Non-parametric estimator of conditional survival function
Non-parametric estimator of the conditional survival function of Y given X for censored data, see Akritas and Van Keilegom (2003).
crSurv(x, y, Xtilde, Ytilde, censored, h,
kernel = c("biweight", "normal", "uniform", "triangular", "epanechnikov"))x |
The value of the conditioning variable X to evaluate the survival function at. |
y |
The value(s) of the variable Y to evaluate the survival function at. |
Xtilde |
Vector of length n containing the censored sample of the conditioning variable X. |
Ytilde |
Vector of length n containing the censored sample of the variable Y. |
censored |
A logical vector of length n indicating if an observation is censored. |
h |
Bandwidth of the non-parametric estimator. |
kernel |
Kernel of the non-parametric estimator. One of |
We estimate the conditional survival function
1-F_{Y|X}(y|x)
using the censored sample (\tilde{X}_i, \tilde{Y}_i), for i=1,…,n, where X and Y are censored at the same time. We assume that Y and the censoring variable are conditionally independent given X.
The estimator is given by
1-\hat{F}_{Y|X}(y|x) = ∏_{\tilde{Y}_i ≤ y} (1-W_{n,i}(x;h_n)/(∑_{j=1}^nW_{n,j}(x;h_n) I\{\tilde{Y}_j ≥ \tilde{Y}_i\}))^{Δ_i}
where Δ_i=1 when (\tilde{X}_i, \tilde{Y}_i) is censored and 0 otherwise. The weights are given by
W_{n,i}(x;h_n) = K((x-\tilde{X}_i)/h_n)/∑_{Δ_j=1}K((x-\tilde{X}_j)/h_n)
when Δ_i=1 and 0 otherwise.
See Section 4.4.3 in Albrecher et al. (2017) for more details.
Estimates for 1-F_{Y|X}(y|x) as described above.
Tom Reynkens
Akritas, M.G. and Van Keilegom, I. (2003). "Estimation of Bivariate and Marginal Distributions With Censored Data." Journal of the Royal Statistical Society: Series B, 65, 457–471.
Albrecher, H., Beirlant, J. and Teugels, J. (2017). Reinsurance: Actuarial and Statistical Aspects, Wiley, Chichester.
# Set seed
set.seed(29072016)
# Pareto random sample
Y <- rpareto(200, shape=2)
# Censoring variable
C <- rpareto(200, shape=1)
# Observed (censored) sample of variable Y
Ytilde <- pmin(Y, C)
# Censoring indicator
censored <- (Y>C)
# Conditioning variable
X <- seq(1, 10, length.out=length(Y))
# Observed (censored) sample of conditioning variable
Xtilde <- X
Xtilde[censored] <- X[censored] - runif(sum(censored), 0, 1)
# Plot estimates of the conditional survival function
x <- 5
y <- seq(0, 5, 1/100)
plot(y, crSurv(x, y, Xtilde=Xtilde, Ytilde=Ytilde, censored=censored, h=5), type="l",
xlab="y", ylab="Conditional survival function")Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.