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2 votes
Accepted

Importance of normality testing in clinical trials / AB tests

The requirement for normality is greatly misunderstood. First, distributional assumptions are made about the conditional distribution, not the marginal (in your words, "the data itself"). ...
2 votes

What are some good calculus resources relevant for Machine learning researcher aspirant?

It's not a book and not addressing optimization, but one of the best resources to self-learn calculus are the lectures by Gilbert Strang that were recorded and are available on YouTube. He also wrote ...
  • 127k
4 votes

Formal definition of p-value

But unfortunately I couldn't find the definition of $S_{\alpha}$ The p-value is not defined in an unambiguous way "The probability to get, given the null hypothesis, an effect-size equal to or ...
5 votes

Formal definition of p-value

Lehmann is talking about a nested sequence of critical regions $\langle S_\alpha\rangle$ with the index being the size of the corresponding test. This is due to the fact that he needs to find the ...
  • 5,137
5 votes

What is the roadmap to self-taught probability and statistics for artificial intelligence?

If you were an academic, one must assume you already have a good reference for multivariable calculus, linear algebra, and differential equations – these are not optional. I personally heard from ...
3 votes

Are there families of known parametric copulas for non-standard marginal normal distributions?

The point of copulas is that they do not care about the margins. Therefore, if you want a Gaussian copula as the dependence structure between the margins and margins that are normal but not standard ...
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3 votes
Accepted

Does stacking multiple linear layer have some documented improvements?

Here are some papers giving theoretical guarantees for Multiple Linear Layer Networks (more generally known in the literature as Deep Linear Networks) which should be of interest to you : First, the ...
  • 1,002
0 votes

Cross-validation vs empirical Bayes for estimating hyperparameters

There is actually a paper that connects CV and EB: E Fong, C C Holmes, On the marginal likelihood and cross-validation, Biometrika, Volume 107, Issue 2, June 2020, Pages 489–496 If I understand ...
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1 vote

Are the method-of-moments-based normal confidence intervals asymptotically valid and optimal?

For a normal random variable, the moment-matching estimator (MME) for the mean is the maximum likelihood estimate (MLE). For the variance, the MME and the MLE differ just by the bias adjustment ( n/(n-...
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2 votes

Determine seasonal frequency from the values of the time series alone

(cross-posted from here) Section 3.2 in the following paper offers a possibility for determining the length of the seasonal cycle: ...
0 votes

How to intuitively explain what a kernel is?

The kernel is a function that quantifies similarity between a pair of data points. And mathematically speaking this similarity can be computed using inner product, which has been explained beautifully ...
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0 votes

What are some good books on the philosophy of statistics

Eventhough people speak about Bayesians and frequentist, as if statisticians are some sort of followers of a religion, most of statistics is very straightforward and pragmatic without bothering too ...

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