Some invariance properties (of the laws) of Ocone's martingales
Regression and scale invariant -test procedures are developed for detection of structural changes in linear regression model. Their limit properties are studied under the null hypothesis.
The authors first establish the Marcinkiewicz-Zygmund inequalities with exponent () for -pairwise negatively quadrant dependent (-PNQD) random variables. By means of the inequalities, the authors obtain some limit theorems for arrays of rowwise -PNQD random variables, which extend and improve the corresponding results in [Y. Meng and Z. Lin (2009)] and [H. S. Sung (2013)]. It is worthy to point out that the open problem of [H. S. Sung, S. Lisawadi, and A. Volodin (2008)] can be solved easily...
The structure of linearly negative quadrant dependent random variables is extended by introducing the structure of -linearly negative quadrant dependent random variables (). For a sequence of -linearly negative quadrant dependent random variables and (resp. ), conditions are provided under which in (resp. in ). Moreover, for , conditions are provided under which converges completely to . The current work extends some results of Pyke and Root (1968) and it extends and improves some...