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...
In a stationary ergodic process, clustering is defined as the tendency of events to appear in series of increased frequency separated by longer breaks. Such behavior, contradicting the theoretical “unbiased behavior” with exponential distribution of the gaps between appearances, is commonly observed in experimental processes and often difficult to explain. In the last section we relate one such empirical example of clustering, in the area of marine technology. In the theoretical part of the paper...
We study the fluctuations around non degenerate attractors of the empirical measure under mean field Gibbs measures. We prove that a mild change of the densities of these measures does not affect the central limit theorems. We apply this result to generalize the assumptions of [3] and [12] on the densities of the Gibbs measures to get precise Laplace estimates.