#' @title calculate UMVUE estimate of SSMD between two groups under homoscedasticity
#' @description A function to calculate UMVUE estimate of SSMD between two groups under homoscedasticity
#' @param x the values of response in the first group (i.e., the reference group)
#' @param y the values of response in the second group
#' @param pXtrim proportion of trimmed values in the Sample well to form a negative reference
#' @param approx approx=TRUE, indicating the use of approximation for the coefficient in the UMVUE estimate of SSMD
#' @param method specify the method for estimating SSMD. It must be either 'UMVUE', 'MLE' or'MM'.
#' @author Xiaohua Douglas Zhang originally in 2007, revised in 2020
#' @return a vector
#' @examples x = rnorm(320, mean=0, sd=1)
#' y = rnorm(8, mean=3*sqrt(2), sd=1)
#' ssmdEst.homoVAR.fn( x, y, pXtrim=0.05, approx=FALSE, method="UMVUE")
#' @importFrom stats sd rnorm
#' @export
ssmdEst.homoVAR.fn = function( x, y, pXtrim=0, approx=F, method="UMVUE")
{
#*****************************************************************************************
# A function to calculate UMVUE estimate of SSMD between two groups under homoscedasticity
# Author: Xiaohua Douglas Zhang, originally in 2007, revised in 2020
# Augment
# x: the values of response in the first group (i.e., the reference group)
# y: the values of response in the second group
# approx: approx=TRUE, indicating the use of approximation for the coefficient
# in the UMVUE estimate of SSMD
# method: specify the method for estimating SSMD. It must be
# either 'UMVUE', 'MLE' or'MM'. "
# Example:
# x = rnorm(320, mean=0, sd=1)
# y = rnorm(8, mean=3*sqrt(2), sd=1)
# ssmdEst.homoVAR.fn( x, y, pXtrim=0.05, approx=F, method="UMVUE")
#*****************************************************************************************
x = x[ !is.na(x) ]
xSort = sort(x)
nS1 = length(x)
nRm = round(nS1*pXtrim/2)
xTrim.vec = xSort[ (nRm+1): (nS1-nRm) ]
n1 = nS1 - nRm*2
m1 = mean(xTrim.vec)
sd1 = sd(xTrim.vec)
y = y[ !is.na(y) ]
n2 = length(y)
m2 = mean(y)
sd2 = sd(y)
ssmdEst.homoVAR.vec = ssmdEstCore.homoVAR.fn( m1, m2, sd1, sd2, n1, n2, approx=approx, method=method)
return( ssmdEst.homoVAR.vec )
}
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