NNS.FSD: NNS FSD Test

In NNS: Nonlinear Nonparametric Statistics

NNS FSD Test

Description

Compares empirical first-order stochastic dominance or degree-one area-ratio (Omega/expectile) dominance using partial moments.

Usage

NNS.FSD(x, y, type = "discrete", plot = TRUE)

Arguments

x	a numeric vector.
y	a numeric vector.
type	"discrete" (default) compares empirical CDFs for ordinary first-order stochastic dominance. The legacy option "continuous" compares degree-one ratios L_1/(L_1+U_1), equivalently Omega/expectile order; it does not carry the ordinary FSD guarantee for every increasing utility.
plot	logical; TRUE (default) plots the FSD test.

Value

With type = "discrete", returns "X FSD Y", "Y FSD X", or "NO FSD EXISTS". With type = "continuous", returns "X OMEGA Y", "Y OMEGA X", or "NO OMEGA DOMINANCE EXISTS"; the numerical area-order criterion is unchanged.

Note

The curves are compared on the merged sample points and, for TSD and continuous area order, also at their closed-form extrema between those points. Differences smaller than 64 * .Machine$double.eps * S^d (S = largest absolute value in x and y, d = 1 for SSD and the mean condition, 2 for TSD; a ratio analogue for continuous area order) are treated as ties, so that rounding noise does not decide dominance. Discrete FSD compares exact empirical CDF values.

Author(s)

Fred Viole, OVVO Financial Systems

References

Viole, F. and Nawrocki, D. (2016) "LPM Density Functions for the Computation of the SD Efficient Set." Journal of Mathematical Finance, 6, 105-126. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.4236/jmf.2016.61012")}.

Viole, F. (2017) "A Note on Stochastic Dominance." \Sexpr[results=rd]{tools:::Rd_expr_doi("10.2139/ssrn.3002675")}.

Examples

## Not run: 
set.seed(123)
x <- rnorm(100) ; y <- rnorm(100)
NNS.FSD(x, y)

## End(Not run)

NNS documentation built on Nov. 14, 2026, 1:09 a.m.