lpint: Martingale estimating equation local polynomial estimator of... In lpint: Local polynomial estimators of intensity function or its derivatives

Description

This local polynomial estimator is based on a biased martingale estimating equation.

Usage

 1 2 3 4 5 lpint(jmptimes, jmpsizes = rep(1, length(jmptimes)), Y = rep(1,length(jmptimes)), bw = NULL, adjust = 1, Tau = max(1, jmptimes), p = nu + 1, nu = 0, K = function(x) 3/4 * (1 - x^2) * (x <= 1 & x >= -1), n = 101, bw.only=FALSE)

Arguments

 jmptimes a numeric vector giving the jump times of the counting process jmpsizes a numeric vector giving the jump sizes at each jump time. Need to be of the same length as jmptimes Y a numeric vector giving the value of the exposure process (or size of the risk set) at each jump times. Need to be of the same length as jmptimes bw a numeric constant specifying the bandwidth used in the estimator. If left unspecified the automatic bandwidth selector will be used to calculate one. adjust a positive constant giving the adjust factor to be multiplied to the default bandwith parameter or the supplied bandwith Tau a numric constant >0 giving the censoring time (when observation of the counting process is terminated) p the degree of the local polynomial used in constructing the estimator. Default to 1 plus the degree of the derivative to be estimated nu the degree of the derivative of the intensity function to be estimated. Default to 0 for estimation of the intensity itself. K the kernel function n the number of evenly spaced time points to evaluate the estimator at bw.only TRUE or FALSE according as if the rule of thumb bandwidth is the only required output or not

Value

either a list containing

 x the vector of times at which the estimator is evaluated y the vector giving the values of the estimator at times given in x se the vector giving the standard errors of the estimates given in y bw the bandwidth actually used in defining the estimator equal the automatically calculated or supplied multiplied by adjust

or a numeric constant equal to the rule of thumb bandwidth estimate

Author(s)

Feng Chen <feng.chen@unsw.edu.au.>

References

Chen, F., Yip, P.S.F., & Lam, K.F. (2011) On the Local Polynomial Estimators of the Counting Process Intensity Function and its Derivatives. Scandinavian Journal of Statistics 38(4): 631 - 649. http://dx.doi.org/10.1111/j.1467-9469.2011.00733.x  