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By
Uciński, Dariusz
1 Citations
A computational algorithm is proposed for determinant maximization over the set of all convex combinations of a finite number of nonnegative definite matrices subject to additional box constraints on the weights of those combinations. The underlying idea is to apply a simplicial decomposition algorithm in which the restricted master problem reduces to an uncomplicated multiplicative weight optimization algorithm.
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By
Amendola, Alessandra; Storti, Giuseppe
This paper proposes a modified approach to the combination of forecasts from multivariate volatility models where the combination is performed over a restricted subset including only the best performing models. Such a subset is identified over a rolling window by means of the Model Confidence Set (MCS) approach. The analysis is performed using different combination schemes, both linear and non linear, and considering different loss functions for the evaluation of the forecasting performance. An application to a vast dimensional portfolio of 50 NYSE stocks shows that (a) in nonextreme volatility periods the use of forecast combinations allows to improve over the predictive accuracy of the single candidate models (b) performing the combination over the subset of most accurate models does not significantly reduce the accuracy of the combined predictor.
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By
Nguyen, Hien D.; McLachlan, Geoffrey J.
11 Citations
The Gaussian mixture model (GMM) is a popular tool for multivariate analysis, in particular, cluster analysis. The expectation–maximization (EM) algorithm is generally used to perform maximum likelihood (ML) estimation for GMMs due to the Mstep existing in closed form and its desirable numerical properties, such as monotonicity. However, the EM algorithm has been criticized as being slow to converge and thus computationally expensive in some situations. In this article, we introduce the linear regression characterization (LRC) of the GMM. We show that the parameters of an LRC of the GMM can be mapped back to the natural parameters, and that a minorization–maximization (MM) algorithm can be constructed, which retains the desirable numerical properties of the EM algorithm, without the use of matrix operations. We prove that the ML estimators of the LRC parameters are consistent and asymptotically normal, like their natural counterparts. Furthermore, we show that the LRC allows for simple handling of singularities in the ML estimation of GMMs. Using numerical simulations in the R programming environment, we then demonstrate that the MM algorithm can be faster than the EM algorithm in various large data situations, where sample sizes range in the tens to hundreds of thousands and for estimating models with up to 16 mixture components on multivariate data with up to 16 variables.
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By
Jang, Woncheol; Lim, Johan; Lazar, Nicole A.; Loh, Ji Meng; Yu, Donghyeon
Show all (5)
6 Citations
Identifying homogeneous subgroups of variables can be challenging in high dimensional data analysis with highly correlated predictors. The generalized fused lasso has been proposed to simultaneously select correlated variables and identify them as predictive clusters (grouping property). In this article, we study properties of the generalized fused lasso. First, we present a geometric interpretation of the generalized fused lasso along with discussion of its persistency. Second, we analytically show its grouping property. Third, we give comprehensive simulation studies to compare our version of the generalized fused lasso with other existing methods and show that the proposed method outperforms other variable selection methods in terms of prediction error and parsimony. We describe two applications of our method in soil science and near infrared spectroscopy studies. These examples having vastly different data types demonstrate the flexibility of the methodology particularly for highdimensional data.
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By
Tanokura, Yoko; Kitagawa, Genshiro
A method for constructing a distributionfree indexDistributionfree index
is applied to financial and economic time series data and causations are analyzed based on power contributionsPower contribution
. Highlighting the current sequential financial crises, the applications focus primarily on credit default swap (CDS)Credit default swap
CDS
markets, which often have heavytailed spread distributions. The first application detects that the European debt crisis has already spilled over worldwide in terms of sovereign CDS (SCDS)Sovereign CDS
SCDS
markets. The second application measures the impact of the US subprime crisis on Japanese domestic markets. Finally, in order to examine the usability of a distributionfree index, the clear polarization between advanced and emerging regions by GDP growth regional distributionfree indices,
GDP growth regional distributionfree index and the importance of examining sovereign risks in estimating the economic growth, are observed. Moreover, the Japanese SCDS distributionfree indexJapanese SCDS distributionfree index
can be regarded as an underlying SCDS spread level reflecting a domestic credit strength. These applications verify the effectiveness of a distributionfree index and confirm that applying our method to markets with insufficient information, such as fastgrowing or immature markets, can be effective.
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By
Sokołowski, Andrzej; Markowska, Małgorzata; Strahl, Danuta; Sobolewski, Marek
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The Nomenclature of Territorial Units for Statistics or Nomenclature of Units for Territorial Statistics (NUTS) is a geocode standard for referencing the subdivision of countries for statistical purposes. It covers the member states of the European Union. For each EU member country, a hierarchy of three levels is established by Eurostat. In 27 EU countries we have 97 regions at NUTS1, 271 regions at NUTS2 and 1,303 regions at NUTS3. They are subject of many statistical analysis involving clustering methods. Having a partition of units on a given level, we can ask the question, whether this partition has been influenced by the upper level division of Europe. For example, after finding groups of homogeneous levels of NUTS 2 regions we would like to know if the partition has been influenced by differences between countries. In the paper we propose a procedure for testing the statistical significance of influence of upper level units on a given partition. If there is no such influence, we can expect that the number of betweengroups borders which are also country borders should have a proper probability distribution. A simulation procedure for finding this distribution and its critical values for testing significance is proposed in this paper. The real data analysis shown as an example deals with the innovativeness of German districts and the influence of government regions on innovation processes.
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By
Schwarzer, Guido; Carpenter, James R.; Rücker, Gerta
7 Citations
The world is awash with information. For any question, the briefest of internet searches will throw up a range of frequently contradictory answers. This underlies increasing awareness of the value of systematic evidence synthesis—both qualitative and quantitative—by researchers, policy makers and the broader public. It is reflected in the continuing development of the Cochrane Collaboration (http://www.cochrane.org/), an international collaboration devoted to undertaking, publishing and promoting systematic evidence synthesis [2].
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