1147 search results for "LaTeX"

Learning Kernels SVM

September 25, 2012
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Learning Kernels SVM

Machine Learning and Kernels A common application of machine learning (ML) is the learning and classification of a set of raw data features by a ML algorithm or technique. In this context a ML kernel acts to the ML algorithm … Continue reading →

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Maximum likelihood estimates for multivariate distributions

September 22, 2012
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Maximum likelihood estimates for multivariate distributions

Consider our loss-ALAE dataset, and - as in Frees & Valdez (1998) - let us fit a parametric model, in order to price a reinsurance treaty. The dataset is the following, > library(evd) > data(lossalae) > Z=lossalae > X=Z;Y=Z ...

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Maximum likelihood estimates for multivariate distributions

September 22, 2012
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Maximum likelihood estimates for multivariate distributions

Consider our loss-ALAE dataset, and – as in Frees & Valdez (1998) - let us fit a parametric model, in order to price a reinsurance treaty. The dataset is the following, > library(evd) > data(lossalae) > Z=lossalae > X=Z;Y=Z The first step can be to estimate marginal distributions, independently. Here, we consider lognormal distributions for both components, > Fempx=function(x) mean(X<=x) >...

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Power Analysis and the Probability of Errors

September 22, 2012
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Power Analysis and the Probability of Errors

Power analysis is a very useful tool to estimate the statistical power from a study. It effectively allows a researcher to determine the needed sample size in order to obtained the required statistical power. Clients often ask (and rightfully so) what the sample size should be for a proposed project. Sample sizes end up being

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(nonparametric) Copula density estimation

September 20, 2012
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(nonparametric) Copula density estimation

Today, we will go further on the inference of copula functions. Some codes (and references) can be found on a previous post, on nonparametric estimators of copula densities (among other related things).  Consider (as before) the loss-ALAE data...

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(nonparametric) copula density estimation

September 19, 2012
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(nonparametric) copula density estimation

Today, we will go further on the inference of copula functions. Some codes (and references) can be found on a previous post, on nonparametric estimators of copula densities (among other related things).  Consider (as before) the loss-ALAE dataset (since we’ve been working a lot on that dataset) > library(MASS) > library(evd) > X=lossalae > U=cbind(rank(X)/(nrow(X)+1),rank(X)/(nrow(X)+1)) The standard tool to plot...

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Copulas and tail dependence, part 3

September 18, 2012
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Copulas and tail dependence, part 3

We have seen extreme value copulas in the section where we did consider general families of copulas. In the bivariate case, an extreme value can be writtenwhere is Pickands dependence function, which is a convex function satisfyingObserve that in ...

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Copulas and tail dependence, part 2

September 18, 2012
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Copulas and tail dependence, part 2

An alternative to describe tail dependence can be found in the Ledford & Tawn (1996) for instance. The intuition behind can be found in Fischer & Klein (2007)). Assume that and have the same distribution. Now, if we assume that those vari...

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Side note…

September 18, 2012
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MathJax allows you to customize how \( \LaTeX \) is displayed. Simply right click over the math you’d like to see to access the display menu. Under “math settings” you can see zoom trigger and factor options. Given how small the text ...

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Copulas and tail dependence, part 1

September 17, 2012
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Copulas and tail dependence, part 1

As mentioned in the course last week Venter (2003) suggested nice functions to illustrate tail dependence (see also some slides used in Berlin a few years ago). Joe (1990)'s lambda Joe (1990) suggested a (strong) tail dependence index. For lower t...

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