Publications by arthur charpentier
Binomial regression model
Most of the time, when we introduce binomial models, such as the logistic or probit models, we discuss only Bernoulli variables, . This year (actually also the year before), I discuss extensions to multinomial regressions, where is a function on some simplex. The multinomial logistic model was mention here. The idea is to consider, for insta...
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Conditional densities, on one single graph
With Stéphane Tufféry we’ve been working on credit scoring1 and we’ve been using the popular german credit dataset, > myVariableNames <- c("checking_status","duration","credit_history", + "purpose","credit_amount","savings","employment","installment_rate", + "personal_status","other_parties","residence_since","property_magnitude", + "age","...
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Random points on the Earth
The problem with puzzles is that you keep it in your head for days, until you find an answer. Or at least some ideas about a possible answer. This is what happened to me a few weeks ago, when a colleague of mine asked me the following question : Consider points uniformly distributed on a sphere. What is the probability that the points lie on a ...
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On Wigner’s law (and the semi-circle)
There is something that I love about mathematics: sometimes, you discover – by chance – a law. It has always been there, it might have been well known by some people (specialized in some given field), but you did not know it. And then, you discover it, and you start wondering how comes you never heard about it before… I experienced that fee...
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Conditional dependence measures
This week, I spend some time at the Workshop on Nonparametric Curve Smoothing conference at Concordia. Yesterday afternoon, Noël Veraverbeke show an interesting graph, to illustrate conditional copulas (and the derivation of conditional dependence measures, such as Kendall’s tau, or Spearman’s rho). A long time ago, in my PhD thesis (mainly...
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Random points on some hemisphere
In my previous post, I tried to answer the following question Consider points uniformly distributed on a sphere. What is the probability that the points lie on a same hemisphere, for some hemisphere (there is no south or north here) ? If I have been able to use Monte Carlo simulations in dimension 2 (on a circle, not on a sphere), I could...
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Sequences defined using a Linear Recurrence
In the introduction to the time series course (MAT8181) this morning, we did spend some time on the expression of (deterministic) sequences defined using a linear recurence (we will need that later on, so I wanted to make sure that those results were familiar to everyone). First order recurence The most simple case is the first order recurence,...
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Statistical Interests in Large Cities
I always thought that there were some kind of schools in statistics, areas (not to say universities or laboratories) where people had common interest in term of statistical methodology. Like people with strong interest in extreme values, or in Lévy Processes. I wanted to check this point so I did extract information about articles puslished in a...
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Visualizing Autoregressive Time Series
In the MAT8181 graduate course on Time Series, we started discussing autoregressive models. Just to illustrate, here is some code to plot – causal – process, > graphar1=function(phi){ + nf <- layout(matrix(c(1,1,1,1,2,3,4,5), 2, 4, byrow=TRUE), respect=TRUE) + e=rnorm(n) + X=rep(0,n) + for(t in 2:n) X[t]=phi*X[t-1]+e[t] + plot(X[1:6000],ty...
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Causal Autoregressive Time Series
In the MAT8181 graduate course on Time Series, we will discuss (almost) only causal models. For instance, with , with some white noise , those models are obtained when . In that case, we’ve seen that was actually the innovation process, and we can write which is actually a mean-square convergent series (using simple Analysis arguments on se...
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