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The matrix-variate normal (MxVN) distribution is just a multivariate normal (MVN) distribution with a covariance matrix that is a Kronecker product. The following equivalence holds $$X \sim N_{p,q}(M,U,V) \iff vec(X) \sim N_{pq}(vec(M),V\otimes U).$$ From this equivalence it is straight forward to derive the pdf of the matrix normal distribution as $$|2\... 1 There is a reason that no such cheat sheet exists. The hardest data problems are regime-specific. While some issues arise universally, the reason why data is messed up is because of its lifecycle. Who or what created it? How was it put together? How is it stored? How did it change between the time it was created and the time it was received? Those are ... 1 As others have written, this is compositional data analysis. We have a compositional-data tag, so searching for threads carrying, e.g., this tag and the "time-series" one may be helpful. One paper on forecasting compositional time series is Snyder et al. (2017, IJF). Essentially, the idea is to transform the original compositional time series, then ... 1 Below are two books I have referenced in the past. I particularly like the 2015 book as it also goes into other latent variable modeling techniques (e.g., Item Response Theory) in an accessible way. It may also be worth using the lavaan website (also below) as a learning tool, as it has many good examples. Finch, W. H., & French, B. F. (2015). Latent ... 0 I will recommend you a textbook related with time series analysis. I read this book and got the idea. This book is very easy to understand. The link for the book :https://a-little-book-of-r-for-time-series.readthedocs.io/en/latest/src/timeseries.html This book is very good because it shows everything from scratch. This book shows. how to read time series ... 0 Short approximate derivation For a single sample mean X_N you have the Chebyshev's inequality$$P(\vert X_N -\mu_X \vert \geq k\frac{\sigma_X}{\sqrt{N}}) \leq \frac{1}{k^2}$$or$$P(\vert X_N -\mu_X \vert \geq \epsilon ) \leq \frac{\sigma_X^2}{N\epsilon^2} = \frac{1}{34} The last equality stems from setting $N=34\sigma_X^2/\epsilon^2$. The probability ...

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The first paper cited below includes a review and proof of the median-of-means estimator. The second paper (whose main goal is to show an optimal sample size for mean estimation) also mentions this estimator (near end of section 2.1). REFERENCES: Devroye, L., Lerasle, M., et al. "Sub-Gaussian mean estimators", https://arxiv.org/pdf/1509.05845.pdf ...

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Just five chapters into Paige Harden's new book. Enjoying it but she has a high bar to clear https://lareviewofbooks.org/article/why-dna-is-no-key-to-social-equality-on-kathryn-paige-hardens-the-genetic-lottery/

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Two books come to mind: Trustworthy Online Controlled Experiments by Kohavi, Tang, and Xu Statistical Methods in Online A/B Testing by Georgi Georgiev The first book collects a great deal of wisdom distilled from years of experience that was scattered in obscure field journals and touched only briefly in textbooks on statistics and field experimentation. ...

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Robert R. Sokal and F. James Rolf, Introduction to Biostatistics, W. H. Freeman and Co., San Francisco. 1973. 368pp A second edition is available as a Dover reprint of the 1987 impression. For the assiduous student, the book is indispensable. Electronic availability is noted below. Also by the same authors - Biometry: The Principles and Practices of ...

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In general it's difficult to find patterns in a complex sequence. But for simple sequences like Fibonacci for which there is a linear recurrence relation involving past few terms (e.g., $f_{n}=f_{n-1}+f_{n-2}$), a simple linear model could be used (off course we need to know how many previous terms we need to predict the next term, e.g., for Fibonacci we ...

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