# Stéphane Laurent

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# 151 Actions

 Jan30 comment Different definitions of an ergodic stationary process By "wide-sense stationary" you mean stationary correlation ? Jan29 comment What am I doing wrong in calculating Fisher Information of Triangular Distribution? $x$ is a random variable and you have not calculated the expectation in your last step Jan29 comment Ergodic Process: Does it visit all state? @triomphe Actually this should be equivalent for a discrete-time stationary process. Are you interested in discrete or continuous time ? Jan28 comment Ergodic Process: Does it visit all state? @triomphe Ok, but from your quote by Boltzmann "orbits will typically pass through every point in state space" I suspect he's talking about a measure-preserving transformation (a dynamical system). Jan26 comment Ergodic Process: Does it visit all state? What is the definition of ergodicity you are talking about ? Is it ergodicity of a measure-preserving transformation ? Aug19 awarded Yearling Aug11 comment Spectrum and tower decomposition Thanks. Very elementary actually. I have to overcome the pychological barriers of the newbie. Aug11 accepted Spectrum and tower decomposition Aug11 asked Spectrum and tower decomposition Jul3 accepted Symmetry of Plancherel measure (for $S_n$) Jul3 comment Symmetry of Plancherel measure (for $S_n$) Thank you Marc. Your answers provide more information than I expected. Jun25 accepted Isometric embedding of a finite set into $\mathbb{R}^n$ Jun24 asked Isometric embedding of a finite set into $\mathbb{R}^n$ Jun15 comment Ergodic action of a group It's also nice to mention that the classical ergodicity for a measure-preserving transformation $T$ is the case when $G={\{T^n\}}_{n \in \mathbb{Z}}$ . Jun4 comment estimate population percentage within an interval, given a small sample @SeyhmusGüngören Moreover the efficiency should depend on the parameter of interest. Here we want a confidence interval for the probability $\Pr(X \in [a,b])$ which involves both the mean and the standard deviation. I have already tried bootstrap intervals for variance components in some simple mixed models, and I swear they are really too short. Jun4 comment estimate population percentage within an interval, given a small sample @SeyhmusGüngören I'd like to see the result with the sample $50$, $51$, $52$. I don't believe it can work. Here are some related discussions stat.ethz.ch/pipermail/r-help/2006-April/102828.html and stats.stackexchange.com/questions/33300/… Jun4 comment estimate population percentage within an interval, given a small sample @SeyhmusGüngören Ok but why would it work ? With $n=3$ the bootstrap distribution is "highly discrete". In this situation one cannot expect to achieve a confidence level close to the nominal confidence level. Jun4 comment estimate population percentage within an interval, given a small sample @SeyhmusGüngören These papers are not written by mathematicians. Any theorem about the bootstrap contains "when $n \to \infty$", don't you agree ? If not, could you show me a link to a theorem not assuming $n \to \infty$ ? Jun4 comment estimate population percentage within an interval, given a small sample @SeyhmusGüngören Bootstrap is only asymptotically valid. So your claim "asymptotic theory does not apply then I use bootstrap" is wrong. See any textbook about large sample theory. The reason is clear: when $n \to \infty$, the empirical cumulative distribution function goes to the true cumulative distribution function. Jun4 comment estimate population percentage within an interval, given a small sample @SeyhmusGüngören Bootstrap is not valid for small sample sizes. For instance the effective coverage of the bootstrap $95\%$-confidence interval is not $95\%$, and generally it is really smaller. Mathematical results about bootstrap are asymptotic results ($n \to \infty$). en.wikipedia.org/wiki/Bootstrapping_(statistics)#Disadvantages