bifurcatingr (version 2.1.0)

bfa_ls_bc_ci: 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
)

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 method="BCa"

standard_normal_bc_ci

a matrix containing the lower and upper limits of corrected confidence intervals, if method="boot1" and conf_int="standard_normal_bc" or conf_int="All"

percentile_ci

a matrix containing the lower and upper limits of uncorrected percentile confidence intervals, if method="boot1" and conf_int="percentile" or conf_int="All"

percentile_bc_ci

a matrix containing the lower and upper limits of corrected percentile confidence intervals, if method="boot1" and conf_int="percentile_bc" or conf_int="All"

standard_normal_bc_ci

a matrix containing the lower and upper limits of corrected confidence intervals, if method="boot2fast" and conf_int="standard_normal_bc" or conf_int="All"

percentile_bc_ci

a matrix containing the lower and upper limits of corrected percentile confidence intervals, if method="boot2fast" and conf_int="percentile_bc" or conf_int="All"

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 0.95.

B

number of bootstrap samples (replicates).

burn

number of tree generations to discard before starting the bootstrap sample (replicate). Defaults to 5.

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)