A GENERALIZED EMERSON RECURRENCE RELATION

The Emerson (1968, Biometrics 24 , 695–701) recurrence relation has many important applications in statistics. However, the original derivation applied only to discrete distributions. In the following, a simple derivation is given that generalizes the Emerson recurrence relation to any distribution for which the necessary expectations exist. A modern application is outlined.     

Evaluation of the parameters of su by rational fractions

A rational fraction approximation is given for a function of one of the parameters defining Johnson's S_UError assessment for a segment of the domain of validity shows remarkable accuracy.     

Sums of powers of binomial coefficients

An asymptotic series for sums of powers of binomial coefficients is derived, the general term being defined and usable with a computer symbolic language. Sums of squares of coefficients in the symmetric case are shown to have a link with classical moment problems, but this property breaks down for cubes and higher powers. Problems of remainders for the asymptotic series are mentioned. Using the reflection formula for I'(.), a continuous form for a binomial function is set up, and this becomes oscillatory outstde the usual range. A new contmued fraction emerges for the logarithm of an adjusted sum of binomial squares. The note is a contribution to the problem of the interpretation of asymptotic series and processes for their convergence acceleration.     

Generalised Rank Regression Estimator with Standard Error Adjusted Lasso

One of the standard variable selection procedures in multiple linear regression is to use a penalisation technique in least‐squares (LS) analysis. In this setting, many different types of penalties have been introduced to achieve variable selection. It is well known that LS analysis is sensitive to outliers, and consequently outliers can present serious problems for the classical variable selection procedures. Since rank‐based procedures have desirable robustness properties compared to LS procedures, we propose a rank‐based adaptive lasso‐type penalised regression estimator and a corresponding variable selection procedure for linear regression models. The proposed estimator and variable selection procedure are robust against outliers in both response and predictor space. Furthermore, since rank regression can yield unstable estimators in the presence of multicollinearity, in order to provide inference that is robust against multicollinearity, we adjust the penalty term in the adaptive lasso function by incorporating the standard errors of the rank estimator. The theoretical properties of the proposed procedures are established and their performances are investigated by means of simulations. Finally, the estimator and variable selection procedure are applied to the Plasma Beta‐Carotene Level data set.     

Maximum likelihood estimation of the bimodal failure rate for censored and tied observations

DIMITROV, RACHEV and YAKOVLEV ( 1985 ) have obtained the isotonic maximum likelihood estimator for the bimodal failure rate function. The authors considered only the complete failure time data. The generalization of this estimator for the case of censored and tied observations is now proposed.     

Stochastic metafrontiers

ABSTRACT

We consider the case of production units arranged into a number of groups. All units within a group choose output–input combinations from the same production possibilities set that is represented by a stochastic frontier model. The metafrontier is the envelope of the group-specific frontiers. We are interested in the metafrontier distance, which is the amount by which the group-specific frontier lies below the metafrontier.

Previous work has measured the metafrontier distance using the deterministic portion of the frontier. In a stochastic frontier model, this is not appropriate. We show how to evaluate the metafrontier distance, and we demonstrate the empirical relevance of this issue.     

Accent on Teaching Materials

Review of International Association for Statistical Education Proceedings: Proceedings of the First Scientific Meeting of the International Association for Statistical Education, Lina Brunelli and Guiseppe Cicchitelli, Editors. U.S. $5 (cost of postage) from International Statistical Institute, 428 Prinses Beatrixlann, 2270 AZ Voorburg, The Netherlands. Includes 49 papers presented in Perugia, Italy, in August 1993; 476 pages. Reviewed by Peter Holmes     

Accent on Teaching Materials

A linear combination test for combining several tests of the correlation coefficient in the bivariate normal distribution is proposed. The linear combination test is compared with the well-known Fisher method of combining tests. It is shown by a Monte Carlo study that the linear combination test has a larger power.