tttjjj/elt_bench huggingface dataset:
@PatrickCaldon I understand your point of view, but more parameters to deal with do not always mean better tool, if you do not know how to configure them in a suitable way. Even if possibile, a long study might be needed; or, you might not need so broad tunability for the purpose of your applciation
@rebetan, if this answer was appropriate feel free to mark is as correct.
I don't really see how accuracy could be a property of a particular statistical package rather than the data, unless something goes really wrong with the code (which is not the case with the above R packages, as far as I can tell). Could you tell us more about your data?
@hoof_hearted I think you are dealing with a conditional distribution here. So if $Z$ is the weight of the rats, $X$ is the distribution of the mean, and $Y$ is the distribution of the standard deviations, $Z|(X,Y)\\sim N(X,Y)$. $X$ and $Y$ are independent normally distributed here. The joint distribution of the three would be $f_{X,Y,Z}(x,y,z) = f_{Z|(X,Y)}(z|x,y) f_{X,Y}(x,y)$. To find the (unconditional) distribution of $Z$, you would have to integrate the joint distribution over all possible values of $X$ and $Y$.
I've got the answer from http://test.scs.fsu.edu/presentations/wkshp_Mar2006allgood_rev.pdf: **"When two or more forecasts have same value (most commonly 0), random selection is made for which bin receives the count"**
I think the Particle Filter converge in Distribution.
I think you need to add more information to your question, you can use glmfit to fit a GLM in Matlab. However if you are solving a classification problem you may prefer to use classify
Just to understand the statement: you're supposing that $\\mathbb{E}[X_{n+1}\\mid\\mathscr{F}_n]\\neq X_n$ a.s., and want to prove that $\\mathbb{E}[T(X_{n+1})\\mid\\mathscr{F}_n]\\neq T(X_n)$ a.s. for any measurable $T$. Question: can you do something when $T$ is the indicator $I_A$ for some special measurable set $A$?
Here's a start: http://stats.stackexchange.com/search?tab=relevance&q=irls.
Thank you, the paper is quite helpful.
I am impressed that your eyeballing was this accurate.
@Michael There is only one dependent variable. Regarding nonlinearity, without going into the details, I am in situation where I suspect the presence of, and am not confident that I can rule out, nonlinearity. Worse though, I cannot really derive what the nature of the nonlinear relationship would be, if it is indeed nonlinear (eg. polynomial, exponential, etc.). I posted some further details above.
@gung You are a little faster than I am!
**This response seems essentially wrong** as I forgot about the sampling issue.
In this situation, I think anything you get will be a sample and the population is something like the lifetime of the server or something.
It is possible to write well-formed $\\LaTeX$ on this site.  Please rewrite so that you're sure you know what should be written - otherwise it's guesswork for answerers.
I'd like to add this magnificient flowchart (to mymind anyway) : http://scikit-learn.org/stable/tutorial/machine_learning_map/index.html
Please don't cross-post in future; and the proper way to move to other site is by asking for migrate using flag.
Thanks so much! This is helpful! I'll try it.
Could you elaborate on your answer?  Even pointing to some examples would help.
It's hard to give more detail because you haven't included any idea of what you want to do with the data. That said, R has a package called FDA (functional data analysis). You can read the first chapter here to see what kinds of questions you might be able to answer: http://www.kermanshahmet.ir/MyFiles/admins/xabar/file/ramsay_j__silverman_b__applied_functional_data_analysis___methods_and_case_studies_springer_2002.pdf
+1 Using an actual database is a huge step in the right direction.
I think you should be more specific about what your problem at hand is, and what you're trying to accomplish.  I think as your question is written, you are unlikely to get a satisfactory answer.
Do you mean like the "graphical moments" illustrated [here](http://www.quantdec.com/envstats/notes/class_06/properties.htm)?
What I mean by the conclusion is "there is a relationship between the dependant and independent variables".
@whuber Just to clarify, this was not a test stopped as soon as significance was found. The power study was done afterwards though to get an understanding of how close the sample size that HAD been gathered was to the recommended sample size, given the effect size noted, and the implications (if any) on validity of the result and how strongly the test significance level holds. Apologies to you both (the comments are interesting and appreciated) but I'm still not sure if I'm totally clear on this.
PROC MIXED uses likelihood based estimation, while PROC GLM does the sum-of-squares approach. They also treat missing values differently. The Greenhouse-Geisser correction for sphericity is the giveaway: it is only used during repeated measures ANOVA. PROC MIXED can be used to perform a correct (and arguably preferable) analysis, but the results will not be identical.
The old style of looking at mediation (and moderation) viewed them as either present or not. The seminal article is by Baron & Kenny. More recent work views mediation as a continuum, from non-existent to weak to strong (see work by e.g. MacKinnon)
You don't need `as.numeric`.
That's some incredibly sloppy wording on the part of the authors.
This is really two different questions, because the one about piecewise linear regression does not involve sums of t distributions.  If you still are interested in the one about t distributions, please post it as a separate question.
I have removed your signature. There's no need to sign your posts as your name appears immediately underneath anyway. Please see [this section of the faq](http://stats.stackexchange.com/faq#signatures)
(+1) The power analysis example is a good one. In almost every situation I'm interested in knowing power (or sample size for a particular power) under a particular parameter value, simulation is the only practical way I can get a handle on it.
What are you modeling?  It might help my speculation as to why this would be if I knew that...
Thanks for the code proof of the estimated coefficients being the same. Also the warning on creating my own is useful: I wanted to create my own because then a model variable would tie back directly to a database column by name (which could be useful downstream), but looks like I need to understand the issues with how I go about doing this.
I'm afraid I don't follow this at all--must be Monday morning. :-) What is the relationship, then, between $x_{min}$ and $x_{min}'$ in your answer?
They reason that ES per se is not elicitable, but it is composed of two elicitable components: the quantile ($c = {q_\\alpha }(L)$) and the expectation conditionally on the quantile ($E\\left[ {L|L \\ge c} \\right]$), hence they call ES "conditional elicitable". I do not get the intuition behind  ES integrated by several VaRs. They refer to [On the coherence of expected shortfall](http://arxiv.org/pdf/cond-mat/0104295.pdf) Proposition 3.2, but that does not seem to help me understand it.
Could you perhaps edit your question?
Thanks you @daroczig for the math stuff, looks much more readable now!
Since the 1st condition also is stronger than the usual one, it would be helpful if you could provide the reference for these two conditions.
+1 for "Perhaps she's not talking about the maths!" How's my proof?
Why do you want to know? What will you do if it is normal? What will you do if it is not normal? Is this a testing of residuals from a regression?
(+1) Welcome to the site. A couple notes: (**a**) We generally do not give full answers to homework problems on this site, except in exceptional circumstances . Providing hints as answers is *strongly* preferred. ([FAQ](http://stats.stackexchange.com/faq#questions)). (**b**) The last part can be simplified a little by noting that immediately from the definition of $X_n$ we have $\\mathbb E((X_n - X)^2) \\geq  \\frac{1}{n} (e^n-1)^2 \\to \\infty$.
Hello. Yes, you wrote correctly. I think that you should have a look at wikipedia article about inflection points, there's a video where you see the progress of the slope, explaining your issue.
How do you evaluate the size of the bootstrap test? Can't you use the same approach for the asymptotic test, and if not, then why?
@cassetete, congratulations! It would be good if you posted your solution as an answer. So that somebody can find it by googling it. Or you can accept my answer, wink, wink, hint, hint, if it was the proverbial push over the cliff.
I'm wondering whey you see a need for a special algorithm.  If any matrix has unique eigenvalues, then just decompose it: its eigenbasis will be an eigenbasis for all other simultaneously diagonalizable matrices.  For EVs with multiplicity, iterate recursively by decomposing additional matrices on the eigenspaces.  What is the problem with this approach?
Nifty use of hidden "spoiler-quote" formatting for a `self-study` question.
I like the idea of estimating the fixed parameters and have tried the gee library. There are other libraries too (geepack, for example). Are they worse for some reason? In my field people need to report p-values. Is there a way to get these from the estimates and also conduct pairwise comparisons taking clustering into consideration?
+1, and I also like the paradoxical implications of your rule of thumb.
(+1) You could add [psychometrics](http://en.wikipedia.org/wiki/Psychometrics) to the list of domain specific applications of applied statistics to domain specific problems.
@Aniko I don't know how that would make sense given the context. The authors test their regression algorithm on many different datasets, and then calculate the RE, as per above, for each dataset. Then they average RE across all problems.
Regarding your first comment, yes, it does. Regarding your second, I am not sure ... That is one reason I didn't mark this as a duplicate.
Thanks for the info. I did find the paper interesting. Although it shows a counter example for $R^2$ value I'm trying to find a paper/review that discusses the trend/convention in research involving human behavior/performance. –
I am glad to see that you found the package useful, thanks! BTW I have fixed a typo in the function that plots the results so that in the next release of the package the y-axis will cover the range of both the 
original and the adjusted series.
Also consider trying to utilize the formatting available to questions on the site, see the [advanced markdown help](http://stats.stackexchange.com/editing-help). I see none of your previous questions have answers, and if you edit them to be slightly more readable they will bump to the top of the list and may attract answers.
Could you summarize the main points of that book in relation to the OP?
Classic! My dad loves to quote this one.
I edited my solution.  I should have said A is the event that it came from group $X$.  B is also an event and that event is the actual transaction that occurred.  For example, lets say the transaction was buying a car so B would be the event of buying a car.  So Pr(B) = "the probability of buying a car" or in your jargon the probability of a certain transaction.  Hopefully that clarifies now.
There are plenty of **great answers** on this site that try to answer your question. Please see [Training with the full dataset after cross-validation?](http://stats.stackexchange.com/questions/11602/training-with-the-full-dataset-after-cross-validation), [this answer](http://stats.stackexchange.com/a/72324/2798) and [many](http://stats.stackexchange.com/questions/79905/cross-validation-including-training-validation-and-testing-why-do-we-need-thr?rq=1) of the [other](http://stats.stackexchange.com/questions/65128/nested-cross-validation-for-model-selection) threads on this topic.
FYI, I have updated the question again with even more details. Thanks !
Move to StackOverflow?
If you generate correlated random variables with each having mean zero, then add a constant to each individual variable, what is the outcome?
What precisely do you mean by "uncertainty"?  But whatever you mean, if you have only annual figures the answer is almost certainly "no", because of the (literally) seasonal effects.
I edited the answer
We can draw two connections here. First, @bnaul's example is illustrative because the exponential is a special case of the Weibull, the latter of which has a *monotone* hazard function. Depending on the shape parameter, it can cover both the case of "the longer you wait, the longer you expect to wait" and also the case of "the longer you wait, the shorter you expect to have to continue to wait". Your example is nice because the Pareto is the exponentiation of an exponential, and from this fact many of its properties are derived, including the one you mention.
After three days of reading all comments & looking at the data I think I finally understand. Basically, I should make sure my samples for both Agents are the same size and see if their variance is similar, if I have this then I can do ANOVA to determine if there is difference between the agents. I need to be comparing apples to apples essentially, in order to determine if there is indeed difference in what is being measured. Also, I can't do the ANOVA straight up on the data points, but rather bucket them into time intervals and average those because of CLT, which gives me normal distribution.
@Joel: If they are independent I would just check the probability that as many or more than the seen responses are in the appropriate (skewed) direction. I only have a minor clue that some participants may be more susceptible to the effects studied than others, however there is no indication other than the answer as to which ones. I am not so much interested in differences between participants as in differences between answering behavior of the same participants in different settings.
In my opinion, the workflow {Smiles->Chemical Structure->Molecular descriptors->Statistical Model} should be used
@gung thank you for pointing that out, it was typo. Btw: Reference used is Hartung: Statistik, Oldenbourg 14th Edition (unfortunately only available in german)
What problem are you trying to solve? What is a copula? What have you read? What have you tried? Where did you get stuck? What is a QPE?
Please be more specific -- this site is not a place for *do-the-job-please* questions.
"Heavily correlated" because meany correlations are high (near their maximum value). The diagram [here](http://en.wikipedia.org/wiki/Correlation_and_dependence) may be of some use in seeing the relationship between the 'nearly linear' plots and the correlation values.
I have added a paragraph to my answer to address your question.
I cannot confirm it. I can see both columns that you miss. Are you doing everything right? Can you show the syntax of the command?
Actually the CART algorithm is the method in my opinion for constructing a classification/decision tree.  It involve pruning and cross-validation which adds to the computational complexity.
Thank you very much @Glen_b, I'll certainly consider whuber's comment.
I've hosted it on my dropbox account.  Here is the link.  https://www.dropbox.com/s/fjv2lz8z9bem5au/data.txt.zip  Let me know if it doesn't work.
@julieth:  That was my sense of the 2001 paper upon reading the abstract alone, but the formulas in the paper (e.g. 27 - 30) do seem to involve a quantity referred to as q.  Then again, so does this 1999 paper you cite.  My sense though is that the 1999 paper implements a re-sampling approach which is clearly (from looking at the code) is not what my stats program is doing (R; p.adjust)... but I may be wrong.
You are -and in a more clear manner than one usually finds, which is good.
Yes, but worth mentioning and at the time of posting, I didn't have authority to make comments
@Jens the problem with that comparison is that with Gaussian **errors** (not response!) the function calls go `gamm()` -> `lme()` -> compiled code and iterate between the GAM and LMM bits. With non-Gaussian errors, you are using a PQL approach to fitting GLMMs in a LMM framework. So the calls now go `gamm()` -> `glmmPQL()` -> `lme()` etc and each of those steps need to be iterated to convergence. So you can't compare timing of compiler compiled code versus non-compiler code between Guassian and non-Gaussian runs.
+1 for there is no one best solution.
From Laurberg: "Theorem 8 states that the NMF is unique if the row vectors in W are boundary close and the column vectors in H are sufﬁciently spread".  AFAICT, NMF is *not* generally unique to within permutation/scaling.
If you are looking at $I_A$ the indicator random variable for the event $A$ and similarly $I_B$, then I do not think you can get the correlation between them greater than about $0.5216$, and that happens when $\\Pr(A\\cap B) = \\Pr(B)$.
Warning: it's not clear that what you're trying to do is something that ought to be done, although I can't quite tell what's going on here. Are you trying to jackknife? What are your cases? Is each a single observation? (This is a common use of *case*.) Ie, is each case an ordered 4-tuple?
with the revised model...please take a look...based on your comment, can I interpret the coefficient for the interaction as the following: A male worker earn $6 (-.69+.0888 = -.6) less than a female worker?
"I'm interested in predicting the effect of some ordinal IVs on performance" suggests that the *independent* variables are discrete and ordered.  It is not clear--unless I missed something in the comments--what the dependent variable is like.  It might or might not have a "bell shaped" distribution and it might or might not be discrete.  This is a very confusing question due to its vagueness.
I would need $\\: t > n \\;\\;$. $\\;\\;\\;\\;$
For the sample size in binomial designs, sometimes one uses the 'worst' case p = 0.5 because usually the proportions are not known in advance. Further note that there are slightly better methods that the simple z approximation, e.g. Wilson's method. But your solution looks nice anyway.
I'm at a loss to understand how I failed to be clear. None of the $\\theta$ values listed can produce a sample {1, 2, 3}. Forget statistics and imagine instead this experiment: I have an ordinary 6-sided die, and a coin with sides labelled "1" and "2". One of the two devices is to be selected and tossed. You will work out the chances for me after I observe the result, but you have to be elsewhere right away, so I will send you the result (just before I leave on vacation). I write outcome on a postcard and send it to you. When you get the card, it says "8". Which is more likely to give 8?
Thank you so much! I think it should be work here.
That's actually somewhat more advanced thinking that my answer was aimed at, as I did not even approach identification issues. And yes, you need to follow the rank and order conditions and have enough excluded instruments to make things work. My reading of the rank condition, though, is that $z_2$ must have a non-zero coefficient in the *structural* form for $y_2$; or, with more instruments, that at least one of the instruments excluded from the first equation has a non-zero coefficient in the structural form for the second. Or something like that.
Good graph but I would remove the gridlines to make the data clearer.
It means that, regardless of whether it is significant or not.
@AndyW, I think that we are interpreting the original question differently.  My answer gets the researcher started by letting them know if there is something more that they need to look for, or if the residual plot is reasonable.  What to do if it does not look reasonable is then the next step and beyond my answer (though some additional assumptions could be compared using a new set of simulations).
@this.is.not.a.nick The complication is that classical causal inference does not make a difference between confoundng variable and 'feature of the treatment group'. That is, treatment may have more than one effect (say on Y and on Z) or there may a causal chain (treatment affects Y, which affect Z). It is true that controlling for Z then does not make any sense. There is more recent work on causal graphs, which includes these causal mechanisms in the equations. A good introduction is Morgan & Winship (2007). Conterfactuals and Causal Inference.
It sounds like you tried your model 2 ways, entering smoking first or entering sex first, and found 2 different patterns of results. Is this the basis for your question?
What is the original source of this?
@ttnphns Exactly. I plotted toy data in 2d and checked the rotation. It works the same as if data was mean-centered, but just a pivot point of rotation is not located in the mean (honestly, I don't know where it is). My concern now is if it can affect optimization results in some way.
After receiving optimized coefficients, i just multiply them by transposed eigenvectors.
See also this question: [Calculate probability for LibLinear classification results](http://stats.stackexchange.com/questions/36167/calculate-probability-for-liblinear-classification-results/36204#36204)
(1) no, because the total correlation will include the error covariance. (2) see my answer [here](http://stats.stackexchange.com/questions/93861/kalman-filter-and-box-cox/93862#93862)
Kriging is good, but there are lots of ways to do it. Some kind of inverse distance-weighted interpolation is simpler to do and to explain.
+1! I'm glad you nominated yourself. I don't think the community could ask for a better combination of (i) statistical/mathematical knowledge and (ii) the even-keeled, common sense approach required for a moderator. You have my strong endorsement.
Also, why isn't $f_X$ just `pdf2`
The list of topics is typical of a first *probability* course. For a decent treatment, you need to look at Internet books/notes that assume at least a first year calculus course, and preferably a little more.
Is the question about the statistic itself or about its significance test?
@DJE I'm trying to see if the dataset only with complete cases is a significant sample of the whole dataset. And if it is I will use only the complete cases otherwise impute the missing values.
$s_1$ and $s_2$ are data-dependent, but the data are fixed, this is like a posterior distribution in Bayesian statistics. In the expression of $\\tau$, each of $\\bar x_1$, $\\bar x_2$, $s_1$ and $s_2$ is fixed, and $\\delta$ is random.
Thanks @ Druss2k Glen_b Greg Snow
(cont'd) For kurtosis - I thought that "heavy-tailed" distributions had **more** of the data within one $\\sigma$ of the mean, due to the heavy effect of outliers on $\\sigma$. Wouldn't the forth moment be much more influenced by the density far from the mean than closer to the mean, in the sense that no matter how concentrated the probability is within 1 sd, you can adjust the tails to counterbalance it with only minor changes? Either way, I agree that kurtosis has a controversial interpretation (see Taleb "The Black Swan") and peakedness and tails are part of it, but asymmetry affects it too.
If you assume the covariance matriz of the errors is diagonal you can estimate the covariance matrix and then WLS regression with the estimated weights. To do this you can check feasible generalized least squares on http://en.wikipedia.org/wiki/Generalized_least_squares
Sorry, I can't see your notes from here. The statement might make some sense in context. You haven't defined "better".
The nice thing about this answer is that it applies whether or not the random variables in question admit a density function, as opposed to other answers on this thread. This is true due to the fact that expectations can be defined with Stieltjes integrals using the CDF, with no mention of the density.
This is not generally true.  Take, for instance, $(X,Y)$ for which $Y=0$ and $X$ has any nondegenerate non-continuous distribution. Although the rank of the covariance matrix is $1$, this distribution does not have a density on any one-dimensional submanifold of $\\mathbb{R}^2$.