The functions use Gaussian basis functions to estimate the noncentrality parameters (ncp) from a large number of t-statistics.
nparncpt(tstat, df, ...)
nparncpt.sqp(tstat, df, penalty=3L, lambdas=10^seq(-1,5,by=1), starts,
IC=c('BIC','CAIC','HQIC','AIC'), K=100,
bounds=quantile(tstat,c(.01,.99)),
solver=c('solve.QP','lsei','ipop','LowRankQP'),
plotit=FALSE, verbose=FALSE, approx.hess=TRUE, ... )Numeric vector of noncentrality parameters
Numeric vector of degrees of freedom
An integer scalar among 1 through 5, indicating the order of derivatives of the estimated density funciton of ncp. The integral of square of such derivatives is the penalty to the log likelihood function. A character value among c('1st.deriv','2nd.deriv','3rd.deriv','4th.deriv','5th.deriv') is also accepted but deprecated.
Numeric vector of smoothness tuning parameter lambda to be tried. The one that minimizes NIC will be chosen.
Optional numeric vector of starting values. If missing, parncpt will be called with zeromean set to FALSE
to get an initial esimate of pi0. And the starting values (theta) will be set all equal to each other and sum to 1-pi0.
Note that this is the starting value for the largest lambdas only. For smaller lambdas, the estimates from larger lambdas
will be used as starting values (i.e., warm start).
Character; one of AIC, BIC, CAIC, HQIC, specifying the factor multiplied to the ENP in computing Information Criterion (IC).
The number of basis Gaussian density functions.
A numeric vector of length 2, giving the approximate bounds where most of the probability of ncp lies.
Character. The name of the function for solving quadratic programming problems. Note that ipop and kernlab are not very reliable. solve.QP is faster but lsei is more stable.
logical; indicating if plot.nparncpt should be called after estimation. This is always recommended before accepting the results.
logical; if TRUE, extensive messages will be printed.
either logical or a number between 0 and 1. This helps in reducing time in evaluating the hessian matrix. If it is set to TRUE,
for the kth Gaussian basis function and the gth tstat, the marginal t-statistic density evaluated at this tstat will be set to zero
if it is below the average of all K*length(tstat) such values. If it is set to FALSE or 0, then none of the density will be treated as zero,
no matter how small they are. If it is set to a number between 0 and 1, values below this quantile will be treated as zero. Note that this approximation
only affects the computation of hessian matrix, which does not need to be exact in an optimization routine. Hence, a reasonable sparseness speeds
up computation of a hessian matrix but might increase the number of iterations to converge. Set this to TRUE seems a reasonable trade-off between
the two effects and usually saves computing time.
other paramters passed to dtn.mix. Usually, the approximation argument.
A list with class attribute c("nparncpt", "ncpest")
estimated proportion of true nulls
mean of ncp
SD of ncp
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.
estimated ENP
estimated parameters theta
the lambda that minimizes NIC
analytic gradiant at the estimate
analytic hessian at the estimate
estimated mixing proportions for the NCP distribution
the information criterion specified by the user
mean of each basis Gaussian density
SD of each basis Gaussian density
a list of tstat and df
the index of lambdas that minimizes NIC
estimated pi0 for each lambda
ENP for each lambda
parameter estimates for each lambda
Network information criterion (NIC) for each lambda
SD of NIC for each lambda
the lambdas argument itself
the number of test statistics
nparncpt is a wrapper for nparncpt.sqp, the latter of which uses a sequential quadratic programming algorithm to find the mixing proportions
of the basis Gaussian density functions.
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.
parncpt, sparncpt,
fitted.nparncpt, plot.nparncpt, summary.nparncpt,
coef.ncpest, logLik.ncpest, vcov.ncpest,
AIC, dncp
# 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)
# }
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