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非线性回归的拟合不足检验AI 解读

The problem of testing the correctness of a nonlinear response function against unspecified general alternatives is considered. The proposed test statistic is a modification of a nonlinear analogue to the well-known linear regression lack-of-fit test and can be used with or without replication. Asymptotically valid critical points can be obtained from a central $F$-distribution. Also, when the null model is the orthogonal projection of the true model, the test statistic is…

无重复观测时线性回归函数适切性的检验AI 解读

The well known pure error-lack of fit test, which can be used to assess the adequacy of a linear regression model, is generalized to accommodate the case of nonreplication. The asymptotic null distribution of the proposed test statistic is derived. Also, the proposed test statistic is shown to be asymptotically comparable under general alternatives to the test statistic obtained in the case of replication. Consistency properties associated with pseudo lack of fit and pure…