| fingerprint {dacc} | R Documentation |
Optimal Fingerprinting via total least square regression.
Description
This function detects the signal factors on the observed data via total least square linear regression model.
Usage
fingerprint(
X,
Y,
cov,
nruns.X,
ctlruns,
precision = FALSE,
conf.level = 0.9,
conf.method = c("none", "TSB", "PBC", "both"),
cov.method = c("l2", "mv"),
B = 1000
)
Arguments
X |
signal pattern to be detected. |
Y |
observed data. |
cov |
Weight matrix used in prewhitening process, can be estimate of covariance matrix or precision matrix. |
nruns.X |
number of ensembles to estimate the corresponding pattern. It is used as the scale of the covariance matrix for Xi. |
ctlruns |
a group of independent control runs for estimating covariance matrix, which is used in two stage bootstrap and the parametric bootstrap calibration. |
precision |
indicator for precision matrix, if precision matrix estimate is used, precision should be set to TRUE. |
conf.level |
confidence level for confidence interval estimation. |
conf.method |
method for calibrating the confidence intervals, including no calibration (none), two stage bootstrap (TSB), and parametric bootstrap calibration (PBC). |
cov.method |
method for estimation of covariance matrix in confidence interval procedure. It should be consistent to the method to get cov. (only valid if TSB or PBC is considered.) |
B |
number of replicates in two stage bootstrap and/or parametric bootstrap calibration, default value is 1000. (only valid if TSB or PBC is considered.) |
Value
a list of the fitted model including point estimate and interval estimate of coefficients and corresponding estimate of standard error.
Author(s)
Yan Li
References
Gleser (1981), Estimation in a Multivariate "Errors in Variables" Regression Model: Large Sample Results, Ann. Stat. 9(1) 24–44.
Golub and Laon (1980), An Analysis of the Total Least Squares Problem, SIAM J. Numer. Anal. 17(6) 883–893.
Pesta (2012), Total least squares and bootstrapping with applications in calibration, Statistics 47(5), 966–991.
Li et al (2021), Uncertainty in Optimal Fingerprinting is Underestimated, Environ. Res. Lett. 16(8) 084043.
Examples
data(simDat)
## set the true covariance matrix and expected pattern
Cov <- simDat$Cov[[1]]
ANT <- simDat$X[, 1]
NAT <- simDat$X[, 2]
## estimate the covariance matrix
Z <- MASS::mvrnorm(100, mu = rep(0, nrow(Cov)), Sigma = Cov)
## linear shrinkage estimator under l2 loss
Cov.est <- Covest(Z, method = "l2")$output
## generate regression observation and pattern
nruns.X <- c(1, 1)
Y <- MASS::mvrnorm(n = 1, mu = ANT + NAT, Sigma = Cov)
X <- cbind(MASS::mvrnorm(n = 1, mu = ANT, Sigma = Cov),
MASS::mvrnorm(n = 1, mu = NAT, Sigma = Cov))
fingerprint(X, Y, Cov.est, nruns.X, ctlruns = Z, conf.method = "TSB", B = 5)