Weak Convergence of Empirical Distribution Functions of Random Variables Subject to Perturbations and Scale Factors

Open Access

1 March 1975

journal article
Published by Institute of Mathematical Statistics in The Annals of Statistics

Vol. 3 (2) , 299-313
https://doi.org/10.1214/aos/1176343058

Abstract

The weak convergence of empirical distribution functions subject to random perturbations and scale factors to a Gaussian process is established. This result is used to study the efficiencies of tests based on spacings in goodness-of-fit problems.

Keywords

EMPIRICAL DISTRIBUTION FUNCTION
GOODNESS OF FIT TESTS
RANDOM VARIABLES
STOCHASTIC PROCESSES
WEAK CONVERGENCE
STATISTICAL TESTS
GOODNESS OF FIT TEST
CONVERGENCE
GOODNESS OF FIT
TOPOLOGY
DISTRIBUTION FUNCTIONS
GAUSSIAN PROCESS
RANDOM VARIABLE
THEOREMS

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