KDE {drcte}

Kernel estimator for the cumulative distribution function

Description

This function provides the kernel estimator for the distribution function for interval‐grouped data.

Usage

KDE(bw = c("AMISE", "boot"))
KDE.fun(x, start, end, count, h)

Arguments

x

for time-to-event data, the predictor variable is time

start

for each assessment interval, this is the start time

end

for each assessment interval, this is the end time

count

for each assessment interval, this is the number of events

h

bandwidth value

bw

Method for bandwidth selection

Details

The function 'KDE.fun()' provides the kernel estimator for the distribution function, as modified for interval-grouped data. The equation is:

F(x) = \sum {w_i * pnorm( \frac{x - t_i}{h}) }

where 'w_i' is the observed proportion of individuals getting the event in the i-th interval, 't_i' is the mid-point of the i-th time interval, 'x' is the time and 'h' is the bandwidth. The function KDE() is meant to be used with the 'drmte()' function, to estimate the optimal bandwidth, according to a bootstrap selector (Barreiro-Ures et al., 2019).

Value

The 'KDE.fun()' functions returns the CDF, for given values of time. The KDE() function returns a list containing the nonlinear function and other facilities, which are internally used by the 'drmte()' function.

Author(s)

Andrea Onofri. Codes for the estimation of optimal bandwidth have been largely taken from the 'binnednp' package (Barreiro-Ures et al., 2019).

References

Barreiro‐Ures, D., Francisco‐Fernández, M., Cao, R., Fraguela, B.B., Doallo, R., González‐Andújar, J.L., Reyes, M., 2019. Analysis of interval‐grouped data in weed science: The binnednp Rcpp package. Ecol Evol 9, 10903–10915.

Cao, R., Francisco-Fernández, M., Anand, A., Bastida, F., González-Andújar, J.L., 2013. Modeling Bromus diandrus Seedling Emergence Using Nonparametric Estimation. Journal of Agricultural, Biological, and Environmental Statistics 18, 64–86.

Cao, R., Francisco-Fernández, M., Anand, A., Bastida, F., González-Andújar, J.L., 2011. Computing statistical indices for hydrothermal times using weed emergence data. The Journal of Agricultural Science 149, 701–712.

Gonzalez-Andujar, J.L., Francisco-Fernandez, M., Cao, R., Reyes, M., Urbano, J.M., Forcella, F., Bastida, F., 2016. A comparative study between nonlinear regression and nonparametric approaches for modelling Phalaris paradoxa seedling emergence. Weed Research 56, 367–376.

Examples

data(chickweed)
mod <- drmte(count ~ start + end, data=chickweed,
              fct = KDE())
summary(mod)
plot(mod, ylim = c(0, 0.25), log = "")