BCA1SG_degradation {BCA1SG}

BCA1SG algorithm for degradation data

Description

This function implements the BCA1SG algorithm on the semiparametric random-effects inverse Gaussian process model for degradation data to solve the ML estimates of the model parameters.

Usage

BCA1SG_degradation(input_data, initial_delta, initial_r, initial_Lambda = function(x){x},
threshold = 1e-05, max_iter = 5000, max_stepsize = 1e+05, xi = 0.3, contraction = 0.5)

Arguments

input_data

An object of class data.frame. The structure of the data frame must be {subject ID, time of measurement, measurement}.. This data frame cannot contain missing values. See the dataset "liner" for an example.

initial_delta

The initial value of the shape parameter of the gamma distributed scale parameter in the random-effects inverse Gaussian process. See Wang and Xu (2010) for details.

initial_r

The initial value of the rate parameter of the gamma distributed scale parameter in the random-effects inverse Gaussian process. See Wang and Xu (2010) for details.

initial_Lambda

An R function which serves as the initial value of the baseline mean function.

threshold

Convergence threshold. The algorithm is terminated when the infinity norm of the difference between successive iterates is less than the convergence threshold.

max_iter

Maximum number of iterations allowed.

max_stepsize

Maximum stepsize allowed.

xi

The xi parameter in the inexact backtracking line search algorithm. See Wang et al. (2020) for details.

contraction

The contraction parameter in the inexact backtracking line search algorithm. See Wang et al. (2020) for details.

Details

Details about the BCA1SG algorithm can be found in Wang et al. (2020), and the details concerning the semiparametric random-effects inverse Gaussian process model can be found in Section 3 of Wang and Xu (2010).

Value

distinct_time

The set of distinct observation time points.

est_Lambda

The estimated baseline mean function at the set of distinct observation time points.

est_delta

The estimated shape parameter of the gamma distributed scale parameter in the random-effects inverse Gaussian process.

est_r

The estimated rate parameter of the gamma distributed scale parameter in the random-effects inverse Gaussian process.

iteration

The number of iterations.

timecost

The computational time in seconds.

Author(s)

Wang Y., Ye Z., and Cao H.

References

Wang Y., Ye, Z.-S., and Cao, H.(2020). On Computation of Semi-Parametric Maximum Likelihood Estimators with Shape Constraints. Submitted.

Wang X. and Xu, D.(2010). An Inverse Gaussian Process Model for Degradation Data. Technometrics, 52(2), 188-197.

Examples

data(liner)
res<-BCA1SG_degradation(liner, initial_delta = 1, initial_r = 1, threshold = 5e-2)
res$est_delta
res$est_r
res$iteration
res$timecost
plot(res$distinct_time,res$est_Lambda,type="s",lwd=3,xlab="time",ylab="Baseline mean function")