Asymptotic chi-square tests, such as the normal theory likelihood ratio test, are often used to evaluate the goodness-of-fit of a covariance structure analysis model. Another approach is to use the bootstrap test, which is known to have the desired asymptotic level if model restrictions are taken into account in designing a resampling algorithm. The bootstrap test is, however, computationally very tedious and the problem of nonconvergence and improper solutions often arise in bootstrap resampling. In this paper, we propose a bootstrap test which is based on an approximation, by a quadratic form, to the minimum value of a discrepancy function calculated from each bootstrap sample. Hence, the proposed bootstrap test is efficient in the sense of the amount of computing needed and is free from the problem of nonconvergence and improper solutions with resampling. A Monte Carlo experiment is conducted to compare the performance of the proposed method with that of asymptotic chi-square tests for each combination of three distributions and four sample sizes.
In this paper we present an improved hedonic price regression for cases in which many implemented technological characteristics are to be included into a set of explanatory variables. This approach modifies Massy's (1965) principal components regression in which original dummy explanatory variables corresponding to the characteristics are transformed into principal components. The selected subset which we obtained from the principal components regression was further orthogonally rotated by Kaiser's (1957) varimax criterion in order to reconstruct explanatory variables with a simple structure for the final hedonic regression, resulting in a more straightforward understanding of hedonic regression in the case of many explanatory variables. This approach is applied in order to compare different pricing strategies in the digital still camera industry, where the products contain 35 different technical attributes. The pricing strategies were measured using relative errors; differences between log actual prices and log quality-adjusted prices were identified using hedonic regression. The result shows that those companies, which have priced their products cheaper than the value of contained technologies, or than the prices of competitors, seem to have gained a larger market share.
This paper discusses the admissibility of agglomerative hierarchical clustering algorithms with respect to space distortion and monotonicity which were defined by Yadohisa et al. and Batagelj, respectively. Several admissibilities and their properties are given for selecting a clustering algorithm. Necessary and sufficient conditions for an updating formula, as introduced by Lance and Williams, are provided for the proposed admissibility criteria. A detailed explanation of the admissibility of eight popular algorithms is also given.