This function computes the values of the criterion
convergence function for convergence in probability, almost surely or
in r-th mean, given the sample paths.
Usage
criterion(data,epsilon=0.05,mode="p",r=2)
Value
crit
the vector of criterion values.
Arguments
data
matrix containing the sample paths of Xn-X values.
epsilon
a numeric value giving the interval endpoint.
mode
a character string specifying the mode of
convergence to be investigated, must be one of "p" (default), "as" or "r".
r
a numeric value (r>0) if convergence in r-th mean is to be studied.
Author
P. Lafaye de Micheaux and B. Liquet
Details
The data matrix contains the \(X_n-X\) values. If mode="p",
criterion approximates \(p_n=P[|X_n-X|>\epsilon]\). If mode="as",
criterion approximates \(a_n=P[\exists k\geq
n;|X_k-X|>\epsilon]\). If mode="r",
criterion approximates
\(e_{n,r}=E|X_n-X|^r\). The approximations are
based on the frequentist approach.
References
Lafaye de Micheaux, P. (plafaye@club.fr), Liquet, B. "Understanding Convergence Concepts: a Visual-Minded and Graphical Simulation Based Approach", The American Statistician, 63:2, 173--178, (2009).