Moment inequalities for m-negatively associated random variables and their applications

Alam K, Saxena KML (1981) Positive dependence in multivariate distributions. Commun Stat Theory Method 10:1183–1196 Chen GJ, Lai TL, Wei CZ (1981) Convergence systems and strong consistency of least squares estimates in regression models. J Multivar Anal 11(3):319–333 Chen P, Hu TC, Liu X, Volodin A (2008) On complete convergence for arrays of rowwise negatively associated random variables. Theory Probab Appl 52:323–328 Hu SH (2002) The rate of convergence for the least squares estimator in nonlinear regression model with dependent errors. Sci China Ser A 45(2):137–146 Hu SH (2004) Consistency for the least squares estimator in nonlinear regression model. Stat Probab Lett 67(2):183–192 Hu TC, Chiang CY, Taylor RL (2009) On complete convergence for arrays of rowwise \(m\)-negatively associated random variables. Nonlinear Anal 71:1075–1081 Ivanov AV (1976) An asymptotic expansion for the distribution of the least squares estimator of the nonlinear regression parameter. Theory Probab Appl 21(3):557–570 Ivanov AV (1997) Asymptotic theory of nonlinear regression. Kluwer Academic Publishers, Dordrecht Ivanov AV, Leonenko NN (1989) Statistical analysis of random fields. Kluwer Academic Publishers, Dordrecht Jennrich RI (1969) Asymptotic properties of nonlinear least squares estimators. Ann Math Stat 40(2):633–643 Joag-Dev K, Proschan F (1983) Negative association of random variables with applications. Ann Stat 11(1):286–295 Liang HY, Zhang JJ (2010) Strong convergence for weighted sums of negatively associated arrays. Chin Ann Math Ser B 31B(2):273–288 Ling NX (2008) The Bahadur representation for sample quantiles under negatively associated sequence. Stat Probab Lett 78:2660–2663 Malinvaud E (1970) The consistency of nonlinear regression. Ann Math Stat 41(3):956–969 Matula P (1992) A note on the almost sure convergence of sums of negatively dependent random variables. Stat Probab Lett 15:209–213 Prakasa Rao BLS (1984) The rate of convergence of the least squares estimator in a non-linear regression model with dependent errors. J Multivar Anal 14(3):315–322 Schmetterer L (1974) Introduction to mathematical statistics. Springer, Berlin Shao QM (2000) A comparison theorem on moment inequalities between negatively associated and independent random variables. J Theor Probab 13:343–356 Sung SH (2011) On the strong convergence for weighted sums of random variables. Stat Pap 52:447–454 Wang XH, Hu SH (2012) Complete convergence and complete moment convergence for a class of random variables. J Inequal Appl 2012, Article ID 229, 12 pp Wang XH, Hu SH (2014) Weak laws of large numbers for arrays of dependent random variables. Stoch Int J Probab Stoch Process 86(5):759–775 Wang XJ, Li XQ, Hu SH, Yang WZ (2011) Strong limit theorems for weighted sums of negatively associated random variables. Stoch Anal Appl 29(1):1–14 Wang XJ, Deng X, Zheng LL, Hu SH (2014a) Complete convergence for arrays of rowwise negatively superadditive-dependent random variables and its applications. Stat J Theor Appl Stat 48:834–850 Wang XJ, Xu C, Hu TC, Volodin A, Hu SH (2014b) On complete convergence for widely orthant-dependent random variables and its applications in nonparametric regression models. Test 23:607–629 Yang WZ, Hu SH (2014) Large deviation for a least squares estimator in a nonlinear regression model. Stat Probab Lett 91:135–144 Zarei H, Jabbari H (2011) Complete convergence of weighted sums under negative dependence. Stat Pap 52:413–418