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• W2442100119 abstract "estimator or test statistic from a linear model. The method relies heavily on the general arguments for the validity of Edgeworth approximations, and produces formulae of a similar type, except that, instead of using the cumulative normal distribution, an Imhof distribution is used derived from the exact distribution of a linear combination of the sample data second moments. On theoretical grounds this might be expected to give better approximations for some estimators. In practice comparisons were made between computed approximations of both types for several simple cases. can be derived for the distributions of most econometric estimators and test statistics which are asymptotically distributed in a normal distribution and are derived from a linear model. These are usually better approximations than the corresponding asymptotic distributions but this is model and sample size dependent. The general technique is to express the estimator as a function of the second moments of the data: then to approximate this by a third-order Taylor series expansion about the expected value of these second moments. Next the distribution of the second moments is approximated by a second-order Edgeworth multivariate distribution. Then it is possible to compute from these two approximations a corresponding approximating single variate Edgeworth distribution for the estimator. There are two sources of error in the procedure. Firstly the Taylor expansion of the first function may be poor for values of the second moments which have a non-trivial probability of occurring. Secondly the multivariate Edgeworth distribution may be a poor approximation to the true distribution of the second moments. This second source of error may be important, in the context of second moments generated by stochastic difference equations (vector autoregressive models), particularly when the sample size is small, or when the error variance is large compared with the second moments of the exogenous variables, or when some of the latent roots of the set of linear dynamic equations determining the endogenous variables are near the unit circle (the almost explosive case). In such cases it may be worthwhile considering a poorer approximation to the first function (in fact a first- or second-order Taylor series expansion rather than a third-order approximation) but which then uses the exact distribution of the second moments. The distribution of the sample second moments is exact only when the underlying errors of the linear processes generating the sample data are normally distributed, but the Imhof approximation can be used if these errors are non-normal, and" @default.
• W2442100119 created "2016-06-24" @default.
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• W2442100119 date "1990-01-01" @default.
• W2442100119 modified "2023-09-27" @default.
• W2442100119 title "Imhof Approximations to" @default.
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