你可以看greene的《计量经济分析》;
《计量经济理论和方法》_戴维森_麦金农
《微观经济计量学 方法与应用》 卡梅伦;
Principles of Econometrics 4th-R.Carter Hill,William E. Griffiths,Guay C. Lim
这些书上有介绍
http://www.stata.com/support/faqs/statistics/delta-method/
What is the delta method and how is it used to estimate the standard error of a transformed parameter?| Title | | Explanation of the delta method |
| Author | Alan H. Feiveson, NASA |
| Date | December 1999; minor revisions May 2005 |
The delta method, in its essence, expands a function of a random variable about its mean, usually with a one-step Taylor approximation, and then takes the variance. For example, if we want to approximate the variance of G(X) where X is a random variable with mean mu and G() is differentiable, we can try
G(X) = G(mu) + (X-mu)G'(mu) (approximately)
so that
Var(G(X)) = Var(X)*[G'(mu)]2 (approximately)
where G'() = dG/dX. This is a good approximation only if X has a high probability of being close enough to its mean (mu) so that the Taylor approximation is still good.
This idea can easily be expanded to vector-valued functions of random vectors,
Var(G(X)) = G'(mu) Var(X) [G'(mu)]T
and that, in fact, is the basis for deriving the asymptotic variance of maximum-likelihood estimators. In the above, X is a 1 x m column vector; Var(X) is its m x m variance–covariance matrix; G() is a vector function returning a 1 x n column vector; and G'() is its n x m matrix of first derivatives. T is the transpose operator. Var(G(X)) is the resulting n x n variance–covariance matrix of G(X).
AcknowledgmentsNicholas Cox of Durham University and John Gleason of Syracuse University provided the references.
ReferencesOehlert, G. W. 1992.A note on the delta method.
American Statistician 46: 27–29.Rice, John. 1994.
Mathematical Statistics and Data Analysis. 2nd ed. Duxbury.