bfa_ls_bc_ci {bifurcatingr} | R Documentation |
Bias-Corrected Confidence intervals of Least Squares Estimators for Bifurcating Autoregressive Models
Description
This function performs bias correction confidence intervals on the least squares estimators of the autoregressive coefficients in a BAR(p) model using single, fast-double, and the Bias-corrected and accelerated bootstrapping as described in Elbayoumi and Mostafa (2023).
Usage
bfa_ls_bc_ci(
z,
p,
method = "BCa",
conf_int = "standard_normal_bc",
conf_level = 0.95,
B = 5,
burn = 5
)
Arguments
z |
a numeric vector containing the tree data |
p |
an integer determining the order of bifurcating autoregressive model to be fit to the data |
method |
method of bias correction. Currently, "boot1", "boot2fast", and "BCa" are supported and they implement single bootstrap, fast-double bootstrap, and bias-corrected and accelerated bootstrap, respectively. Defaults to "BCa". |
conf_int |
type of the confidence interval. Currently, "standard_normal_bc", "percentile", and "percentile_bc" are supported and they implement corrected standard normal bootstrap CI, uncorrected percentile bootstrap CI, and corrected percentile bootstrap CI, respectively. If "boot1" method is selected, the "standard_normal_bc", "percentile", "percentile_bc" confidence intervals can be obtained. If "boot2fast" method is selected, the "standard_normal_bc" and "percentile_bc" confidence intervals can be obtained. No effect for conf_int, the "BCa" method is selected. Defaults to standard_normal_bc". |
conf_level |
confidence level to be used in computing confidence intervals
for model coefficients. Defaults to |
B |
number of bootstrap samples (replicates). |
burn |
number of tree generations to discard before starting the bootstrap sample (replicate). Defaults to 5. |
Value
Bias_corrected_coef |
a matrix containing the bias-correction least squares estimates of the autoregressive coefficients |
BCa_ci |
a matrix containing the lower and upper limits of corrected BCa
confidence intervals,if |
standard_normal_bc_ci |
a matrix containing the lower and upper limits of
corrected confidence intervals, if |
percentile_ci |
a matrix containing the lower and upper limits of uncorrected
percentile confidence intervals, if |
percentile_bc_ci |
a matrix containing the lower and upper limits of corrected
percentile confidence intervals, if |
standard_normal_bc_ci |
a matrix containing the lower and upper limits of corrected
confidence intervals, if |
percentile_bc_ci |
a matrix containing the lower and upper limits of corrected percentile
confidence intervals, if |
References
Elbayoumi, T. M. & Mostafa, S. A. (2023). Impact of Bias Correction of the Least Squares Estimation on Bootstrap Confidence Intervals for Bifurcating Autoregressive Models. Journal of Data Science, 1-20, doi.org/10.6339/23-JDS1092.
Examples
# Generating Non-contaminated normal BAR(1) tree and calculating the bias corrected
# standard normal CI for the autoregressive coefficients of the BAR(1) model
# Note that in this example (B=2) for speeding up the calculations.
# B must be set to 499 or more for calculation accuracy.
z <- bfa_tree_gen(15, 1, 1, 1, -0.9, -0.9, 0, 10, c(-0.5))
bfa_ls_bc_ci(z, p=1, method="boot1", B=2)