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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 Nov21 awarded Notable Question Nov16 answered Why is RSS distributed chi square times n-p? Nov14 comment Convolve multivariate gaussian I'm very tired but I think that $a^T\eta \sim \mathcal{N}(a^T\mu_2, a\Sigma_2a^T)$ hence $\eta_\star \sim \mathcal{N}(a^T\mu_2, \Sigma_1+a\Sigma_2a^T)$ Nov10 comment Kruskal Wallis test with high type 1 error Why do you claim that $H_0$ is fulfilled for these negative binomial distributions ? They do not have the same median (I don't know exactly what is the location parameter in the $H_0$ hypothesis of KW). Nov10 comment Difference Between ANOVA and Kruskal-Wallis test I'm not sure to understand this thread: stats.stackexchange.com/q/69448/8402 Does that mean that KW does not respect the nominal significance level when $H_0$ is true but other assumptions are not fulfilled ? Nov10 comment Difference Between ANOVA and Kruskal-Wallis test I just say this is a common belief. According to the help of krusal.test() in R, $H_0$ is the equality of the location parameters of the distribution. In practice I think we often use KW to assess a difference between the distributions. Hence we could assume the same shape (as we do in the Gaussian ANOVA case), and apply KW, this makes sense. Nov10 answered Finding conditional pdf of $Z$ given $X=x$ where $Z=X+Y$ Nov10 comment Difference Between ANOVA and Kruskal-Wallis test @ttnphns I believe you, I don't know. But commonly we consider $H_0$ as the equality (see e.g. the article on wikipedia). Nov10 answered Difference Between ANOVA and Kruskal-Wallis test Nov10 comment Difference Between ANOVA and Kruskal-Wallis test @ttnphns I'm not talking about power comparison, but about the power of KW: this test is made to detect difference between distributions with identical shapes. I mean the test has low power to detect a difference between distributions without this assumption. Nov10 comment Difference Between ANOVA and Kruskal-Wallis test @ttnphns Yes for the type I error. But I think KW is only powerful under such assumptions. Nov10 comment Difference Between ANOVA and Kruskal-Wallis test @Flask, shapes are obviously identical under $H_0$ (equal distributions) 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.