dacc (version 0.0-6)

fingerprint: Optimal Fingerprinting via total least square regression.

Description

This function estimates the signal factors and corresponding confidence interval via the estimating equation or total least squares.

Usage

fingerprint(
  Xtilde,
  Y,
  mruns,
  ctlruns.sigma,
  ctlruns.bhvar,
  S,
  T,
  B = 0,
  Proj = diag(ncol(Xtilde)),
  method = c("EE", "PBC", "TS"),
  cov.method = c("l2", "mv"),
  conf.level = 0.9,
  missing = FALSE,
  cal.a = TRUE,
  ridge = 0
)

Value

a list of the fitted model including point estimate and interval estimate of coefficients and corresponding estimate of standard error.

Arguments

Xtilde

\(n \times p\) matrix, signal pattern to be detected.

Y

\(n \times 1\) matrix, length \(S \times T\), observed climate variable.

mruns

number of ensembles to estimate the corresponding pattern. It is used as the scale of the covariance matrix for \(X_i\).

ctlruns.sigma

\(m \times n\) matrix, a group of \(m\) independent control runs for estimating covariance matrix, which is used in point estimation of the signal factors.

ctlruns.bhvar

\(m \times n\) matrix, another group of \(m\) independent control runs for estimating the corresponding confidence interval of the signal factors, in EE or PBC approach should be same as ctlruns.sigma.

S

number of locations for the observed responses.

T

number of time steps for the observed responses.

B

number of replicates in bootstrap procedure, mainly for the PBC and TS methods, can be specified in "EE" method but not necessary. By default B = 0 as the default method is "EE".

Proj

The projection matrix for computing for scaling factors of other external forcings with the current input when using EE. For example, when ALL and NAT are used for modeling, specifying the Proj matrix to return the results for ANT and NAT.

method

for estimating the scaling factors and corresponding confidence interval

cov.method

method for estimation of covariance matrix in confidence interval estimation of PBC method. (only for PBC method).

conf.level

confidence level for confidence interval estimation.

missing

indicator for whether missing values present in Y.

cal.a

indicator for calculating the a value, otherwise use default value a = 1. (only for EE method)

ridge

shrinkage value for adjusting the method for missing observations if missing = TRUE. (only for EE method)

Author

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.

• Sai et al (2023), Optimal Fingerprinting with Estimating Equations, Journal of Climate 36(20), 7109–-7122.

• Li et al (2024), Detection and Attribution Analysis of Temperature Changes with Estimating Equations, Submitted to Journal of Climate.

Examples

## load the example dataset
data(simDat)
Cov <- simDat$Cov[[1]]
ANT <- simDat$X[, 1]
NAT <- simDat$X[, 2]

## generate the simulated data set
## generate regression observation
Y <- MASS::mvrnorm(n = 1, mu = ANT + NAT, Sigma = Cov)
## generate the forcing responses
mruns <- c(1, 1)
Xtilde <- cbind(MASS::mvrnorm(n = 1, mu = ANT, Sigma = Cov / mruns[1]),
               MASS::mvrnorm(n = 1, mu = NAT, Sigma = Cov / mruns[2]))
## control runs
ctlruns <- MASS::mvrnorm(100, mu = rep(0, nrow(Cov)), Sigma = Cov)
## ctlruns.sigma for the point estimation and ctlruns.bhvar for the interval estimation
ctlruns.sigma <- ctlruns.bhvar <- ctlruns
## number of locations
S <- 25
## number of year steps
T <- 10

## call the function to estimate the signal factors via EE
fingerprint(Xtilde, Y, mruns,
          ctlruns.sigma, ctlruns.bhvar,
          S, T,
          ## B = 0, by default
          method = "EE",
          conf.level = 0.9,
          cal.a = TRUE,
          missing = FALSE, ridge = 0)