condQestCopC {CopCTS} R Documentation

## 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)


[Package CopCTS version 1.0.0 Index]