5,085 reputation
1425
bio website quantdec.com
location Northeastern US
age 14
visits member for 4 years, 3 months
seen 14 hours 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 I can be reached through (outdated but still valid) links posted on my web site.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.


2d
comment Show that $\lim_{n\rightarrow\infty}{\displaystyle\sum_{i=1}^{n}{\frac{F_n}{2^n}}}=2$
The limit is $0$, not $2$. Use $(1 +\sqrt{5})/2$ instead of $2$ in the denominator to obtain a finite limit.
2d
awarded  Caucus
Dec
12
comment How can I calculate $\int^{\infty}_{-\infty}\Phi\left(\frac{w-a}{b}\right) \left(\frac{w-a}{b}\right) f(w; \mu, \sigma²)\,\mathrm dw$
You ignore all terms except for the $k=1$ coefficient, which (upon multiplication by $1!=1$) yields the result you are looking for.
Dec
11
comment How can I calculate $\int^{\infty}_{-\infty}\Phi\left(\frac{w-a}{b}\right) \left(\frac{w-a}{b}\right) f(w; \mu, \sigma²)\,\mathrm dw$
The result you reference makes it easily possible (via linear substitutions and completing the square) to compute the integral of $\Phi((w-a)/b)f(w;\mu,\sigma^2) \exp(\lambda (w-a)/b)dw$. The MacLaurin series of that function of $\lambda$ will yield integrals proportional to $\Phi((w-a)/b)((w-a)/b)^k f(w;\mu,\sigma^2)dw$ for $k=0, 1, 2, \ldots$; you want the case $k=1$.
Dec
1
comment How to show the given expression is geometric mean
Hint: Take logs and apply L'Hopital.
Oct
16
awarded  Good Answer
Oct
8
comment Probability/Decision- infimum over set of expectations (can be interpreted as decision problem)
I edited the answer to expand on this point, Eric.
Oct
8
revised Probability/Decision- infimum over set of expectations (can be interpreted as decision problem)
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Oct
7
revised Probability/Decision- infimum over set of expectations (can be interpreted as decision problem)
added 235 characters in body
Oct
6
answered Probability/Decision- infimum over set of expectations (can be interpreted as decision problem)
Sep
30
awarded  Explainer
Sep
9
comment Mean of squared “sum of squared errors”
See Advanced Theory of Statistics, Volume I, chapters 3 ("Moments and Cumulants") and 12 ("Cumulants of Sampling Distributions--(2)").
Sep
9
comment Mean of squared “sum of squared errors”
Jonas, the very first comment to your question indicates how such derivations can be done. Your example, when fully expanded, is a quartic form in the data and therefore the expectation (because it's a linear operator) becomes a homogeneous polynomial (in a suitable sense) of the first four moments of $X_1$. Mathematica merely is doing that routine algebra under the hood. An algebraic theory has been developed; it is explained in great detail in Kendall & Stuart (5th Ed.).
Sep
8
comment How to find a mapping function from n dimensional space to m dimensional space
Could you perhaps add some information to this question to show readers why it might be of interest on this site?
Aug
25
awarded  Yearling
Aug
21
revised Is there a name (and use) for an average based on the unique values of a set of data?
Improved theTeX markup
Aug
4
comment Does affine equivariance implies shape unbiasedness?
(Due to lack of answers on CV, this question has been migrated to Math at the OP's request.)
Jul
30
revised How to simplify a sum with binomial coefficients multiplied by $k^3/2^k$?
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Jul
30
revised How to simplify a sum with binomial coefficients multiplied by $k^3/2^k$?
added 176 characters in body
Jul
30
answered How to simplify a sum with binomial coefficients multiplied by $k^3/2^k$?