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Timeline for Why are we using a biased and misleading standard deviation formula for $\sigma$ of a normal distribution?

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Dec 21, 2023 at 5:57 comment added Carl @RichardHardy I think it is clear that the bias of standard deviation is that type of statistical bias called "estimator bias." Sure, there are many other types of bias, but when one is discussing estimator bias, the context is predicted parameter inaccuracy, which in simulation parlance is a theoretically recovered parameter value minus a generalized known value used for data generation. Frankly, I do not see any jargon problem for "estimator bias," but would if one defined it using the word "expectation," which in statistical parlance is jargonesque.
S Dec 21, 2023 at 2:15 vote accept Carl
Nov 26, 2022 at 9:13 comment added Carl @RichardHardy Indeed, to call OLS unbiased when as typically used it has missing variable bias is a stretch. Yes, OLS is unbiased in certain contexts, but the assumptions leading to that typically do not hold in practice. Least squares in y indeed yields a best estimate within the x-value range of y-values, however, that is often neither what one thinks one is doing, nor relevant.
Apr 13, 2017 at 12:44 history edited CommunityBot
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Feb 17, 2017 at 11:19 history edited amoeba CC BY-SA 3.0
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Dec 15, 2016 at 8:09 comment added Richard Hardy @Carl, Glad to hear. You must be on the right track.
Dec 15, 2016 at 7:38 comment added Carl @RichardHardy Trust me, if I knew how to do that, I would. I actually am closest to a tag badge in terminology and I am working on perfecting my use of statistical language, and in fact, if reputation per post is any indication, I get more points for that than for anything.
Dec 15, 2016 at 6:51 comment added Richard Hardy @Carl, agree with Glen_b. Honestly, for me discussions with you are often more difficult than usual precisely because you are using well-established statistical terms to denote something quite different than they denote in statistics (which may probably make sense in physics). So purely for convenience, I would recommend sticking to the classical statistical definitions and terms when discussing with statisticians (e.g. here at Cross Validated).
Dec 15, 2016 at 4:03 comment added Carl @Glen_b My point is that 'bias' is jargon like 'cosine' or 'maximum likelihood' is jargon.
Dec 15, 2016 at 3:50 comment added Glen_b "bias" is certainly a term of jargon -- special words or expressions used by a profession or group that are difficult for others to understand seems pretty much what "bias" is. It's because such terms have precise, specialized definitions in their application areas (including mathematical definitions) that makes them jargon terms.
Dec 15, 2016 at 3:45 comment added Carl @Glen_b Oh and I do, I never say 'biased' without saying what, how and why. I do not understand bias to be jargon, the meaning either translates exactly into physics and math or it is incorrect.
Dec 15, 2016 at 3:35 comment added Glen_b @Carl many terms are used differently in different application areas. If you're posting to a stats group and you use a jargon term like "bias", you would naturally be assumed to be using the specific meaning(s) of the term particular to statistics. If you mean anything else, it's essential to either use a different term or to define clearly what you do mean by the term right at the first use.
Dec 14, 2016 at 21:33 comment added Carl @RichardHardy 1) There appears to be a problem with how the term bias is used, and 2) some things that are biased are not so recognized, whereas some things that are thought unbiased actually are biased. I also suspect there may be a terminology problem. Perhaps the term 'bias' is being used in different contexts in different fields, e.g., stats versus physics versus math?
Dec 14, 2016 at 21:25 comment added Carl @RichardHardy Best estimator is one candidate for the combination of accuracy and precision, but exactly what that means in general is vague. Certainly, in specific cases, when Method A is both more accurate and precise than Method B, we would have no problem say which is a better estimator. Moreover, either without the other is useless, that is accuracy without precision is just as worthless as precision without accuracy.
Dec 14, 2016 at 21:23 comment added Richard Hardy @Carl, is it a common use of the word bias? Let us not assign another meaning to an already heavily loaded term. Perhaps another term could suit better?
Dec 14, 2016 at 21:17 comment added Carl @RichardHardy Bias of fit can be both theoretically and for application to data defined and quantified as the latent structure or tendency of residuals over their range.
Dec 14, 2016 at 20:54 comment added Richard Hardy @Carl, good point, I did not use the proper term there (accuracy vs. precision). I wonder what adjective combine the two, meaning both accurate and precise? Also, how can one define bias of fit?
Dec 14, 2016 at 20:45 comment added Carl @RichardHardy Would prefer to say: (1) Bias is a reduced accuracy price one may be willing to pay for increased precision. (2) Alternatively, (e.g., for regularization,) bias of one thing (e.g., of fit) can be used to increase accuracy and precision of another (regression parameter target). Question here is when to use what.
Dec 14, 2016 at 20:20 comment added Richard Hardy Nonzero bias of an estimator is not necessarily a drawback. For example, if we wish to have an accurate estimator under square loss, we are willing to induce bias as long as it reduces the variance by a sufficiently large amount. That is why (biased) regularized estimators may perform better than the (unbiased) OLS estimator in a linear regression model, for example.
Dec 14, 2016 at 18:40 vote accept Carl
S Dec 21, 2023 at 2:15
S Dec 14, 2016 at 18:40 history bounty ended Carl
S Dec 14, 2016 at 18:40 history notice removed Carl
Dec 14, 2016 at 18:33 vote accept Carl
Dec 14, 2016 at 18:40
Dec 14, 2016 at 18:33 vote accept Carl
Dec 14, 2016 at 18:33
Dec 14, 2016 at 17:45 history edited Carl CC BY-SA 3.0
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Dec 14, 2016 at 17:35 vote accept Carl
Dec 14, 2016 at 18:33
Dec 14, 2016 at 15:31 answer added Neil G timeline score: 0
Dec 13, 2016 at 6:11 vote accept Carl
Dec 14, 2016 at 17:35
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Dec 12, 2016 at 16:09 answer added Scortchi♦ timeline score: 16
Dec 12, 2016 at 4:57 history edited Carl CC BY-SA 3.0
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Dec 11, 2016 at 2:37 answer added civilstat timeline score: 9
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Dec 8, 2016 at 23:14 comment added Carl @Scortchi Helpful (+1), that is what I was looking for for Q1. If you would be so kind as to run through it as an answer, I can edit to put in Q2 to later award the bounty.
Dec 8, 2016 at 15:57 comment added Scortchi♦ Q1: See the Lehmann-Scheffe theorem.
S Dec 8, 2016 at 14:16 history mod moved comments to chat
S Dec 8, 2016 at 14:16 comment added whuber♦ Comments are not for extended discussion; this conversation has been moved to chat.
Dec 8, 2016 at 9:24 history tweeted twitter.com/StackStats/status/806791639586869248
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Dec 8, 2016 at 6:49 answer added Carl timeline score: 1
Dec 8, 2016 at 5:10 history edited GeoMatt22 CC BY-SA 3.0
fix Gamma-ratio in "small-number bias" correction formula
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S Dec 7, 2016 at 22:29 history bounty started Carl
S Dec 7, 2016 at 22:29 history notice added Carl Canonical answer required
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