Since the design matrix of the balanced linear model with no interactions has special form, the general solution of the normal equations can be easily found. From the relationships between the minimum norm least squares solution and the Moore-Penrose inverse we can obtain the explicit form of the Moore-Penrose inverse X⁺ of the design matrix of the model y=Xβ+ε for the balanced model with no interaction.

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Sensitivity analysis procedures have been proposed so far by Tanaka and Odaka (1989a, b, c) for detecting influential observations in principal factor analysis, maximum likelihood factor analysis and least squares factor analysis. This paper shows that a similar method can be developed also in canonical factor analysis. Two numerical examples are given for illustration.

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In this paper we propose a new test statistic which is a modification of the Shapiro-Wilk W statistic for testing the goodness of fit for the exponential distribution. The test statistic is obtained by dividing the best linear unbiased estimate of the scale parameter by the probability weighted moment estimate of the same parameter. This ratio is both scale and location invariant and hence is an appropriate statistic for a test of the composite hypothsis of exponentiatily. The proposed test statistic is also modified for the case where the location parameter of the distribution is specified. Power comparisons are made by performing Monte Carlo experiments. It is shown that the suggested statistic is computationally simple and has good power properties. Some examples are given to illustrate test procedure.

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A sensitivity analysis procedure is proposed for a canonical correlation model of contingency tables (Goodman, 1986). The approach to influence is a numerical one suggested by Cook and Weisberg (1982), using sample influence curves and first-step estimates. This kind of model will show a great stability from the numerical and interpretative viewpoints.

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A sensitivity analysis in Hayashi's third method of quantification is studied from its local aspects, in the sense that the influences on output statistics caused by infinitesimal change of input data are to be assessed. Our scheme allows elementwise perturbation of the input data matrix as wll as row or column perturbations. It extends the previous results by Tanaka (1984).

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This paper studies a comparison of the estimation results by k-class estimators and the simulation performances of an econometric model for the Philippine economy. The k-class estimators are here represented by ordinary least squares (OLS), two stage least squares (2SLS), limited information maximum likelihood (LIML), and Morimune's modified limited information maximum likelihood (MF-LIML). In addition to economic knowledge, the Hausman test was applied for model specification. The simulation performances are evaluated by the root mean square error, and the Theil's inequality coefficient. Through estimation and simulation, MF-LIML estimator seems slightly better and more stable than LIML estimator which is better than OLS and 2SLS estimators during the within-sample period. The multiplier effects based on the MF-LIML and LIML estimators are larger than those based on OLS and 2SLS estimators during the post-sample period. It can be concluded that MF-LIML estimator is the practically best to build a simultaneous equation model even by small samples.

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