Re-examining two tests for bivariate normality

Many goodness of fit tests for bivariate normality are not rigorous procedures because the distributions of the proposed statistics are unknown or too difficult to manipulate. Two familiar examples are the ring test and the line test. In both tests the statistic utilized generally is approximated by a chi-square distribution rather than compared to its known beta distribution. These two procedures are re-examined and re-evaluated in this paper. It is shown that the chi-square approximation can be too conservative and can lead to unnecessary

rejection of normality.     

Moment properties of estimators for a type 1 extreme-value regression model

A regression model is considered in which the response variable has a type 1 extreme-value distribution for smallest values. Bias approximations for the maximum likelihood estimators are pivm and a bias reduction estimator for the scale parameter is proposed. The small sample moment properties of the maximum likelihood estimators are compared with the properties of the ordinary least squares estimators and the best linear unbiased estimators based on order statistics for grouped data.     

Slope-rotatable designs with equal maximum directional variance for second order response surface models

The concept of sloperotaiability with equal maximum directional vari ance for second order response surface models is introduced as a new design property. This requires that the maximum variance of the estimated slope over all possible directions be only a function of p, which is the distance from the design originif is shown that a rotatable design satisfies this property Also, minimization of tiie maximum variance of the estimated slope over all possible directions is proposed as a new design optirnality criterion, and op¬timal designs are called slope-directional minirnax designs. For the class of cquiradial designs, the slope-directional minirnax designs are compared with D— optimal designs.     

Smoothing techniques via the bezier curve

Although the Bezier curve is very popular in the area of computational graphics it has rarely been used by statisticians. In this paper we develop methods and techniques for use of the Bezier curve in estimation of density and regression function. Also, asymptotic mean integrated square error for both estimators are derived. Comparisons with kernel estimator are conducted using simulation.     

The power series distribution wite unknown truncation parameter: Two sample problem

The uniformly most powerful unbiased tests are formulated for the two sample problem of the power series distribution with unknown truncation parameter.