Copulas and non-Normal Multivariate Distributions

Cancelled Posted Mar 8, 2012 Paid on delivery
Cancelled Paid on delivery

this is a 3-part project with two (relatively) straight-forward "proofs" (they are more like theoretical derivations but could be considered as proofs) regarding how to use the properties of univariate poisson and exponential distributions to construct their multivariate analogues. the third question is an applied question concerning data analysis and fitting two bivariate Copula models with Pareto and Burr marginals to insurance data using R (no other software, please. i need to see this in R code). for the applied data-analytic part, three estimation methods are need and the three **must** be implemented in order to be compared: traditional maximum likelihood, two-stage maximum likelihood as described in Joe (2005, Journal of Multivariate Analysis) and pseudo-maximum likelihood as described in (Genest,Ghoudi & Rivest, 1993 Biometrika)

my ideal candiadte is a statistician, actuary, economist or a quantitative analyst who is very well-versed in Copula models and who is either good at derivations/theoretical results or who at least remembers how to work with them (kudos to you if you're in academia because chances are you work on this stuff all the time).

i'm in a little bit of a hurry since i need this by monday.

what i would expect from you:

- for the theoretical questions both a LaTeX pdf AND the LaTEx code file with a very, VERY clear and precise step-by-step description of what was found and how it was found. no step is too trivial to be skipped :)

- a file with the R code that implements the analysis of both Copula models using the three estimation methods. a well-commented code is a *MUST*

what you can expect from me:

- the details of the project including the mathematical definitions of the Copulas and of the estimation methods described

- sample R code of how the applied data-analysis question should be solved using the nlm() optimization function and coding the loglikelihood functions explicitly. no packages such as 'copula' or 'fCopulae' can be used (the copulas are closed-form parametric ones so it shouldn't be too bad).

- the dataset to be analyzed.

ps- if we hit it off and you're interested, there'll be more business going your way from me.

ps2- i actually have some of the answers (but not how to get them) for the data analysis part and the sketch of a proof for one of the theoretical questions so i know what i am looking for and how it should look, just in case there's anyone out there getting some strange ideas... just dont, please i know my stuff ;)

i value good, professional and corteous communication so it is vital for me to stay in touch with whoever i work with. in exchange i can say that i'm a very, very fast payer ;)

Algorithm C++ Programming Mathematics Matlab and Mathematica Statistics

Project ID: #1491578

About the project

3 proposals Remote project Active Mar 11, 2012