By Laura Azzimonti, Francesca Ieva (auth.), Matteo Grigoletto, Francesco Lisi, Sonia Petrone (eds.)
The use of computational equipment in facts to stand complicated difficulties and hugely dimensional facts, in addition to the frequent availability of computing device expertise, isn't any information. the variety of purposes, as a substitute, is unparalleled.
As usually happens, new and intricate info varieties require new suggestions, hard for the advance of novel statistical tools and suggesting stimulating mathematical difficulties.
This publication is addressed to researchers operating on the leading edge of the statistical research of advanced structures and utilizing computationally extensive statistical methods.
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Additional info for Complex Models and Computational Methods in Statistics
In the paper this difference is ascribed to the high number of nuisance parameters involved in the optimization. Also, they show that the CML estimator favorably compares with the McGyver method being, by far, more efficient than the latter. In the light of these results, in this paper our attention will be focused on CML estimation. Both the CML and the McGyver method reformulate the estimation problem in terms of simpler lower dimensional problems but while, in the McGyver method, the final estimate is obtained as a function of the results of several low-dimensional optimizations, in CML estimation the optimization is performed just once leading to a substantial reduction of the computing time.
Shephard, N. ) The Methodology and Practice of Econometrics: Papers in Honour of David F Hendry. Oxford University Press, Oxford (2009) 8. : Multivariate simultaneous generalized ARCH. Economet. Theor. 11, 122–150 (1995) Inference for Vast Dimensional Covariance Models 49 9. : Fitting vast dimensional time-varying covariance models. NYU Working Paper No. FIN-08-009 (2008) 10. : The conditional autoregressive Wishart model for multivariate stock market volatility. J. Eonomet. 167, 211–223 (2012) 11.
D . St 1 Ct / (8) where . /D n 2 n log. 2/ 2 n X logŒ f. C 1 i /=2g: i D1 The last two terms on the right-hand side of (8) are proportional to the value of the Wishart shape parameter . a1 ; : : : ; ap ; b1 ; : : : ; bq /0 is given by @`t D @Âc Â Ã 1 @St tr St 2 @Âc Â Ã 1 @St 1 tr Ct St : S @Âc t (9) This implies that the value of is not affecting the estimation of Âc that can be consistently estimated independently of the value of this parameter. We also note, similar to , that, under the assumption that the dynamic model for the conditional expectation of Ct is correctly specified, the score in (9) is a martingale difference sequence even if the Wishart assumption is not satisfied.
Complex Models and Computational Methods in Statistics by Laura Azzimonti, Francesca Ieva (auth.), Matteo Grigoletto, Francesco Lisi, Sonia Petrone (eds.)