ECDF=empirical cumulative distribution function. The exact computation needs a
common reference minimum (refmin) return for computation of
dominance orders SD1 to SD4.
This function inputs `mtx' (n X p) matrix data (e.g., monthly returns on p stocks).
Its output has four matrices SD1 to SD4, each with dimension (n X p). They measure
exact dominance areas between empirical CDF for each column to the ECDF of
(x.ref) an artificial stock with minimal return in all time periods. A fifth
output matrix `out' has 4 rows and p columns containing column sums of SD1 to SD4. The
`out' matrix produced by this function is input to summaryRank function to
indicate the choice of the best column in `mtx' for investment based on ranks.
exactSdMtx(mtx, howManySd = 0.1)five matrices. SD1 to SD4 contain four orders of stochastic dominance areas using the ECDF pillars and a common (x.ref). The fifth "out" matrix is another output having 4 rows for SD1 to SD4 and p columns (p=No. of columns in data matrix mtx) having a summary of ranks using all four, SD1 to SD4.
(n X p) matrix of data. For example, returns on p stocks n months
used to define (x.ref)= lowest return number. If the grand minimum of all returns in `mtx' is dented GrMin, then howManySd equals the number of max(sd) (maximum standard deviation for data columns) below the GrMin used to define (x.ref). Thus, (x.ref)=GrMin-howManySd*max(sd). default howManySd=0.1
Prof. H. D. Vinod, Economics Dept., Fordham University, NY
x1=c(2,5,6,9,13,18,21)
x2=c(3,6,9,12,14,19,27)
st1=exactSdMtx(cbind(x1,x2))
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