simulecdf {robusTest}

Simulate the distribution of the test statistic for the robust independence test of Kolmogorov-Smirnov's type

Description

For two independent continuous uniform variables on [0,1] compute the maximal distance between the joint empirical cumulative distribution function and the product of the marginal empirical cumulative distribution functions using Monte-Carlo simulations.

Usage

simulecdf(n, N)

Arguments

n

the size of the sample.

N

the number of replications in the Monte-Carlo simulation.

Details

Let (x1,y1), ..., (x_n,y_n) be a bivariate sample of n independent continuous uniform variables. Its corresponding bivariate e.c.d.f. (empirical cumulative distribution function) Fn is defined as:

Fn(t1,t2) = #{xi<=t1,yi<=t2}/n = sum_{i=1}^n Indicator(xi<=t1,yi<=t2)/n.

Let Fn(t1) and Fn(t2) be the marginals e.c.d.f. Based on N Monte_Carlo simulations, the function computes the e.c.d.f. of

n^(1/2) sup_{t1,t2} |Fn(t1,t2)-Fn(t1)*Fn(t2)|.

Value

Returns the e.c.d.f. based on the N Monte_Carlo simulations. The returned object is a stepfun object obtained from the function ecdf.

See Also

indeptest, stat_indeptest, ecdf2D.