SDHazardRateEst {NPHazardRate}

Kernel Second Derivative Hazard Rate Estimation

Description

Implements the kernel estimate of the second derivative of the hazard rate for right censored data defined - based on the estimate of Tanner and Wong (1983). The implementation is based on the second derivative of the Biweight Kernel.

Usage

SDHazardRateEst(xin, xout, h, ci)

Arguments

xin

A vector of data points. Missing values not allowed.

xout

A vector of grid points at which the estimates will be calculated.

h

A scalar, the bandwidth to use in the estimate.

ci

A vector of censoring indicators: 1's indicate uncensored observations, 0's correspond to censored obs.

Details

The function SDHazardRateEst implements the kernel estimate of the second derivative of the hazard rate estimator, given by

$\hat \lambda_2(x;h) = \sum_{i=1}^n \frac{K_h''(x-X_{(i)})\delta_{(i)}}{n-i+1}$

where $K$ is taken to be the Biweight kernel. The function is used for estimation of the functional $R(\lambda'')$ in PlugInBand so a default bandwidth rule is used for $h$ provided in (16), Hua, Patil and Bagkavos (2018).

Value

A vector with the second derivative of the hazard rate at the designated points xout.

References

1. Tanner and Wong (1983), The Estimation Of The Hazard Function From Randomly Censored Data By The Kernel Method, Annals of Statistics, 3, pp. 989-993.

2. Hua, Patil and Bagkavos, An $L_1$ analysis of a kernel-based hazard rate estimator, Australian and New Zealand J. Statist., (60), 43-64, (2018).