Cumulative Chi-Squared Statistic as a Tool for Testing Goodness of Fit
研究了单因素方差分析模型中累积卡方统计量的性质，提出其可作为检验模型拟合优度的统计量，并针对线性与凸性对比提出了新统计量。
The cumulative chi-squared statistic in the one-way analysis of variance model is characterized as the weighted sum of independent one degree of freedom chi-squared random variables, which are linear, quadratic, and so on, components in the sense of Čebyšev's orthogonal polynomials for finite points. This suggests that the cumulative chi-squared should be an appropriate goodness-of-fit test statistic for a hypothesized model against a systematic departure that is mainly but not exclusively linear. This, together with the follow-up analysis of residuals, will give a good statistical technique for analysing data. As a natural extension of the cumulative chi-squared, a new statistic is proposed for testing for linearity against convexity.