Computational Statistics in Data Science. Группа авторов

      We obtain the asymptotic distribution of . A similar argument can be made for the off‐diagonals of . Under the conditions of Theorem 1,

      where is

      Under IID sampling, the infinite sum above reduces to

      Applying the delta method for function , we obtain

      3.4 Confidence Regions for Means

      Suppose that is an estimate of the limiting Monte Carlo variance–covariance matrix, for IID sampling, and for MCMC sampling. Let be the ‐quantile of a distribution. The CLT yields a large‐sample confidence region around as

      Let denote the determinant. The volume of this ellipsoidal confidence region, which depends on , , and , is given by

(2)

Sometimes a joint sampling distribution may be difficult to obtain, or the limiting variance–covariance matrix may be too complicated to estimate. In such cases, one can consider hyperrectangular confidence regions. Let Скачать книгу