Description Usage Arguments Details Value Author(s) References See Also Examples
Estimates the non-centrality parameter associated with an observed statistic following an optimal Sharpe Ratio distribution.
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Let F be an observed statistic distributed as a non-central F with df1, df2 degrees of freedom and non-centrality parameter delta^2. Three methods are presented to estimate the non-centrality parameter from the statistic:
an unbiased estimator, which, unfortunately, may be negative.
the Maximum Likelihood Estimator, which may be zero, but not negative.
the estimator of Kubokawa, Roberts, and Shaleh (KRS), which is a shrinkage estimator.
The sropt distribution is equivalent to an F distribution up to a square root and some rescalings.
The non-centrality parameter of the sropt distribution is
the square root of that of the Hotelling, i.e. has
units 'per square root time'. As such, the 'unbiased'
type can be problematic!
an estimate of the non-centrality parameter, which is the maximal population Sharpe ratio.
Steven E. Pav shabbychef@gmail.com
Kubokawa, T., C. P. Robert, and A. K. Saleh. "Estimation of noncentrality parameters." Canadian Journal of Statistics 21, no. 1 (1993): 45-57. https://www.jstor.org/stable/3315657
Spruill, M. C. "Computation of the maximum likelihood estimate of a noncentrality parameter." Journal of multivariate analysis 18, no. 2 (1986): 216-224. https://www.sciencedirect.com/science/article/pii/0047259X86900709
F-distribution functions, df
.
Other sropt Hotelling:
sric()
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 | # generate some sropts
nfac <- 3
nyr <- 5
ope <- 253
# simulations with no covariance structure.
# under the null:
set.seed(as.integer(charToRaw("determinstic")))
Returns <- matrix(rnorm(ope*nyr*nfac,mean=0,sd=0.0125),ncol=nfac)
asro <- as.sropt(Returns,drag=0,ope=ope)
est1 <- inference(asro,type='unbiased')
est2 <- inference(asro,type='KRS')
est3 <- inference(asro,type='MLE')
# under the alternative:
Returns <- matrix(rnorm(ope*nyr*nfac,mean=0.0005,sd=0.0125),ncol=nfac)
asro <- as.sropt(Returns,drag=0,ope=ope)
est1 <- inference(asro,type='unbiased')
est2 <- inference(asro,type='KRS')
est3 <- inference(asro,type='MLE')
# sample many under the alternative, look at the estimator.
df1 <- 3
df2 <- 512
ope <- 253
zeta.s <- 1.25
rvs <- rsropt(128, df1, df2, zeta.s, ope)
roll.own <- sropt(z.s=rvs,df1,df2,drag=0,ope=ope)
est1 <- inference(roll.own,type='unbiased')
est2 <- inference(roll.own,type='KRS')
est3 <- inference(roll.own,type='MLE')
# for del_sropt:
nfac <- 5
nyr <- 10
ope <- 253
set.seed(as.integer(charToRaw("fix seed")))
Returns <- matrix(rnorm(ope*nyr*nfac,mean=0.0005,sd=0.0125),ncol=nfac)
# hedge out the first one:
G <- matrix(diag(nfac)[1,],nrow=1)
asro <- as.del_sropt(Returns,G,drag=0,ope=ope)
est1 <- inference(asro,type='unbiased')
est2 <- inference(asro,type='KRS')
est3 <- inference(asro,type='MLE')
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