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Asymptotic Equivalence (asymptotic + equivalence)
Selected AbstractsAsymptotic equivalence and contiguity of some random graphsRANDOM STRUCTURES AND ALGORITHMS, Issue 1 2010Svante Janson Abstract We show that asymptotic equivalence, in a strong form, holds between two random graph models with slightly differing edge probabilities under substantially weaker conditions than what might naively be expected. One application is a simple proof of a recent result by van den Esker, van der Hofstad, and Hooghiemstra on the equivalence between graph distances for some random graph models. © 2009 Wiley Periodicals, Inc. Random Struct. Alg., 2010 [source] Unit-root testing: on the asymptotic equivalence of Dickey,Fuller with the log,log slope of a fitted autoregressive spectrumJOURNAL OF TIME SERIES ANALYSIS, Issue 3 2010Evangelos E. Ioannidis In this article we consider the problem of testing for the presence of a unit root against autoregressive alternatives. In this context we prove the asymptotic equivalence of the well-known (augmented) Dickey,Fuller test with a test based on an appropriate parametric modification of the technique of log-periodogram regression. This modification consists of considering, close to the origin, the slope (in log,log coordinates) of an autoregressively fitted spectral density. This provides a new interpretation of the Dickey,Fuller test and closes the gap between it and log-periodogram regression. This equivalence is based on monotonicity arguments and holds on the null as well as on the alternative. Finally, a simulation study provides indications of the finite-sample behaviour of this asymptotic equivalence. [source] Fractional Bayesian Lag Length Inference in Multivariate Autoregressive ProcessesJOURNAL OF TIME SERIES ANALYSIS, Issue 1 2001Mattias Villani The posterior distribution of the number of lags in a multivariate autoregression is derived under an improper prior for the model parameters. The fractional Bayes approach is used to handle the indeterminacy in the model selection caused by the improper prior. An asymptotic equivalence between the fractional approach and the Schwarz Bayesian Criterion (SBC) is proved. Several priors and three loss functions are entertained in a simulation study which focuses on the choice of lag length. The fractional Bayes approach performs very well compared to the three most widely used information criteria, and it seems to be reasonably robust to changes in the prior distribution for the lag length, especially under the zero-one loss. [source] Asymptotic equivalence and contiguity of some random graphsRANDOM STRUCTURES AND ALGORITHMS, Issue 1 2010Svante Janson Abstract We show that asymptotic equivalence, in a strong form, holds between two random graph models with slightly differing edge probabilities under substantially weaker conditions than what might naively be expected. One application is a simple proof of a recent result by van den Esker, van der Hofstad, and Hooghiemstra on the equivalence between graph distances for some random graph models. © 2009 Wiley Periodicals, Inc. Random Struct. Alg., 2010 [source] | ||||||||||