments Details Value

View source: R/estimate_fixed_pi0.R

Description

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

Usage

1
2
3
4
5
6
7
8
9
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
)

Arguments

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"

Details

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.

Value

Estimate of pi0(z)


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