88,282 reputation
8150306
bio website quantdec.com
location Northeastern US
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visits member for 4 years, 1 month
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Consultant (environmental and spatial stats a specialty), expert witness, and teacher. I can be reached through (outdated but still valid) links posted on my web site.

Twitter: @WilliamAHuber // ASA-P website: http://amstatphilly.org/


Why waste time learning, when ignorance is instantaneous?

--T(iger) Hobbes.

For any complex problem there is a simple solution. And it's always wrong.

--[Mis?]attributed to H.L. Mencken by Dava Sobel, Longitude.


49s
revised WLLN: can expectation exist but be infinite?
Clarified some points.
6m
comment Why is this probability statement true?
How many points can there be where $\eta^2$ is not continuous?
14m
comment Correlation coefficient in case where dependent variable cannot be larger than independent
Do you have any thoughts or information about the mechanisms behind, or the statistical nature of, those deviations?
17m
comment Asymmetric Error Bars
Perhaps this thread is related to your question? stats.stackexchange.com/questions/13086 Other threads on data-transformation and Box-Cox transformation may also be of direct interest.
23m
comment Absolutely continuous probability distribution and its probability density
It is unclear what you want to prove in the second question, because the Chinese quotation is often taken as the definition of absolutely continuous. What definition are you starting from? As far as your first question goes, what do you mean by "takes values in $\mathcal{R}$ everywhere"? If it means the range of $X$ is all of $\mathcal{R}$, then counterexamples are easy to come by. For instance, taking $X=(2U-1)V^2$ where $V$ is standard Normal and $U$ is Bernoulli$(1/2)$, it is clear that $X=0$ is possible (it would arise when $V=0$) but nevertheless $f_X(0)=0$.
31m
revised Absolutely continuous probability distribution and its probability density
deleted 100 characters in body
33m
comment Logistic regression gives very different result to Fisher's exact test - why?
Consider editing your question (and its title) to focus on that last comment, since it seems to be what your concern really is.
36m
comment Why there is no significant difference between a number list and its 100 times list
One problem with the reasoning in this answer is that it is possible (and often occurs) that the mean of data $(x)$ is not significantly different from $0$, the mean of data $(y)$ is not significantly different from $0$, yet the difference of means can still be significantly different from $0$. Although, to make a point, @Scortchi may have exaggerated a little (but only a little) in asserting a comparison to $0$ is "irrelevant," it is therefore clear that a comparison to $0$ is more of a distraction than an illumination.
44m
comment Proof that the coefficients in an OLS model follow a t-distribution with (n-k) degrees of freedom
$A$ is merely a matrix representation of a quadratic form. Every quadratic form has a symmetric representation, so the requirement of symmetry of $A$ is implicit in the statement of the theorem. (People do not use asymmetric matrices to represent quadratic forms.) Thus the quadratic form $(x_1,x_2)\to x_1^2+x_1x_2$ is uniquely represented by the matrix $A=\begin{pmatrix}1&1/2\\1/2&0\end{pmatrix}$ which is not idempotent.
50m
comment Proof that the coefficients in an OLS model follow a t-distribution with (n-k) degrees of freedom
Because $\hat\beta_i$ is a linear combination of jointly Normal variables, it has a Normal distribution. Therefore all you need do are (1) establish that $\mathbb{E}(\hat\beta_i)=\beta_i$; (2) show that $s_{\hat\beta_i}^2$ is an unbiased estimator of $\text{Var}(\hat\beta_i)$; and (3) demonstrate the degrees of freedom in $s_{\hat\beta_i}$ is $n-k$. The latter has been proven on this site in several places, such as stats.stackexchange.com/a/16931. I suspect you already know how to do (1) and (2).
59m
comment Find variable k when given 2 marginal distributions
I wonder whether you have transcribed this problem correctly (btw,you should add the self-study tag to the question). There are two strange things about it: (1) $k$ can be found using either $f_x$ or $f_y$; you don't need them both. (2) Neither $f_x$ nor $f_y$ are valid PDFs, as you have found out. I suspect that either the domains of these marginals should be restricted (perhaps to $0\le x\le 1$) or else there should be some power in the denominator, which perhaps should be $1+4x^2$.
1h
reviewed Approve suggested edit on Seasonal adjustment for a series that has already been adjusted
1h
reviewed Reopen How do I estimate P(skill(player1)>skill(player2)) when I know the number of (presumably independent) 'wins' and 'losses' of player1 and player2?
1h
comment Why is the intersect negative and what does my regression show
+1 The plot is helpful. Based on comments by the OP I suspect that the use of "revenue" here may be unconventional; it seems to refer to some form of net revenue. That interpretation resolves the apparent problem of projecting nonzero "revenue" for zero subscribers.
1h
comment Why is the intersect negative and what does my regression show
In that case Umair, your question is misleading, because the intercept is only -190, not -190 million as it currently states. It is important to be consistent--or at least explicit--about the units of measurement you use when reporting numbers.
1h
comment Formal definition of thin-tailed distribution in terms of regular variation, etc.?
That edit helps, thank you. Have you considered the possibility that the limit simply does not exist? You might want to replace "lim" by "lim inf". Even worse, that fraction isn't even defined except for distributions that are eventually continuous for large $z$. A definition of "fat-tailed" and "not fat-tailed" would be much more satisfying if it could be applied to all distributions.
1h
comment About the Bonferroni correction
Although that is the right formula for correcting $1225$ nearly-independent tests, the huge degree of interdependence among the correlations of $50$ variables would suggest including a strong cautionary note against relying on the Bonferroni method in this situation (except perhaps in interpreting its result as a lower bound on the correct p-value).
16h
awarded  Necromancer
17h
comment Formal definition of thin-tailed distribution in terms of regular variation, etc.?
It all comes down to what you want to use your definition for. Different applications may require different definitions of "thin tailed" which, after all, is merely a vague qualitative concept.
17h
revised WLLN: can expectation exist but be infinite?
added 460 characters in body