Search

In this article we propose two minimum chi-square estimators for a bivariate probit model. We call one estimator the Full Information and the other Limited Information Minimum Chi-Square because the first takes account of all the a priori information while the second does not. Both estimators are shown to be consistent. Moreover, the first is shown to be asymptotically as efficient as the maximum likelihood estimator and yet is computationally much simpler. For illustration, estimates are computed for the data used by Ashford and Sowden [1970.] [ABSTRACT FROM AUTHOR]

The asymptotic non-null distribution is obtained for the modified form of the Pearson chi-square statistic studied by Dahiya and Gurland [3]. By utilizing this result the power is obtained for specific alternative distributions in testing for normality, This enables recommendations to be made as to the number of class intervals to be employed in applying the aforementioned modification of the Pearson chi-square test of normality. [ABSTRACT FROM AUTHOR]

A step-by-step method is presented herein far partitioning a certain kind of hypothesis H about the m-way contingency table into (a) a series of hypotheses about marginal tables formed from the m-way table by ignoring one or more of table's m dimensions; and (b) a hypothesis about independence, conditional independence, or conditional equiprobability in the m-way table. This step-by-step method facilitates both the testing of H and the calculation of F, the estimated expected frequencies in the m-way table under FI. The method introduced herein for calculating F is easier to apply than the usual iterative-scaling method in many cases. [ABSTRACT FROM AUTHOR]

This article presents information regarding parole prediction variables and the time factor in violations by burglars. Parole prediction studies have shown that it is possible to determine, before an inmate is released from prison under parole supervision, what are his relative chances for making a successful extramural adjustment. The original data were set up in 23 contingency tables with the number of months before violation as the independent variable in each case and one of the 23 parole prediction factors as the dependent variable. The Chi-square test was undertaken to test the probability that differences between the actual and the theoretical frequencies would occur by chance. In these instances where the probability that the differences were due to chance was very small the coefficient of mean square contingency was determined in order to measure the amount of the relationship that exists between the variables. Whether the relationship is a positive or a negative, one was determined by inspection of the data and the signs of the differences.

A "blowup factor" is defined for the measurement of the effect on forecast error variance of two types of misspecification which may be implicit in the choice of a particular adaptive forecasting scheme: (1) misspecification of the number of non-zero parameters of the stationary linear stochastic process generating the observed time series, and (2) misspecification arising from postulating stationarity when in fact the generating process is non-stationary in mean. [ABSTRACT FROM AUTHOR]