Combined with advantages of moving least squares approximation, a new method for estimating higher-order conditional moment is established, which is useful for application in importance analysis and provides a supplement of the standard variance-based importance analysis. On the other hand, after obtaining the first four-order moments, the probability density function can be emulated by use of the Edgeworth expansion procedure, thereby a new method to compute the moment independent importance measure index _i proposed by Borgonovo is presented in this article. Two examples are employed to demonstrate that it is necessary to analyze higher-order conditional moment in importance analysis. At the same time, we study the feasibility of the Edgeworth expansion-based method for estimating the index _i by applying it to these examples.