Talk:Score test

Shouldn't "identifying the C above with log(K)" actually read "identifying the C above with log(K)/n"? — Preceding unsigned comment added by Stefan.karpinski (talk • contribs) 00:54, 13 July 2006 (UTC)

Anais: And what happens under the alternative hypothesis (if H0 is not true) ? Does it tend to infinity ? It is quite important if you want to define the critical region... —Preceding unsigned comment added by 90.46.131.123 (talk) 11:26, 20 January 2008 (UTC)

The initial single-parameter section and the "multiple parameters" section take different approaches at present that need to relate to each other better. The single-parameter section is showing that a test based on the score is locally most powerful (LMP) without saying anything about its distribution or mentioning Fisher's information I. The multiple parameters section gives the asymptotic distribution of the score test statistic, which involves both the score U and the information I, without saying it's LMP. Would be better to do the whole thing for a single parameter first then show how it generalises to multiple parameters. Afraid i don't have the textbooks to hand that i'd need to be sure about changing it myself. --Qwfp (talk) 17:52, 23 January 2008 (UTC)

Article title: LM test vs. score test

(Moving discussion here that was initiated on my Talk page about the recent page move --Qwfp (talk))

Maybe it is personal bias coming from my own field, but in econometrics the term "score test" is almost never used even though—curiously—the LM test is usually calculated using Rao's score form rather than the Lagrangean. How are we going to settle this issue though? Citing the main textbooks from different fields? In that case, see Hayashi, Econometrics, Wooldridge, Introductory Econometrics, and Kennedy, Guide to Econometrics. --bender235 (talk) 02:07, 29 March 2019 (UTC)

Hmm... well under WP:COMMONNAME, note 5 says "...Discussions about article titles commonly look at additional off-site sourcing, such as frequency of usage in news publications, books, and journals." News publications are irrelevant, so lets look at:

• Books: In Google Ngram Viewer: [1] "Score test" was far ahead of "Lagrange multiplier test" and "LM test" until the late 1970s, since when the sum of the latter two has come to dominate (due to Breusch & Pagan's 1980 paper I guess) but not greatly.
• Journals: Google Scholar search for "LM test" OR "Lagrange multiplier test" gives "About 17,500 results", while "score test" -"test score" statistics OR econometrics gives "About 23,700 results". Limiting both to since (say) 2010 gives "About 17,400" and "About 12,200" respectively, suggesting a reasonably similar pattern to that for books.

So on that basis I'm happy with your article move from Score test to Lagrange multiplier test. I've just edited the lead, which you expanded before moving the article. I'd be grateful if you could define the terms "restricted estimator" and "non-binding" that you added as they're not entirely clear to me and I don't think they'll be clear to readers coming to this for the first time. --Qwfp (talk) 22:03, 29 March 2019 (UTC)

Restricted estimator^{[definition needed]}

@DavidMCEddy: I'm pinging you as someone who seems to be involved in these articles. How shall we define "restricted estimator" (which was tagged by Qwfp)? I was thinking of defining in set notation, $\theta _{0}\in \Theta _{0}\subset \Theta$, but that might be too technical and confusing for non-experts. --bender235 (talk) 04:58, 12 April 2019 (UTC)

Unrelated: "log-rank test for difference in survival between two groups is most powerful when the proportional hazards assumption holds."

"When the data consists of failure time data in two groups, the score statistic for the Cox partial likelihood is the same as the log-rank statistic in the log-rank test. Hence the log-rank test for difference in survival between two groups is most powerful when the proportional hazards assumption holds."

The score-test is not even most powerful. You're confusing score-tests with the most powerful tests. 68.134.243.51 (talk) 02:42, 5 August 2022 (UTC)

suggestion:add an example for uses in nuisance parameters case

suggestion:add an example for uses in nuisance parameters case 68.134.243.51 (talk) 20:34, 5 August 2022 (UTC)