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ASYMPTOTIC THEORY AND THE FOUNDATIONS OF STATISTICS
"... ABSTRACT. Statistics in the 20th century has been enlivened by a passionate, occasionally bitter, and still vibrant debate on the foundations of statistics and in particular on Bayesian vs. frequentist approaches to inference. In 1975 D. V. Lindley predicted a Bayesian 21st century for statistics. ..."
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. This prediction has often been discussed since, but there is still no consensus on the probability of its correctness. Recent developments in the asymptotic theory of statistics are, surprisingly, shedding new light on this debate, and may have the potential to provide a common middle ground. 1. Introduction. I
Statistics 552: Asymptotic Theory
"... • Additional papers and lecture notes will be given later. The course begins with the classical asymptotic theory. Topics include Information Inequality, delta method, variancestabilizing transformation, Edgeworth expansion, and their applications. Asymptotic properties of the MLE and superefficien ..."
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• Additional papers and lecture notes will be given later. The course begins with the classical asymptotic theory. Topics include Information Inequality, delta method, variancestabilizing transformation, Edgeworth expansion, and their applications. Asymptotic properties of the MLE
Asymptotic theory for multivariate GARCH processes
 Journal of Multivariate Analysis
, 2003
"... We provide in this paper asymptotic theory for the multivariate GARCH(p, q) process. Strong consistency of the quasimaximum likelihood estimator (MLE) is established by appealing to conditions given in Jeantheau [19] in conjunction with a result given by Boussama [9] concerning the existence of a s ..."
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Cited by 56 (0 self)
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We provide in this paper asymptotic theory for the multivariate GARCH(p, q) process. Strong consistency of the quasimaximum likelihood estimator (MLE) is established by appealing to conditions given in Jeantheau [19] in conjunction with a result given by Boussama [9] concerning the existence of a
ASYMPTOTIC THEORY FOR SPATIAL PROCESSES
, 2008
"... Recent years have seen a marked increase in the application of spatial models in economics and the social sciences, in general. However, the development of a general asymptotic estimation and inference theory for spatial estimators has been hampered by a lack of central limit theorems (CLTs), unifor ..."
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Recent years have seen a marked increase in the application of spatial models in economics and the social sciences, in general. However, the development of a general asymptotic estimation and inference theory for spatial estimators has been hampered by a lack of central limit theorems (CLTs
On the Asymptotic Theory of Permutation Statistics
 Mathematical Methods of Statistics
, 1999
"... : In this paper limit theorems for the conditional distributions of linear test statistics are proved. The assertions are conditioned on the #field of permutation symmetric sets. Limit theorems are proved both for the conditional distributions under the hypothesis of randomness and under general co ..."
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Cited by 24 (2 self)
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of symmetrized product measures. The results of the paper have implications for statistical applications. By example it is shown that minimum variance partitions which are defined by observed data (e.g. by LVQ) lead to asymptotically optimal adaptive tests for the ksample problem. As another application
Asymptotic theory for a vector ARMAGARCH model. Econometric Theory 19
, 2003
"... This paper investigates the asymptotic theory for a vector ARMAGARCH model. The conditions for the strict stationarity, ergodicity, and the higherorder moments of the model are established. Consistency of the quasi maximum likelihood estimator (QMLE) is proved under only the secondorder moment ..."
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Cited by 178 (85 self)
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This paper investigates the asymptotic theory for a vector ARMAGARCH model. The conditions for the strict stationarity, ergodicity, and the higherorder moments of the model are established. Consistency of the quasi maximum likelihood estimator (QMLE) is proved under only the secondorder mo
SOME NOTES ON ASYMPTOTIC THEORY IN PROBABILITY
"... This brief note summarizes some important results in asymptotic theory in probability. The main motivation of this theory is to approximate distribution of large sample statistics with a limiting distribution which is often much simpler to work with. ..."
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This brief note summarizes some important results in asymptotic theory in probability. The main motivation of this theory is to approximate distribution of large sample statistics with a limiting distribution which is often much simpler to work with.
Estimation and Inference in Econometrics
, 1993
"... The astonishing increase in computer performance over the past two decades has made it possible for economists to base many statistical inferences on simulated, or bootstrap, distributions rather than on distributions obtained from asymptotic theory. In this paper, I review some of the basic ideas o ..."
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Cited by 1204 (4 self)
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The astonishing increase in computer performance over the past two decades has made it possible for economists to base many statistical inferences on simulated, or bootstrap, distributions rather than on distributions obtained from asymptotic theory. In this paper, I review some of the basic ideas
On the asymptotic theory of subsampling
 Statistica Sinica
, 2001
"... Abstract: A general approach to constructing confidence intervals by subsampling was presented in Politis and Romano (1994). The crux of the method is recomputing a statistic over subsamples of the data, and these recomputed values are used to build up an estimated sampling distribution. The method ..."
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Cited by 7 (1 self)
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construction). The arguments apply to both the i.i.d. setting and the dependent data case. Key words and phrases: Confidence intervals, datadependent block size choice, hypothesis tests, large sample theory, resampling. 1.
Longitudinal data analysis using generalized linear models”.
 Biometrika,
, 1986
"... SUMMARY This paper proposes an extension of generalized linear models to the analysis of longitudinal data. We introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence. The estimating ..."
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Cited by 1526 (8 self)
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. The estimating equations are derived without specifying the joint distribution of a subject's observations yet they reduce to the score equations for multivariate Gaussian outcomes. Asymptotic theory is presented for the general class of estimators. Specific cases in which we assume independence, m
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