condQestCopC {CopCTS}

Conditional Quantile Estimation

Description

Given estiamted copula with copula parameter and specified marginal distribution, obtain the conditional qth quantile of Y_n+1 given Y1,...,Yn.

Usage

condQestCopC(tao,Yc,d,delta,copula,cop=NULL,theta=NULL,nIS=10000,
MARGIN=NULL,MARGIN.inv=NULL,...)

Arguments

tao

the desired quantile level, a numeric value between 0 and 1.

Yc

the Nx1 vector of observed responses that are subject to lower detection limit.

d

the lower detection limit.

delta

the Nx1 vector of censoring indicator with 1 indicating uncensored and 0 indicating left censored.

copula

the input copula object with copula parameter plugged in. If specified, cop and theta can be omitted.

cop

the choice of copula function. There are currently five available copula funcitons, including Clayton copula, Gaussian copula, Gumbel copula, Joe copula and Frank copula. Specify one from "Clayton","Gaussian","Gumbel","Joe" and "Frank".

theta

the copula parameter.

nIS

the size for sequential importance sampling. The default is 10000.

MARGIN

the marginal distribution of the latent time series.

MARGIN.inv

the inverse marginal distribution of the latent time series.

...

additional parameters for the marginal distribution of the latent time series.

Value

condQestCopC returns the conditional tao-th quantile of Y_n+1 given Y1,...,Yn based on the specified copula function and marginal distribution.

References

Li, F., Tang, Y. and Wang, H. (2018). Copula-Based Semiparametric Analysis for Time Series Data with Detection Limits, technical report.

Examples

set.seed(20)
Y = genLatentY(cop = "Clayton", theta = 1, N = 30)
d = -0.5
delta = (Y>d)
Yc = pmax(d,Y)
cq60.real = condQestCopC(0.6,Yc,d,delta,copula=claytonCopula(1),nIS = 50,
                        MARGIN=pnorm,MARGIN.inv=qnorm)
### Use selected copula
selCopC = selectCopC(cop.type = c("Clayton","Frank"),Yc,d,delta,nIS=50)
cq60.est = condQestCopC(0.6,Yc,d,delta,selCopC$Selected,nIS=50)