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On the Distribution of a Statistic Used for Detecting First-Order Serial Correlation
Deepak Sanjel,하형태,Serge B. Provost 한국자료분석학회 2008 Journal of the Korean Data Analysis Society Vol.10 No.1
This paper provides a simple methodology for approximating the distribution of a test statistic proposed by J. Durbin and G. S. Watson. After expressing the statistic as a ratio of quadratic forms, its exact moments are evaluated by making use of a recursive formula. Its density function is then approximated by a beta density function multiplied by a linear combination of Jacobi orthogonal polynomials. The coefficients of the linear combination are determined by making use of a moment-based methodology. An integral representation of the moments of the statistic under the alternative hypothesis is also provided. As verified by a simulation study, the approach used in this paper, which takes into account the observation matrix of explanatory variables associated with the assumed regression model, yields very accurate critical values for testing independence versus first-order serial correlation.