In [1]:

    

are <- function(eps, sc2) {
    "Return asymptotic relative efficiency of a contaminated normal distribution"
    return(2 * (1+eps*(sc2-1)) * (1 - eps + eps/sqrt(sc2))^2 / pi)
}


    

In [2]:

    

eps <- seq(0, 0.15, by=0.05)
round(are(eps, 9), 3)


    

    
Out[2]:





	
0.637
	
0.833
	
0.998
	
1.134

In [3]:

    

are_min_1 <- function(eps, sc2) {
    return (are(eps, sc2) - 1)
}


    

In [4]:

    

uniroot(are_min_1, sc2=9, interval=c(0.1, 0.15))$root


    

    
Out[4]:




0.10059207725643