Time Series Analysis - Recent Advances, New Perspectives and Applications [Working Title]
In this chapter, the problem of model selection in neural networks for nonlinear time series data... more In this chapter, the problem of model selection in neural networks for nonlinear time series data is addressed. A systematic review and an appraisal of previously published research on the topic are presented and discussed with emphasis on a complete strategy to select the topology of the model. The procedure attempts to explain the black box structure of a neural network by providing information on the complex structure of the relationship between a set of inputs and the output. The procedure combines a set of graphical and inferential statistical tools and allows to choose the number and the type of inputs, considered as explanatory variables, by using a formal test procedure based on relevance measures and to identify the hidden layer size by looking at the predictive performance of the neural network model. To obtain an approximation of the involved statistics, the approach heavily uses the subsampling technique, a computer-intensive statistical methodology. The results on simul...
A recollection of some of the most significant contributions to Probability and Statistics by Ita... more A recollection of some of the most significant contributions to Probability and Statistics by Italian mathematicians over the 20th century seems definitely suited to open the First Italian Meeting on Probability and Mathematical Statistics. The journey will start from the efforts of Guido Castelnuovo (1865-1952) aiming at promoting both the study and the applications of Probability and Statistics and will move on to the analysis of the crucial results obtained by Francesco P. Cantelli (1875-1966) concerning the convergence of sequences of random numbers, in particular the first formulation of a strong law of large numbers dating back to 1917. Since 1926 a vital role has, then, been played by Bruno de Finetti (1906-1985) who, between 1926 and 1931, launched-among others-completely new ideas concerning: (a) stochastic processes with independent and stationary increments; (b) the subjective interpretation of probability and the ensuing mathematical theory based on the "axiom of coherence"; (c) the probabilistic foundations of the inductive reasoning by means of the concept of exchangeability. Since the 50's, de Finetti's ideas mentioned in (b) and (c) are considered decisive toward the modern regeneration of the Bayesian theory of Statistics. From a statistical viewpoint, the figure of Corrado Gini (1884-1965) stood out because of both his distinguished research activity and his capability in reorganizing the entire Italian official statistics system. I shall confine myself to illustrating his project toward an organic treatment of the so-called descriptive statistics, including the pioneering idea of dissimilarity (dissomiglianza) between probability distributions, nowadays well-known as Wasserstein distance. The journey will, then, be completed by a quick glance at the fundamental function the journals Metron and Giornale dell'Istituto Italiano degli Attuari-founded by Gini and Cantelli, respectively-had in spreading, at an international high-level, new methods and results, at least till the outbeak of the Second World War.
Parametric And Non-parametric Methods In Non-linear Time Series Analysis: A Critical Evaluation
this paper is to evaluate the performance of the two different approaches when future volatility ... more this paper is to evaluate the performance of the two different approaches when future volatility is of interest in addition to the conditional mean. In particular, we propose a method to deal with the non-parametric estimation of the functions f() and g().
The use of general descriptive names, registered names, trademarks, etc. in this publication does... more The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
Artificial neural networks are powerful tools for data analysis, particularly in the context of h... more Artificial neural networks are powerful tools for data analysis, particularly in the context of highly nonlinear regression models. However, their utility is critically limited due to the lack of interpretation of the model given its black-box nature. To partially address the problem, the paper focuses on the important problem of feature selection. It proposes and discusses a statistical test procedure for selecting a set of input variables that are relevant to the model while taking into account the multiple testing nature of the problem. The approach is within the general framework of sensitivity analysis and uses the conditional expectation of functions of the partial derivatives of the output with respect to the inputs as a sensitivity measure. The proposed procedure extensively uses the bootstrap to approximate the test statistic distribution under the null while controlling the familywise error rate to correct for data snooping arising from multiple testing. In particular, a p...
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Papers by Cira Perna