# Stéphane Laurent

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PhD in theoretical probability. Author of a few papers in probability and statistics. Currently work as a statistical consultant.

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 Nov9 comment Difference Between ANOVA and Kruskal-Wallis test @chl The $H_0$ hypothesis is the equality of the distributions, thus the identical shape assumption is only related to the power, isn't it ? Nov9 comment Conditional expectation subscript notation The last line makes no sense. It does after substituting $f(x)$ for $f(X)$ and $p_{Y|X}(y|X=x)$ for $p_{Y|X}(y|X)$. Nov4 comment Convergence in probability of minimum Have you noticed $P(|X_{(1)} -\theta| > \epsilon) = P(X_{(1)} -\theta > \epsilon)$ ? Nov1 comment Show that the best mean square estimator of $X$ given $(X_{1},…,X_{n})$ is $\hat X =E[X|\sigma(X_{1},…,X_{n})]$ The $X_i$ are discrete random variables ? Oct30 comment Show that the best mean square estimator of $X$ given $(X_{1},…,X_{n})$ is $\hat X =E[X|\sigma(X_{1},…,X_{n})]$ Ok but what is your definition of the conditional expectation ? Oct30 comment Show that the best mean square estimator of $X$ given $(X_{1},…,X_{n})$ is $\hat X =E[X|\sigma(X_{1},…,X_{n})]$ Do you know the definition of the conditional expectation as a projection in a $L^2$ space ? Oct25 awarded Nice Answer Oct24 comment Possible Paradox: Calculating a confidence interval with within-experiment error You have a sharp mind. I think I see why you are puzzled. Consider my notations here for the random one-way ANOVA model. The between-variance $\sigma^2_b$ is the variance of the theoretical means of the groups. It is not related to the within-variance $\sigma^2_w$. But the variance of the observed means $\bar y_{i\bullet}$ is $\sigma^2_b+\frac{\sigma^2_w}{J}$. You may think about this. Oct24 comment Possible Paradox: Calculating a confidence interval with within-experiment error Sorry, I like to give less mathematical answers when needed, but I'm too busy. The important variance is $\sigma^2_b+\frac{\sigma^2_w}{J}$, which is the variance of the observed means. Here you're looking at one example only, but if you run simulations, the dispersion of the observed means increase with $\sigma^2_w$. Oct24 comment Possible Paradox: Calculating a confidence interval with within-experiment error The answer is given by my answer in the first link: take the group means and draw a classical confidence interval for a Gaussian mean. So obivously CI are the same if group means are the same. Oct21 comment Calculation of an “unconstrained” normal distribution (starting from a censored one) Ok sorry, I'm at the office and the LaTeX rendering does not work. The shorter way I had in mind is the one given by @RayKoopman, without integral calculations. If you really want to calculate an integral, you don't need to calculate the normalization constant. Oct21 comment Calculation of an “unconstrained” normal distribution (starting from a censored one) Maybe I'm missing something, but you have only derived the distribution of $Y$, whereas the OP requires the conditional distribution of $Y$ given $Y \leq W$. Moreover there's no need to do all these calculations in order to derive the distribution of $Y$. Oct19 comment Recalculate log-likelihood from a simple R lm model The REML estimates of the variance components in a mixed models are like the "corrected for bias" ML estimates. I have not seen your post on GuR yet :) Oct19 comment Does relative Kullback-Leibler divergence exist? What is the deterministic example you have in mind ? I don't see what could be interpreted as a deterministic analogous of a divergence between two distributions. Oct19 comment Recalculate log-likelihood from a simple R lm model @PatrickCoulombe No : intercept + slope Oct19 comment Recalculate log-likelihood from a simple R lm model By the way you have to similarly be careful with the REML/ML option for lme/lmer models. Oct19 answered Recalculate log-likelihood from a simple R lm model Oct18 comment Recalculate log-likelihood from a simple R lm model With lm(), you are using $\sqrt{\hat\sigma}$ instead of $\hat\sigma$. Oct14 comment Probability of having real roots @whuber Yes, I do not pretend this is the expected answer :) (though my answer could help to perform the "true" triple integral calculation). Oct14 comment Probability of having real roots @whuber Why mysterious ? I only use the formula $E[f(X,Y)]=E[E[f(X,Y) \mid Y]]$ at each step.