Top new questions this week:
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In almost any textbook introducing the topic of frequentist statistics, null hypotheses of the form $H_0: \mu=\mu_0$ or similar are presented (the coin is unbiased, two measurement devices have …
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In the Lasso, and ElasticNet, we use, as penalty, the l1 norm without squaring. But in the ElasticNet and Ridge, we use the l2 norm squared. Why is that, is there a particular reason (computational, …
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Let be $(X_n)_{n \in\mathbb{N}}$ a sequence of random variables and $Z$ another random variable such that, when $n$ goes to infinity: $X_n$ converges to $Z$ in distribution : $X_n \overset{\mathcal{D}…
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I know that you reject the null at the 5% significance level. But I read someone writing that they reject at the 95% level. I assume the confidence level. But can you technically say that?
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Consider a random sample $X_i = (U_i,V_i)$ where $i=1,2,…,n$ from a bivariate normal population with mean $(\mu_1,\mu_2)$ and variances $(\sigma_1 ^2, \sigma_2 ^2)$ and correlation $\rho$. Let’s …
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I have had a question since graduate school. For a given significance level alpha, the test with smallest confidence interval length expectation should be optimal, because it usually also means a …
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Are there any known ways of getting an unbiased estimate of the condition number of the true covariance matrix being estimated, or at least correct within a small number of orders of magnitude? For …
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Greatest hits from previous weeks:
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I would have expected the correlation coefficient to be the same as a regression slope (beta), however having just compared the two, they are different. How do they differ – what different information …
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…assuming that I’m able to augment their knowledge about variance in an intuitive fashion ( Understanding “variance” intuitively ) or by saying: It’s the average distance of the data …
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I am working with a small dataset (21 observations) and have the following normal QQ plot in R: Seeing that the plot does not support normality, what could I infer about the underlying distribution? …
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In simple terms, how would you explain (perhaps with simple examples) the difference between fixed effect, random effect and mixed effect models?
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I have plotted this after I did a Shapiro-Wilk normality test. The test showed that it is likely that the population is normally distributed. However, how to see this “behaviour” on this plot? …
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After taking a statistics course and then trying to help fellow students, I noticed one subject that inspires much head-desk banging is interpreting the results of statistical hypothesis tests. It …
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I am training a simple neural network on the CIFAR10 dataset. After some time, validation loss started to increase, whereas validation accuracy is also increasing. The test loss and test accuracy …
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Can you answer these questions?
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i was comparing the results of 3 different techniques for regression task( Deep ensembles, variational inference and concrete dropout) and i got these results from the table looks like everything is …
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Consider Gaussian white noise $\varepsilon_t$ with variance $\sigma^2$. Is the following stochastic process $$X_t = \varepsilon_t – t\varepsilon_{t-1}, \hspace{1cm} t \in \mathbb{Z},$$ a Gaussian …
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I have some survey results where one of the metrics I am evaluating is being looked at on the state-level (i.e. comparing Delaware’s average score of 79% to Virginia’s average score of 52%). The …
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