Questions tagged [martingale]

In probability theory, a martingale is a model of a fair game where knowledge of past events never helps predict the mean of the future winnings and only the current event matters.

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1answer
197 views

log transform fixed PH in Cox model - how?

I have survival data to which I am fitting a Cox model with a continuous predictor. The cumulative martingale residual method (supremum test) of Lin, Wei and Ying suggested that both proportional ...
20
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4answers
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The magic money tree problem

I thought of this problem in the shower, it was inspired by investment strategies. Let's say there was a magic money tree. Every day, you can offer an amount of money to the money tree and it will ...
3
votes
2answers
752 views

Cox PH model: managing continuous variables and linearity assumption

In an epidemiological study, I'm using martingale plot to assess the linearity of continuous variables. Here are the Martingale Residuals (from Null Model) using R's ...
5
votes
1answer
1k views

Cox PH linearity assumption: reading martingal residual plots

According to a lot of ressources about Cox PH model, continuous numeric variables should be tested for linearity assymption by plotting the Martingale residuals. In R, you can use ...
2
votes
2answers
141 views

Does a martingale difference sequence (mds) imply strong mixing?

I read this from an econometrics paper " The typical hypothesis which is imposed in the time series literature is that the $u_t$'s are either independent and identically distributed (i.i.d.) or a ...