diff --git a/NAMESPACE b/NAMESPACE
index 3405d737..05ffb3d1 100644
--- a/NAMESPACE
+++ b/NAMESPACE
@@ -154,6 +154,7 @@ export(psislw)
 export(relative_eff)
 export(scrps)
 export(sis)
+export(srs_diff_est)
 export(stacking_weights)
 export(tis)
 export(waic)
diff --git a/NEWS.md b/NEWS.md
index 6f182376..8ebccfd6 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -17,6 +17,7 @@
 * Added contribution section. by @VisruthSK in #286
 * Update LOO uncertainty paper to use BA doi by @avehtari in #311
 * Update documentation for `E_loo()` function by @avehtari in #312
+* Export `srs_diff_est()` function by @vinniott and @avehtari in #340
 
 
 # loo 2.8.0
diff --git a/R/loo_subsample.R b/R/loo_subsample.R
index bcac4b17..a5c44141 100644
--- a/R/loo_subsample.R
+++ b/R/loo_subsample.R
@@ -24,7 +24,7 @@
 #'   same length containing the posterior density and the approximation density
 #'   for the individual draws.
 #'
-#' @seealso [loo()], [psis()], [loo_compare()]
+#' @seealso [loo()], [psis()], [loo_compare()], [srs_diff_est()]
 #' @template loo-large-data-references
 #'
 #' @export loo_subsample loo_subsample.function
@@ -1166,12 +1166,88 @@ loo_subsample_estimation_diff_srs <- function(x) {
   update_psis_loo_ss_estimates(x)
 }
 
-#' Difference estimation using SRS-WOR sampling (Magnusson et al., 2020)
-#' @noRd
-#' @param y_approx Approximated values of all observations.
-#' @param y The values observed.
-#' @param y_idx The index of `y` in `y_approx`.
-#' @return A list with estimates.
+#' Difference estimator with simple random sampling without replacement.
+#'
+#' The difference estimator `srs_diff()` estimates
+#' the expectation \eqn{n E[y]} when we have \eqn{n} approximate values \eqn{\tilde{y}_i},
+#' \eqn{i = 1, \ldots, n} and \eqn{m < n} accurate values \eqn{y_j}, \eqn{j \in \mathcal{S}},
+#' where \eqn{m} is the subsample size and \eqn{\mathcal{S}} is
+#' a simple random subsample without replacement.  The original
+#' approach is by Cochran (1977) and we follow the equations 7--9 by
+#' Magnusson et al. (2020).
+#'
+#' @details In Magnusson et al. (2020) Eq (9) first row, the second `+` should
+#'   be a `-`; Supplementary Material Eq (6) has this correct.
+#'   As `srs_diff_est()` in the `loo` package is used for \eqn{n E[y]}, there is
+#'   a proportional difference of \eqn{1/n} compared to the paper.
+#'
+#' @param y_approx (numeric) `n` approximated values.
+#' @param y (numeric) `m<n` subsampled values.
+#' @param y_idx (integerish) The index of `y` in `y_approx`.
+#'
+#' @return A named list containing numeric values:
+#' * `y_hat`: estimated mean of \eqn{y} (Eq 7),
+#' * `v_y_hat`: variance of the mean estimate (Eq 8), and
+#' * `hat_v_y`: estimated variance of \eqn{y} (Eq 9).
+#'
+#' @references
+#' Magnusson, M., Riis Andersen, M., Jonasson, J. and Vehtari, A. (2020).
+#' Leave-One-Out Cross-Validation for Model Comparison in Large Data.
+#' In _Proceedings of the 23rd International Conference on Artificial
+#' Intelligence and Statistics (AISTATS)_, PMLR 108:341-351.
+#'
+#' Cochran, W. G. (1977). _Sampling Techniques, 3rd Edition_. John Wiley.
+#'
+#' Cortez, P., Cerdeira, A.L., Almeida, F., Matos, T., & Reis, J. (2009).
+#' Modeling wine preferences by data mining from physicochemical properties.
+#' _Decis. Support Syst._, _47_, 547-553.
+#'
+#' @seealso [loo_subsample()]
+#'
+#' @examples
+#' ### This example predicts wine quality (data from Cortez et al., 2009).
+#' ## The code is commented out for easier installation of the package
+#' ## because brm() takes two or three seconds to fit.
+#' ## A log_lik_matrix is generated from a fit, then it is used for srs_diff_est().
+#' # library(dplyr)
+#' # library(brms)
+#' # options(brms.backend = "cmdstanr")
+#' # options(mc.cores = 4)
+#' # library(loo)
+#' #
+#' # wine <- read.delim(root("winequality-red", "winequality-red.csv"), sep = ";") |>
+#' #   distinct()
+#' #
+#' # wine_scaled <- as.data.frame(scale(wine))
+#' #
+#' # fitos <- brm(ordered(quality) ~ .,
+#' #              family = cumulative("logit"),
+#' #              prior = prior(R2D2(mean_R2 = 1/3, prec_R2 = 3)),
+#' #              data = wine_scaled,
+#' #              seed = 1,
+#' #              silent = 2,
+#' #              refresh = 0)
+#' #
+#' # log_lik_matrix <- log_lik(fitos)
+#' #
+#' # N <- nrow(wine_scaled)
+#' # Nsub <- 100
+#' #
+#' # # posterior log-score
+#' # lpd <- elpd(log_lik_matrix)
+#' # sum(lpd$pointwise[,"elpd"])
+#' # # Use PSIS-LOO for subsample of Nsub randomly selected observations
+#' # set.seed(1)
+#' # idx <- sample(1:N, Nsub)
+#' # elpd_loo_sub <- loo(log_lik_matrix[,idx])
+#' # sum(elpd_loo_sub$pointwise[,"elpd_loo"]) / Nsub * N
+#' #
+#' # # Use difference estimator to combine fast result and subsampled accurate result
+#' # loo:::srs_diff_est(lpd$pointwise[,"elpd"], elpd_loo_sub$pointwise[,"elpd_loo"], idx)
+#' #
+#' # # Comparison to using PSIS-LOO for all observations
+#' # loo(log_lik_matrix)
+#' @export
 srs_diff_est <- function(y_approx, y, y_idx) {
   checkmate::assert_numeric(y_approx)
   checkmate::assert_numeric(y, max.len = length(y_approx))
diff --git a/man/loo_subsample.Rd b/man/loo_subsample.Rd
index 6f381db6..5889be1e 100644
--- a/man/loo_subsample.Rd
+++ b/man/loo_subsample.Rd
@@ -196,5 +196,5 @@ In \emph{Proceedings of the 23rd International Conference on Artificial
 Intelligence and Statistics (AISTATS)}, PMLR 108:341-351.
 }
 \seealso{
-\code{\link[=loo]{loo()}}, \code{\link[=psis]{psis()}}, \code{\link[=loo_compare]{loo_compare()}}
+\code{\link[=loo]{loo()}}, \code{\link[=psis]{psis()}}, \code{\link[=loo_compare]{loo_compare()}}, \code{\link[=srs_diff_est]{srs_diff_est()}}
 }
diff --git a/man/srs_diff_est.Rd b/man/srs_diff_est.Rd
new file mode 100644
index 00000000..72f8faf5
--- /dev/null
+++ b/man/srs_diff_est.Rd
@@ -0,0 +1,97 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/loo_subsample.R
+\name{srs_diff_est}
+\alias{srs_diff_est}
+\title{Difference estimator with simple random sampling without replacement.}
+\usage{
+srs_diff_est(y_approx, y, y_idx)
+}
+\arguments{
+\item{y_approx}{(numeric) \code{n} approximated values.}
+
+\item{y}{(numeric) \code{m<n} subsampled values.}
+
+\item{y_idx}{(integerish) The index of \code{y} in \code{y_approx}.}
+}
+\value{
+A named list containing numeric values:
+\itemize{
+\item \code{y_hat}: estimated mean of \eqn{y} (Eq 7),
+\item \code{v_y_hat}: variance of the mean estimate (Eq 8), and
+\item \code{hat_v_y}: estimated variance of \eqn{y} (Eq 9).
+}
+}
+\description{
+The difference estimator \code{srs_diff()} estimates
+the expectation \eqn{n E[y]} when we have \eqn{n} approximate values \eqn{\tilde{y}_i},
+\eqn{i = 1, \ldots, n} and \eqn{m < n} accurate values \eqn{y_j}, \eqn{j \in \mathcal{S}},
+where \eqn{m} is the subsample size and \eqn{\mathcal{S}} is
+a simple random subsample without replacement.  The original
+approach is by Cochran (1977) and we follow the equations 7--9 by
+Magnusson et al. (2020).
+}
+\details{
+In Magnusson et al. (2020) Eq (9) first row, the second \code{+} should
+be a \code{-}; Supplementary Material Eq (6) has this correct.
+As \code{srs_diff_est()} in the \code{loo} package is used for \eqn{n E[y]}, there is
+a proportional difference of \eqn{1/n} compared to the paper.
+}
+\examples{
+### This example predicts wine quality (data from Cortez et al., 2009).
+## The code is commented out for easier installation of the package
+## because brm() takes two or three seconds to fit.
+## A log_lik_matrix is generated from a fit, then it is used for srs_diff_est().
+# library(dplyr)
+# library(brms)
+# options(brms.backend = "cmdstanr")
+# options(mc.cores = 4)
+# library(loo)
+#
+# wine <- read.delim(root("winequality-red", "winequality-red.csv"), sep = ";") |>
+#   distinct()
+#
+# wine_scaled <- as.data.frame(scale(wine))
+#
+# fitos <- brm(ordered(quality) ~ .,
+#              family = cumulative("logit"),
+#              prior = prior(R2D2(mean_R2 = 1/3, prec_R2 = 3)),
+#              data = wine_scaled,
+#              seed = 1,
+#              silent = 2,
+#              refresh = 0)
+#
+# log_lik_matrix <- log_lik(fitos)
+#
+# N <- nrow(wine_scaled)
+# Nsub <- 100
+#
+# # posterior log-score
+# lpd <- elpd(log_lik_matrix)
+# sum(lpd$pointwise[,"elpd"])
+# # Use PSIS-LOO for subsample of Nsub randomly selected observations
+# set.seed(1)
+# idx <- sample(1:N, Nsub)
+# elpd_loo_sub <- loo(log_lik_matrix[,idx])
+# sum(elpd_loo_sub$pointwise[,"elpd_loo"]) / Nsub * N
+#
+# # Use difference estimator to combine fast result and subsampled accurate result
+# loo:::srs_diff_est(lpd$pointwise[,"elpd"], elpd_loo_sub$pointwise[,"elpd_loo"], idx)
+#
+# # Comparison to using PSIS-LOO for all observations
+# loo(log_lik_matrix)
+}
+\references{
+Magnusson, M., Riis Andersen, M., Jonasson, J. and Vehtari, A. (2020).
+Leave-One-Out Cross-Validation for Model Comparison in Large Data.
+In \emph{Proceedings of the 23rd International Conference on Artificial
+Intelligence and Statistics (AISTATS)}, PMLR 108:341-351.
+
+Cochran, W. G. (1977). \emph{Sampling Techniques, 3rd Edition}. John Wiley.
+
+Cortez, P., Cerdeira, A.L., Almeida, F., Matos, T., & Reis, J. (2009).
+Modeling wine preferences by data mining from physicochemical properties.
+\emph{Decis. Support Syst.}, \emph{47}, 547-553.
+}
+\seealso{
+\code{\link[=loo_subsample]{loo_subsample()}}
+}