This paper discusses a randomized Logistic equation N（t）=（r+αB（t））N（t）[1-（N（t）/K）] with an initial value N（0）=N0,and N0 is a random variable satisfying 0＜N0＜K.The existence, uniqueness and global attractivity of positive solutions and maximum likelihood estimate（MLE）of the parameters of the equation are studied.
Da-qing JIANGBao-xue ZHANGDe-hui WANGNing-zhong SHI
This paper discusses the maximum likelihood estimate of β under linear inequalities A0β≥ a in a linear model with missing data, proposes the restricted EM algo rithm and proves the convergence.
ZHENG Shurong, SHI Ningzhong & GUO Jianhua School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China
This paper studies non-convex programming problems. It is known that, in statistical inference, many constrained estimation problems may be expressed as convex programming problems. However, in many practical problems, the objective functions are not convex. In this paper, we give a definition of a semi-convex objective function and discuss the corresponding non-convex programming problems. A two-step iterative algorithm called the alternating iterative method is proposed for finding solutions for such problems. The method is illustrated by three examples in constrained estimation problems given in Sasabuchi et al. （Biometrika, 72, 465472 （1983））, Shi N. Z. （J. Multivariate Anal., 50, 282-293 （1994）） and El Barmi H. and Dykstra R. （Ann. Statist., 26, 1878 1893 （1998））.
