Timeline for Calculating the distribution of the sum of the squares of the predictors in linear regression
Current License: CC BY-SA 4.0
6 events
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| May 22, 2023 at 16:49 | comment | added | whuber♦ | Right: my point was only that it could be helpful to point out how you used the full-rank assumption in this solution. My comment about being critical originates from a general sense of negativity in the post, beginning with stating what $X=UDV^\prime$ is not and culminating with a summary of what is incorrect. The same points can be made in the same (mathematical and statistical) ways from a positive perspective. Just start off by saying what the SVD really is and end by summarizing what the correct result is. IMHO, such a positive approach is less likely to be misread. | |
| May 22, 2023 at 14:09 | history | edited | Zhanxiong | CC BY-SA 4.0 |
added 295 characters in body
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| May 22, 2023 at 14:04 | comment | added | Zhanxiong | As for the full-rank assumption, it was clearly mentioned in OP's question. | |
| May 22, 2023 at 14:00 | comment | added | Zhanxiong | @whuber I am not really "criticizing/distracting" OP. IMO, I have to clarify all the dimensions and basic concepts first before answering this question correctly. For the dimensionality of $D$ (either $n \times p$ in my answer or $p \times p$ as you suggested), I believe I follow the widely-accepted SVD formulation (en.wikipedia.org/wiki/Singular_value_decomposition). I do have seen some author made $D$ to be $p \times p$, but in that case the dimension of $U$ needs to be adapted accordingly. But I see your point and will edit the wording a bit. | |
| May 22, 2023 at 13:44 | comment | added | whuber♦ | (+1) But the complaints about notation are distracting. There is a standard formulation of SVD in which "$D^{-2}$" is often used to refer to the $p\times p$ (not $n\times n$) matrix whose nonzero diagonal elements are $d_i^{-2},$ where $d_i$ are the nonzero diagonal elements of $D.$ Although that needs clarifying, it could be done a little less critically. It might also be worth pointing out that you used the full-rank assumption about $X$ when you concluded there are $p$ terms in the sum. | |
| May 22, 2023 at 12:48 | history | answered | Zhanxiong | CC BY-SA 4.0 |