Finite sample properties of maximum likelihood and quasi-maximum likelihood estimators of egarch models

In this paper I examine finite sample properties of the maximum likelihood and quasi-maximum likelihood estimators of EGARCH(1,1) processes using Monte Carlo methods. I use response surface methodology to summarize the results of a wide array of experiments which suggest that the maximum likelihood estimator has reasonable finite sample properties. The Gaussian quasi-maximum likelihood estimator has poor finite sample properties when the data generating process has conditional excess kurtosis. Some of these poor properties appear to be asymptotic in nature.     

Empirical Bayes estimation in directional data

Empirical Bayes procedures have been developed extensively in the literature, under the assumption that the underlying parameter space (or the sample space) is Euclidean in nature. However, there has been almost no research carried out into when the data comes from a different space. We develop empirical Bayes techniques to estimate the mean direction of the Fisher-von Mises distribution. In this case, the underlying space is non-Euclidean. The special case when the data are angles on the unit circle is illustrated with an example.     

A multimodal skewed extension of normal distribution: its properties and applications

A multimodal skewed extension of normal distribution is proposed by applying the general method as in [Huang WJ, Chen YH. Generalized skew-Cauchy distribution. Stat Probab Lett. 2007;77:1137–1147] for the construction of skew-symmetric distributions by using a trigonometric periodic skew function. Some of its distributional properties are investigated. Properties of maximum likelihood estimation of the parameters are studied numerically by simulation. The suitability of the proposed distribution in empirical data modelling is investigated by carrying out comparative fitting of two real-life data sets.     

On some problems arising from Professor Rawls' conception of distributive justice

This paper is concerned with two specific aspects of Professor Rawls' conception of distributive justice. In Section I Rawls' controversial difference principle is discussed in the context of individual decision under uncertainty, as well as the problem of interpersonal comparison of utilities. It is noted that, contrary to some recent accounts, Rawls' conception of the original position is considerably different from that to be found in the works of Harsanyi. In Section II an attempt is made to articulate in a precise way Rawls' intergenerational savings principle. While it is noted that the Rawlsian savings rule possesses a number of attractive properties, it is demonstrated that it conflicts with the principle of intertemporal Pareto efficiency.This is a revised and expanded version of the text of a lecture delivered at the Moral Sciences Club of the University of Cambridge in February, 1973. I would like to acknowledge the many instructions that I have received on the matters discussed in this paper from Kenneth Arrow, Simon Blackburn, Frank Hahn, Philip Pettit, John Rawls, Abhijit Sen, Amartya Sen, and Robert Solow. While I doubt very much if any of these gentlemen would agree with all that I assert in this paper, I hope that each agrees with some of the propositions madehere.     

MODELING DEMAND DURING LEAD TIME*

This paper treats some of the important considerations in constructing an analytical model for the distribution of demand during lead time. It presents a formal model that can be developed along one of two lines. The first has order size and order intensity leading to a compound distribution of period demand, then period demand and lead time giving rise to a compound distribution of demand during lead time. The second has order intensity and lead time giving rise to a compound distribution of lead-time order intensity, then lead-time order intensity and order size leading to a compound distribution of demand during lead time. The paper also condenses the state of the art in a table and proposes some simple classification schemes that could help researchers extend that state of the art.