<Para ID="Par1">In this paper, some basic properties for negatively superadditive-dependent (NSD, in short) random variables are presented, such as the Rosenthal-type inequality and the Kolmogorov-type exponential inequality. Using these properties, we further study the complete convergence for weighted sums of...</para>

By using a large deviation theory of the stochastic process and the moment information of errors, some large deviation results for the least squares estimator θn in a nonlinear regression model are obtained when errors satisfy some general conditions. For some p1, examples are presented to show...

In this paper, some probability inequalities and moment inequalities for widely orthant-dependent (WOD, in short) random variables are presented, especially the Marcinkiewicz–Zygmund type inequality and Rosenthal type inequality. By using these inequalities, we further study the complete...

In this paper, by relaxing the mixing coefficients to α(n) = O(n <Superscript>−β</Superscript>), β  3, we investigate the Bahadur representation of sample quantiles under α-mixing sequence and obtain the rate as <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${O(n^{-\frac{1}{2}}(\log\log n\cdot\log n)^{\frac{1}{2}})}$$</EquationSource> </InlineEquation>. Meanwhile, for any δ  0, by...</equationsource></inlineequation></superscript>

We extend the Brunk-Prokhorov strong law of large numbers and obtain a strong growth rate for martingale differences. Some results for demimartingales are also given.

Some exponential inequalities for a negatively orthant dependent sequence are obtained. By using the exponential inequalities, we study the asymptotic approximation of inverse moment for negatively orthant dependent random variables, which generalizes and improves the corresponding results of...

Fazekas and Klesov [Fazekas, I., Klesov, O., 2000. A general approach to the strong law of large numbers. Theory of Probability and its Applications 45, 436-449] established a Hájek-Rényi-type maximal inequality and obtained a strong law of large numbers (SLLN) for the sums of random...

A Hjek-Rnyi-type inequality for associated random variables was obtained by Prakasa Rao [Prakasa Rao, B.L.S., 2002. Hjek-Rnyi-type inequality for associated sequences. Statist. Probab. Lett. 57, 139-143]. Recently, Sung [Sung, H.S., 2008. A note on the Hjek-Rnyi inequality for associated random...