Abstract Let $(Z_n)_{n\geq0}$ be a supercritical Galton–Watson process. Consider the Lotka–Nagaev estimator for offspring mean. In this paper we establish self-normalized Cramér-type moderate deviations and Berry–Esseen bounds estimator. The results are believed to optimal or near-optimal.

The forensic economics literature hosts a continuing debate about the appropriateness of using historical verses current rates to predict future net discount rates. If the net discount rate series is stationary, which means that shocks are transitory and the series reverts to a long-term mean value, estimates based on historical values are reasonable. Alternatively, if the series exhibits a uni...

This paper presents a model of optimal control of corporate boards of directors. In particular, we determine when one would expect inside directors or outside directors to control the board, when the controlling party will delegate decision-making to the other party, the extent of communication with the deciding party, and the number of outside directors. Our model incorporates the traditional ...

The task of covert intelligence agents is to detect and interdict terror plots. Kaplan (2010) treats terror plots as customers and intelligence agents as servers in a queuing model. We extend Kaplan’s insight to a dynamic model that analyzes the inter-temporal trade-off between damage caused by terror attacks and prevention costs to address the question of how many agents to optimally assign to...

This paper considers the optimal induced L2gain estimator design problem for infinite dimensional systems with finite dimensional outputs. It is shown that this problem is equivalent to a dual regulator design problem. Moreover the relationship between the dual problem and a two player differential game is established. A solution to the latter problem is derived which, in turn solves the dual r...

Many attitude estimation methods are based on an optimization problem posed in 1965 by Grace Wahba. All these methods will yield the same optimal estimate, except for inevitable computer roundoff errors. This note shows that Shuster’s Quaternion Estimator (QUEST) and Mortari’s Estimator of the Optimal Quaternion (ESOQ) are essentially identical even in the presence of computer roundoff errors. ...

Godambe (1960, 1985) and Hansen (1982) proposed the method of estimating function which makes a bridge between least squares estimator and maximum likelihood estimator. In this paper we apply the estimating function approach to CHARN models which include many well-known nonlinear time series models as special cases. The innovation density is permitted to be skew-symmetric. Since the estimation ...

inverse sampling design is generally considered to be appropriate technique when the population is divided into two subpopulations, one of which contains only few units. in this paper, we derive the horvitz-thompson estimator for the population mean under inverse sampling designs, where subpopulation sizes are known. we then introduce an alternative unbiased estimator, corresponding to post-str...