90,227 reputation
8153315
bio website quantdec.com
location Northeastern US
age 14
visits member for 4 years, 2 months
seen 29 mins ago

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 I can be reached through (outdated but still valid) links posted on my web site.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.


35m
awarded  Revival
1h
comment Test for non-uniform sampling from a sequence without replacement?
You might want to consider a much more informative approach than that, such as viewing a plot of the empirical cumulative distribution (which would amount to a QQ plot). Any pattern of deviations from the expected linear behavior not only would reveal a violation of the null hypothesis, but would also indicate how the null is violated. A Kolmogorov-Smirnov statistic could be used as a formal test.
2h
comment p-value over q-value?
I believe that first remark reflects the same confusion. Hypothesis testing concerns probabilities rather than sizes of meteors, costs of damage, or anything else. When people write "as extreme or more extreme than" in the context of hypothesis testing, then they mean--or ought to mean--extreme in terms of probabilities of critical regions. The theory that justifies this is the Neyman-Pearson Lemma which, as you can see, is expressed solely in terms of probabilities (via likelihood functions).
2h
answered Posterior Probability Question
3h
comment Posterior Probability Question
@Hassan is right: the really interesting aspect of this question concerns how multiple unreliable witnesses can change the posterior probability (and in which direction they change it). For many people this result may be unintuitive.
3h
comment What are desirable characteristics of a test statistics?
Because both historically and theoretically it is not the case that statistics are developed with the sole aim of obtaining something whose sampling distribution can easily be derived mathematically, there must be more to the story than this. And indeed there is: there are many criteria used to develop statistics, including invariance, most powerful (MP), unbiased, robust, and more.
3h
comment Does the central limit theorem apply to these probability density functions?
I am only addressing the logic of your answer, Arthur. By applying exactly your reasoning to this exponential variable I have obtained a contradiction: the distribution of $z$ in the exponential case cannot both be $0$ and Normal (as your post would ask us to believe). Therefore, even though your conclusion is correct, it cannot be correct by virtue of the reasons you have offered.
4h
comment What are the implications of estimating a covariance matrix from a correlated sample?
Your first paragraph does not define a matrix, but only a number (the sample variance). Because the entire point of estimating a covariance matrix is to assess correlations among non-independent variables, there is a disconnect between the first and second paragraphs, making it difficult to determine what you might be trying to ask.
4h
comment Does the central limit theorem apply to these probability density functions?
Suppose instead the $X_i$ were iid exponential, shifted to the left by $1$ to center them at zero. Then the numerator of $z$ would converge a.s. to $1$ while the denominator would diverge a.s., making $z$ converge to a constant $0$ rather than a normal distribution. It would therefore seem that your reasoning is not sufficient to demonstrate the conclusion.
4h
comment What is the distribution of the conditional mean E(Y|X) in a multiple regression?
I suspect nobody is yet sure what you are asking. The notation suggests both the $X_i$ and $D$ are random variables but the model explicitly makes only $e$ random. Please edit the question to clarify the meanings of your notation.
4h
comment Confidence intervals for median
The formulas you link to at "this website" are based on a Normal approximation to the sampling distribution of the median, which itself is an asymptotic result. (I have no idea to which statistic you are referring, since the only one you have mentioned is the median and there's no conceivable way "Poissonian" would apply to it.)
4h
revised Sum of RV : probability for the value of operands when the result is known
edited tags
11h
awarded  Enlightened
11h
awarded  Nice Answer
15h
reviewed No Action Needed Problem displaying st. errors after lincom using outreg2
15h
reviewed Reopen Expand scale bias correction factor (infinite series)
19h
comment Choosing between LM and GLM for a log-transformed response variable
The characterization of the glm does not look correct: on the left hand side is a random variable $\epsilon$ while the right hand side contains only data and parameters but no random variables.
19h
comment Why can't we add all the individual Pearson's $r$'s in a multiple regression and calculate $R^2$ based on this sum?
When there are just two variables and $r$ is negative, you have no hope of creating a nonnegative $R^2$ from its sum, do you? Instead of inventing a formula and asking why it doesn't work, why not study the theory and the formulas that do work? That is a much faster and surer way towards understanding.
20h
comment confidence intervals and type II errors
If you are sceptical of a borderline p-value, then you don't believe in the test you are using--and maybe you shouldn't be performing a test at all. A hypothesis test leads to a binary decision: either you reject the null or you don't. There's no going back to say "well, it was borderline, so maybe I'll decide/not decide to reject." Except in heavily regulated situations, most people find that too Procrustean: whence the appeal of reporting a CI.
20h
comment Expand scale bias correction factor (infinite series)
Please explain where this series comes from and what $m$ and $T$ mean. We can only guess what assumptions are being made and what the context is, but that's not good enough! Surely there is some specific estimator involved here, but which one is it?