sparncp: Semiparametric density estimation for noncentrality...

In pi0: Estimating the proportion of true null hypotheses for FDR

Description

Semiparametric density estimation for noncentrality parameters using the combination method of Olkin and Spiegelman (1987), based on fits from both parncpt and nparncpt.

Usage

sparncpt(obj1, obj2, ...)
## S3 method for class 'parncpt'
sparncpt(obj1, obj2, ...)
## S3 method for class 'nparncpt'
sparncpt(obj1, obj2, ...)
## S3 method for class 'numeric'
sparncpt(obj1, obj2, ...)

Arguments

obj1, obj2	Case 1: obj1 and obj2 are of class parncpt and nparncpt respectively; or vice versa; Case 2: obj1 is a numeric vector of t-statistics and obj2 is a vector degrees of freedom
...	other arguments passed to dtn.mix, most notably the approximation argument.

Details

This is a two-component mixture of a parametric fit from parncpt and a nonparametric fit from nparncpt, with mixing proportion rho. If obj1 and obj2 are t-statistics and degrees of freedom respectively, calls to each of parncpt and nparncpt are made and their results are used in combination.

Value

a list with class c('sparncpt','ncpest'):

pi0	estimated proportion of true nulls
mu.ncp	mean of ncp
sd.ncp	SD of ncp
logLik	an object of class logLik. The associated df is the estimated effective number of parameters (enp). The log likelihood is also penalized likelihood. See also logLik.ncpest and AIC.
enp	estimated ENP
par	estimated mixing proportion rho
gradiant	analytic gradiant at the estimate (not implemented)
hessian	analytic hessian at the estimate (not implemented)
parfit	the fitted parncpt object
nparfit	the fitted nparncpt object
nobs	the number of test statistics

Author(s)

Long Qu

References

I. Olkin and C. H. Spiegelman. (1987) A Semiparametric Approach to Density Estimation. Journal of the American Statistical Association. 82,399,858–865

Qu L, Nettleton D, Dekkers JCM. (2012) Improved Estimation of the Noncentrality Parameter Distribution from a Large Number of $t$-statistics, with Applications to False Discovery Rate Estimation in Microarray Data Analysis. Biometrics, 68, 1178–1187.

See Also

parncpt, nparncpt, fitted.sparncpt, plot.sparncpt, summary.sparncpt, coef.ncpest, logLik.ncpest, vcov.ncpest, AIC, dncp

Examples

## Not run: 
data(simulatedTstat)
(npfit=nparncpt(tstat=simulatedTstat, df=8)); 
(pfit=parncpt(tstat=simulatedTstat, df=8, zeromean=FALSE)); plot(pfit)
(pfit0=parncpt(tstat=simulatedTstat, df=8, zeromean=TRUE)); plot(pfit0)
(spfit=sparncpt(npfit,pfit)); plot(spfit)

## End(Not run)

Example output

pi0= 0.7483634
mu.ncp= -0.02254265
sd.ncp= 1.523897
enp= 2.408478
lambda= 100
Warning message:
In nparncpt.sqp(tstat, df, ...) :
  Less than half of the estimated coefficients (betas) are less than 0.01. Your might want to try enlarging the `bounds` argument.
pi0 (proportion of null hypotheses) = 0.7483103
mu.ncp (mean of noncentrality parameters) = -0.03791745
sd.ncp (SD of noncentrality parameters) = 1.624555
pi0 (proportion of null hypotheses) = 0.7486391
mu.ncp (mean of noncentrality parameters) = 0
sd.ncp (SD of noncentrality parameters) = 1.626181
pi0= 0.7483134
mu.ncp= -0.03704109
sd.ncp= 1.534416
rho= 0.943
enp= 3.966283

pi0 documentation built on May 2, 2019, 4:47 p.m.