shen {DTDA} | R Documentation |
This function computes the NPMLE of a lifetime distribution function observed under one-sided (right or left) and two-sided (double) truncation. The NPMLE of the joint distribution of the truncation times along with its marginal distributions are also computed. It provides bootstrap pointwise confidence limits too.
shen(X, U = NA, V = NA, wt = NA, error = NA, nmaxit = NA, boot = TRUE, boot.type = "simple", B = NA, alpha = NA, display.FS = FALSE, display.UV = FALSE, plot.joint = FALSE, plot.type = NULL)
X |
Numeric vector with the times of ultimate interest. |
U |
Numeric vector with the left truncation times. If there are no truncation times from the left, put U =NA . |
V |
Numeric vector with the right truncation times. If there are no truncation times from the left, put V =NA . |
wt |
Numeric vector of non-negative initial solution, with the same length as X . Default value is set to 1/n, being n the length of X . |
error |
Numeric value. Maximum distance among the densities computed in two successive steps. If this is missing, it is set to 10% of 1/n. |
nmaxit |
Numeric value. Maximum number of iterations. If this is missing, it is set to nmaxit =100 . |
boot |
Logical. If TRUE (default), the simple bootstrap method is applied to lifetime and truncation times distributions estimation. Pointwise confidence bands are provided. |
boot.type |
A character string giving the bootstrap type to be used. This must be one of "simple" or "obvious" , with default "simple" . |
B |
Numeric value. Number of bootstrap resamples . The default NA is equivalent to B =500 . |
alpha |
Numeric value. (1-alpha ) is the nominal coverage for the pointwise confidence intervals. |
display.FS |
Logical. Default is FALSE. If TRUE, the estimated cumulative distribution function and the estimated survival function associated to X , (F) and (S) respectively, are plotted. |
display.UV |
Logical. Default is FALSE. If TRUE, the marginal distributions of U (fU) and V (fV) , are plotted. |
plot.joint |
Logical. Default is FALSE. If TRUE, the joint distribution of the truncation times is plotted. |
plot.type |
A character string giving the plot type to be used to representing the joint distribution of the truncation times.
This must be one of "image" or "persp", with default NULL . |
The NPMLE of the lifetime is computed by a single algorithm proposed in Shen (2008). This is an alternative algorithm which converges to the NMPLE after a number of iterations. Initial solutions are given by the ordinary empirical distribution functions. If the second (respectively third) argument is missing, computation of the Lynden-Bell estimator for right-truncated (respectively left-truncated) data is obtained. Note that individuals with NAs in the three first arguments will be automatically excluded.
A list containing the following values:
time |
The timepoint on the curve. |
n.event |
The number of events that ocurred at time t . |
events |
The total number of events. |
density |
The estimated density values associated to X . |
cumulative.df |
The estimated cumulative distribution values of X . |
truncation.probs |
The probabilities of truncation values, in each region. |
S0 |
error reached in the algorithm. |
Survival |
The estimated survival values. |
density.joint |
The estimated joint densities values associated to (U,V ). |
marginal.U |
The estimated cumulative univariate marginal values of the U . |
marginal.V |
The estimated cumulative univariate marginal values of the V . |
cumulative.joint |
The estimated joint cumulative distribution values. |
n.iterations |
The number of iterations used by this algorithm. |
biasf |
The estimated probabilities of observing the lifetimes. |
Boot |
The type of bootstrap method applied. |
B |
Number of bootstrap resamples computed. |
alpha |
The nominal level used to construct the confidence intervals. |
upper.df |
The estimated upper limits of the confidence intervals for F. |
lower.df |
The estimated lower limits of the confidence intervals for F. |
upper.Sob |
The estimated upper limits of the confidence intervals for S. |
lower.Sob |
The estimated lower limits of the confidence intervals for S. |
upper.fU |
The estimated upper limits of the confidence intervals for fU . |
lower.fU |
The estimated lower limits of the confidence intervals for fU . |
upper.fV |
The estimated upper limits of the confidence intervals for fV . |
lower.fV |
The estimated lower limits of the confidence intervals for fV . |
Carla Moreira, Jacobo de Uña-Álvarez and Rosa Crujeiras
Lynden-Bell, D. (1971) A method of allowing for known observational selection in small samples applied to 3CR quasars. Monograph National Royal Astronomical Society 155, 95-118. Astronomical Society, 155, 95-118.
Shen, P-S. (2008) Nonparametric analysis of doubly truncated data. Annals of the Institute of Statistical Mathematics DOI 10.1007/s10463-008-0192-2.
## Generating data which are doubly truncated n<-25 X<-runif(n,0,1) U<-runif(n,0,0.67) V<-runif(n,0.33,1) for (i in 1:n){ while (X[i]<U[i]|X[i]>V[i]){ U[i]<-runif(1,0,0.67) X[i]<-runif(1,0,1) V[i]<-runif(1,0.33,1) } } res<-shen(X,U,V,boot.type="obvious",plot.joint=TRUE, plot.type="persp") ## Generating data which are left truncated n<-25 X<-runif(n,0,1) U<-runif(n,0,0.67) for (i in 1:n){ while (X[i]<U[i]){ U[i]<-runif(1,0,0.67) X[i]<-runif(1,0,1) } } res<-shen(X,U,V=NA,boot=FALSE)