The negative contagion reflection of the polya-eggenberger distribution

The Polya-Eggenberger distribution Involves drawing a ball from an urn containing black and white balls and, after each drawing, returning the ball together with s balls of the same color, The model represents positive contagion since the added balls are the same color as the one drawn, See Johnson and Kotz, (1977),

This paper derives and examines the probability distribution which results from the Polya-Eggenberger model with only one change namely, the s additional balls added after each drawing are of the opposite color, producing a negative contagion model.

Formulas in closed form are presented for the probability distribution function, the mean and variance, all binomial moments and, where s is greater than or equal to the number of balls in the urn at start, the mode, A formula for the mode is conjectured where s is less than the number of balls in the urn at start.

Finally, the probability of obtaining k black balls in n drawings is shown in certain instances to be equal to A_nk/n!

where A_nk are the Eulerian numbers.     

Least absolute value estimation in regression models: an annotated bibliography

This paper presents a comprehensive listing of articles on least absolute value (LAV) estimation as applied to linear and non-linear regression models and in systems of equations. References to the LAV method as applied in approximation theory are also included. Annotations describing the content of each article follow each reference.     

Prediction under uncertainty of degree of polynomial in growth curve models

Random coefficient polynomial regression model has been considered for prediction purpose when there is uncertainty about the degree of the polynomialo Expressions for mean square errors of two predictors based on simple estimators have been derived and their perfomaiices have been compared when parameters are estimated from the sample. A modified predictor has also been suggested when parameters in the predicting equations are to be estimated from the sample. Perform-ance ofseveral predictors haife been compared by cross validation technique from a real set of data.     

Numerical algorithms for solving nonlinear L р-norm estimation problems: part II - a mixture method for large residual and illo-conditioned problems

The nonlinear least squares algorithm of Gill and Murray (1978) is extended and modified to solve nonlinear L _р-norm estimation problems efficiently. The new algorithm uses a mixture of 1st-order derivative (Guass-Newton) and 2nd-order derivative (Newton) search directions. A new rule for selecting the “grade” r of the p-jacobiab matrix J_p was also incorporated. This brought about rapid convergence of the algorithm on previously reported test examples.     

Admissibility of a test procedure in a conditionally specified random model

Admissibility of a test procedure is a desirable property though not a compelling one; while lack of it often results in discarding a given test procedure. In this paper we have proved necessary conditions for admissibility for a test procedure.     

Spatial–temporal interpolation of non methane hydrocarbon levels in Kuwait

This article handles the prediction of hourly concentrations ofnon methane hydrocarbon (NMHC) pollutants at 15 unmonitored sites in Kuwait using the data recorded from 6 monitored stations at successive time points. The trend model depends on hourly meteorological variables and seasonal effects. The stochasticcomponent of the trend model which has spatiotemporal features is modeled as autoregressive temporal process. A spatial predictive distribution for residuals of the AR model is developed for the unmonitored sites. By transforming the predicted residuals back to the original data scales, we impute Kuwait’s hourly NMHC field.     

Quasi-likelihood Bridge estimators for high-dimensional generalized linear models

In this article, we consider the variable selection and estimation for high-dimensional generalized linear models when the number of parameters diverges with the sample size. We propose a penalized quasi-likelihood function with the bridge penalty. The consistency and the Oracle property of the quasi-likelihood bridge estimators are obtained. Some simulations and a real data analysis are given to illustrate the performance of the proposed method.     

A class of linear transformation models for interval censored data with a cured proportion

Interval-censored data arise due to a sequence random examination such that the failure time of interest occurs in an interval. In some medical studies, there exist long-term survivors who can be considered as permanently cured. We consider a mixed model for the uncured group coming from linear transformation models and cured group coming from a logistic regression model. For the inference of parameters, an EM algorithm is developed for a full likelihood approach. To investigate finite sample properties of the proposed method, simulation studies are conducted. The approach is applied to the National Aeronautics and Space Administration’s hypobaric decompression sickness data.     

The indirect method for stochastic logistic growth models

We developed the indirect method for stochastic logistic growth models involving both birth and death rates in the drift and diffusion coefficients, and not only propose two indirect estimators, but also construct a likelihood ratio-type indirect statistic for testing hypotheses concerning parameters. Simulations show that the proposed two indirect estimators can correct the discretization bias, and the proposed indirect test possesses very good estimated power and size.     

Optimal designs for discriminating between some extensions of the Michaelis–Menten model

In this paper some results on the computation of optimal designs for discriminating between nonlinear models are provided. In particular, some typical deviations of the Michaelis–Menten model are considered. A common deviation of this pharmacokinetic model consists on adding a linear term. If two linear models differ in one parameter the T-optimal design for discriminating between them is c-optimal for estimating the added linear term. This is not the case for nonlinear models.