Papers by Sengarapillai Arivalzahan
RePEc: Research Papers in Economics, Nov 12, 2009
In this paper we investigate the use of description length principles to select an appropriate nu... more In this paper we investigate the use of description length principles to select an appropriate number of basis functions for functional data. We provide a flexible definition of the dimension of a random function that is constructed directly from the Karhunen-Loève expansion of the observed process. Our results show that although the classical, principle component variance decomposition technique will behave in a coherent manner, in general, the dimension chosen by this technique will not be consistent. We describe two description length criteria, and prove that they are consistent and that in low noise settings they will identify the true finite dimension of a signal that is embedded in noise. Two examples, one from mass-spectroscopy and the one from climatology, are used to illustrate our ideas. We also explore the application of different forms of the bootstrap for functional data and use these to demonstrate the workings of our theoretical results.
Computational Statistics & Data Analysis, Feb 1, 2013
In this paper we investigate the use of description length principles to select an appropriate nu... more In this paper we investigate the use of description length principles to select an appropriate number of basis functions for functional data. We provide a flexible definition of the dimension of a random function that is constructed directly from the Karhunen-Loève expansion of the observed process. Our results show that although the classical, principle component variance decomposition technique will behave in a coherent manner, in general, the dimension chosen by this technique will not be consistent. We describe two description length criteria, and prove that they are consistent and that in low noise settings they will identify the true finite dimension of a signal that is embedded in noise. Two examples, one from mass-spectroscopy and the one from climatology, are used to illustrate our ideas. We also explore the application of different forms of the bootstrap for functional data and use these to demonstrate the workings of our theoretical results.
This thesis was scanned from the print manuscript for digital preservation and is copyright the a... more This thesis was scanned from the print manuscript for digital preservation and is copyright the author. Researchers can access this thesis by asking their local university, institution or public library to make a request on their behalf. Monash staff and postgraduate students can use the link in the References field.
RePEc: Research Papers in Economics, Jun 23, 2010
In the classical approach to statistical hypothesis testing the role of the null hypothesis 0 and... more In the classical approach to statistical hypothesis testing the role of the null hypothesis 0 and the alternative 1 is very asymmetric. Power, calculated from the distribution of the test statistic under 1 , is treated as a theoretical construct that can be used to guide the choice of an appropriate test statistic or sample size, but power calculations do not explicitly enter the testing process in practice. In a significance test a decision to accept or reject 0 is driven solely by an examination of the strength of evidence against 0 , summarized in the Pvalue calculated from the distribution of the test statistic under 0. A small P-value is taken to represent strong evidence against 0 , but it need not necessarily indicate strong evidence in favour of 1. More recently, Moerkerke et al. (2006) have suggested that the special status of 0 is often unwarranted or inappropriate, and argue that evidence against 1 can be equally meaningful. They propose a balanced treatment of both 0 and 1 in which the classical P-value is supplemented by the P-value derived under 1. The alternative P-value is the dual of the null P-value and summarizes the evidence against a target alternative. Here we review how the dual P-values are used to assess the evidential tension between 0 and 1 , and use decision theoretic arguments to explore a balanced hypothesis testing technique that exploits this evidential tension. The operational characteristics of balanced hypothesis tests is outlined and their relationship to conventional notions of optimal tests is laid bare. The use of balanced hypothesis tests as a conceptual tool is illustrated via model selection in linear regression and their practical implementation is demonstrated by application to the detection of cancer-specific protein markers in mass spectroscopy.
In the classical approach to statistical hypothesis testing the role of the null hypothesis H0 an... more In the classical approach to statistical hypothesis testing the role of the null hypothesis H0 and the alternative H1 is very asymmetric. Power, calculated from the distribution of the test statistic under H1, is treated as a theoretical construct that can be used to guide the choice of an appropriate test statistic or sample size, but power calculations do not explicitly enter the testing process in practice. In a significance test a decision to accept or rejectH0 is driven solely by an examination of the strength of evidence againstH0, summarized in the P-value calculated from the distribution of the test statistic underH0. A small P–value is taken to represent strong evidence againstH0, but it need not necessarily indicate strong evidence in favour of H1. More recently, Moerkerke et al. (2006) have suggested that the special status ofH0 is often unwarranted or inappropriate, and argue that evidence againstH1 can be equally meaningful. They propose a balanced treatment of bothH0 a...
In the classical approach to statistical hypothesis testing the role of the null hypothesis H0 an... more In the classical approach to statistical hypothesis testing the role of the null hypothesis H0 and the alternative H1 is very asymmetric. Power, calculated from the distribution of the test statistic under H1, is treated as a theoretical construct that can be used to guide the choice of an appropriate test statistic or sample size, but power calculations do not explicitly enter the testing process in practice. In a significance test a decision to accept or reject H0 is driven solely by an examination of the strength of evidence against H0, summarized in the P-value calculated from the distribution of the test statistic under H0. A small P-value is taken to represent strong evidence against H0, but it need not necessarily indicate strong evidence in favour of H1. More recently, Moerkerke et al. (2006) have suggested that the special status of H0 is often unwarranted or inappropriate, and argue that evidence against H1 can be equally meaningful. They propose a balanced treatment of bo...
Computational Statistics & Data Analysis, 2013
In this paper we investigate the use of description length principles to select an appropriate nu... more In this paper we investigate the use of description length principles to select an appropriate number of basis functions for functional data. We provide a flexible definition of the dimension of a random function that is constructed directly from the Karhunen-Loève expansion of the observed process. Our results show that although the classical, principle component variance decomposition technique will behave in a coherent manner, in general, the dimension chosen by this technique will not be consistent. We describe two description length criteria, and prove that they are consistent and that in low noise settings they will identify the true finite dimension of a signal that is embedded in noise. Two examples, one from mass-spectroscopy and the one from climatology, are used to illustrate our ideas. We also explore the application of different forms of the bootstrap for functional data and use these to demonstrate the workings of our theoretical results.
In this paper we investigate the use of description length principles to select an appropriate nu... more In this paper we investigate the use of description length principles to select an appropriate number of basis functions for functional data. We provide a flexible definition of the dimension of a random function that is constructed directly from the Karhunen-Loève expansion of the observed process. Our results show that although the classical, principle component variance decomposition technique will behave in a coherent manner, in general, the dimension chosen by this technique will not be consistent. We describe two description length criteria, and prove that they are consistent and that in low noise settings they will identify the true finite dimension of a signal that is embedded in noise. Two examples, one from mass-spectroscopy and the one from climatology, are used to illustrate our ideas. We also explore the application of different forms of the bootstrap for functional data and use these to demonstrate the workings of our theoretical results.
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Papers by Sengarapillai Arivalzahan