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量化自助法似然比检验的失效AI 解读

When testing geometrically irregular parametric hypotheses, the bootstrap is an intuitively appealing method to circumvent difficult distribution theory. It has been shown, however, that the usual bootstrap is inconsistent in estimating the asymptotic distributions involved in such problems. This paper is concerned with the asymptotic size of likelihood ratio tests when critical values are computed using the inconsistent bootstrap. We clarify how the asymptotic size of such…

含零协方差约束的协方差矩阵估计AI 解读

We consider estimation of the covariance matrix of a multivariate random vector under the constraint that certain covariances are zero. We first present an algorithm, which we call iterative conditional fitting, for computing the maximum likelihood estimate of the constrained covariance matrix, under the assumption of multivariate normality. In contrast to previous approaches, this algorithm has guaranteed convergence properties. Dropping the assumption of multivariate…

高斯浓度图的模型选择AI 解读

A multivariate Gaussian graphical Markov model for an undirected graph G, also called a covariance selection model or concentration graph model, is defined in terms of the Markov properties, i.e. conditional independences associated with G, which in turn are equivalent to specified zeros among the set of pairwise partial correlation coefficients. By means of Fisher's z‐transformation and Šidák's correlation inequality, conservative simultaneous confidence intervals for the…

双变量似不相关回归模型的似然多峰性AI 解读

We analyse the simplest two‐equation seemingly unrelated regressions model and demonstrate that its likelihood may have up to five stationary points, and thus there may be up to three local modes. Consequently the estimates obtained via iterative estimation methods may depend on starting values. We further show that the probability of multimodality vanishes asymptotically. Monte Carlo simulations suggest that multimodality rarely occurs if the seemingly unrelated regressions…