tttjjj/elt_bench huggingface dataset:
TBATS is an acronym for Trigonometric Box-Cox ARMA Trend Seasonal. They are exponential smoothing state space models with Box-Cox transformation, ARMA errors, Trend and Seasonal components. The reference is De Livera, A.M., Hyndman, R.J., & Snyder, R. D. (2011), Forecasting time series with complex seasonal patterns using exponential smoothing, Journal of the American Statistical Association, 106(496), 1513-1527.
@celiomsj  You might like to raise these points as a new question.  Then they are likely to be seen by more participants, and there is more space for answers than comments permit.
@suncoolsu , the R package diagram may be able to do the same "arc diagram" Shane pointed to. It looks like it would be hard work though to get the "plot web" to look like the visual above though. http://cran.r-project.org/web/packages/diagram/vignettes/diagram.pdf .
@RobertKubrick, Huber (1964) showed that this estimating equation gives statistical inference that is correct in the face of errors that are a mixture between normal and long-tailed errors so it's robust in the sense that it can handle this type of non-normality. Re: your last comment - that's not true. Note that we scale by $\\sigma$ - a poorly fitting model can have normal errors. Once we scale by $\\sigma$ those errors will no longer be "large". This, in some sense, downweights observations with residuals inconsistent with normality although, as I said, this is not how the method was derived.
(+1) Nice work taking a question that is on the border between being domain specific and being a statistics question and providing some good general advice.
Hi @FrankHarrell I've seen you make this remark on trees before. Have you got any links or cites where I could get more info on this? The classic book on trees uses, as I recall, quite small data sets (dozens of observations, not 100's of thousands).  Thanks!
@Flask that's a good point. I've edited my answer to try and make it more general.
"Ranking" per [Everitt](http://www.amazon.com/The-Cambridge-Dictionary-Statistics-Everitt/dp/0521766990/ref=sr_1_2?ie=UTF8&qid=1351444998&sr=8-2&keywords=dictionary+of+statistics) (at least, an earlier edition) just means " the process of sorting a set of variables into ascending or descending order". 

So, what do you mean by ranking?
Thanks Stat-R. I don't know an awful lot about stats. I have looked at the mgf page. If I understand, it's about expressions of the form $e^{tX}$, where $X$ is a random vector but $t$ is deterministic, so in effect it's an exponential of a sum of rvs, as opposed to an exponential of products. So not sure how to proceed from there...
A simple way of doing this with monte carlo is to draw a set of sigma from your constrained distribution and using this sigma, calculate the chance of not making a new hole. Thus, draw many simulated shots from this and count what fraction don't make new holes. This can then be used to update the likelihood. Then move on to the next one and do the same. Now you have your final likelihood.
you have 6 independent variables, is there a particular reason you need only a subset of them in your model? Why not including all of them?
Actually I think well-separated is the only criterion. "Being entities" means you are assuming that they are supposed to have some type of distribution (e.g. Gaussian), if I understand correctly. Do you really expect clusters to have a specific distribution?
Brilliant! Thanks again @Nick!
So what is there to not understand? You have a non-smooth problem, so the bootstrap distribution does not have to be a nice Gaussian (as it would be in the mean of i.i.d. data and other simple problems). Check http://dx.doi.org/10.1002/cjs.5550340103 for a good list of issues you may encounter with the bootstrap.
see [Chebyshev's inequality](http://en.wikipedia.org/wiki/Chebyshev%27s_inequality)
Stepwise algorithms are indeed lousy for revealing the best variables that can explain an outcome.  But they can be quite useful if all one wants is to know are some good, not-too-correlated predictors of an outcome.
You will need some kind of control over the error distributions, for otherwise they could dominate the situation. For instance, make the first $10$ of the $E_i$ standard normal, then the next $100$ of them normal with variance $2$, then the next $1000$ normal with variance $3$, etc.  As $n$ grows larger and if $F$ has finite variance, the variance of the empirical distribution will grow arbitrarily large, so $\\sqrt{n}D_n$ could not possibly converge to the Kolmogorov distribution.
I wouldn't say that NNs rely on kernel functions - they rely on a [transfer function](http://en.wikipedia.org/wiki/Artificial_neuron#Types_of_transfer_functions) to achieve nonlinearity, but this is not the same thing as a kernel function
Isn't a "response variable" the same as a "dependent" (variable)?  How, then, can it be at once "continuous" and "discrete"?
If $X$ and $f(X)$ are independent, then $f(X)$ is constant almost surely. That is, there exists $a$ such that $\\mathbb P(f(X) = a) = 1$.
Note that $Z_i$ are endogenous, i.e. they correlate with regression errors. As stated the system cannot be estimated using simple OLS.
Thank you, I fixed the discrepancy
The parallels in my trapezoid are vertical; in the package they're horizontal, so it's a different distribution. To get a random value from my distribution, generate x,y iid U(0,1); if y > 1+a-2ax then use 1-x else use x.
"Can" is fine.  You are welcome to edit the text.  Otherwise, as stated I trust the language is clear enough to warrant precise responses.
Indeed, this test seems far more appropriate. So I should not use the frequencies for each rating, rather, I should have a table composed of the ratings from each person under the two conditions, such that they're linked. Thanks very much.
@Andy Without any intention of sounding critical or deprecating, the only advantage I can think of for the qualitative method is that it makes no demands on the analyst's understanding or competence: this makes it accessible to more people.  The qualitative approach is fraught with difficulties.  For instance, there can be large *apparent* differences between both the slopes and the intercepts by chance alone.  A qualitative assessment of just the coefficients won't be able to distinguish this situation from real effects.
This seems like the right place, but, since this is homework, you should add the `self-study` tag.
Given the fact you are making parametric assumptions to start with, when you fit your original model you might as well use them and get a better estimate (ie. if you don't believe the model why bootstrap it anyway). You have the correct idea; I just want to highlight though that there is a trade-off between the non-parametric bootstrap you outlined and the parametric bootstrap that `lme4`'s native `bootMer()` function offers.
Can you say a little more? Do you need to control probabilities for each outcome? Do you need to specify particular predictor relationships? Stuff like that may help guide response to your needs.
I love this book too, but I am dyed-in-the-wool Stata user as far as data management is concerned. While I disagree, others on this list have argued that it's too Stata specific to be useful, so caveat emptor/lector.
Sorry about not providing the data and thank you for making it for me. It would be much appreciated if you found out why is it different and explained it, along with how it can not be wrong when SPSS returns correct means using the same model.
Hi. Actually, I agree with you to some extent. But suppose that I had only one variable, i.e. the complexity of writing before and after the treatment operationalized by counting the t-units in the three students' essays before and after treatment, and, hence, coming to sth like 600 for students one before the treatment and 2100 for the same student after the treatment and more or less the same thing for the other two. What statistical procedure would you use? t-test, wilcoxon, or simply chi-square? Thanks
Now I'm getting confused, my professor said that I'm using different sets of data (the search results), despite of the query. If I insisted to use paired t-test (just like how I considered it), I'm afraid my professor wouldn't defend me on my mini-thesis examination date. Sounds cheesy I know. Any more advice?
A paper from 1966 did look into this a little, however I have not seen one more recent.  I maybe things have changed since? http://www.jstor.org/discover/10.2307/2282780?uid=3739464&uid=2&uid=3737720&uid=4&sid=56147667433
Agree strongly. Both great books. Start with Bayesian Computation With R, then get Gelman et al.
I think what you said makes sense, check out this question [link](http://stats.stackexchange.com/questions/32113/question-regarding-sampling-estimation-and-accuray) which is a variation of this one, thanks.
I agree with @Glen_b here and suggest that even this wording misses the key point. Identifying the most appropriate test depends minimally on knowing the exact generating process for the data, which is, shall we say, unusual. It is more common that there are several possible tests with differing advantages and disadvantages.
+1 Thanks for the link and your answer! I'm happy that this question still attracts interest and that more can be added to it. This was insightful.
cite that article please.
Could you explain what you hope this "pseudo R2" will do?  What is it intended to *mean*?
@MegaChunk AFAIK the p-value from KS test is not very informative, as the distribution is never perfectly normal and thus if you have enough number of data points the null hypothesis is almost always rejected.
Thanks for your comment. I will look into that, but need a bit of time.
Retrain the model ? Your question is to vague / unspecific. Where exactly is the problem ? What is the problem with adding the new data to the training data used so far and retrain the model ?
Regarding degrees of freedom, look at [this CV Q&A](http://stats.stackexchange.com/questions/884/what-are-degrees-of-freedom) or [this nice explanation](http://www.jerrydallal.com/LHSP/dof.htm) referred to in one of the answers.
1) This is the same as taking the product of the p-vector; I just do it that way out of habit.  The result is the joint probability (or density, if continuous distn's used) of the input data given the parameter estimates.  2) Zero demand + a gamma distribution = fail.  Something must be done about those zeroes or about the gamma distribution.  3) In that case, stockouts are irrelevant.  The greater point was that even moderate to high demand items can have zero demand days; "stockouts" was just a mechanism by which that can happen.  Zero demand days don't work w/ the gamma dist'n.
@Scortchi, the diploma follows you for many years after graduation regardless of the private/public split. This often means that you are denied accesss to the best positions in a company (say, the lead of a team of statisticians) because of the school you graduated from. Of course, there are some SMEs that are taking the style of "English companies," where they say they care less about your diploma. However, even there you often see people coming from top programs. Side note - I'm an American doing a stats masters in France.
@cardinal Well, I am mostly interested in finding a test to test time-series data against a zero-mean and independantly distrubted stochastic processes (for instance, a random variable at time t: Xt~N(0, f(t)), where f(t) is some non-constant function), practical experiences shows BDS and runs tests works poorly in such cases, as the authors of these methods admitted.
A more general version of this question is addressed at http://stats.stackexchange.com/questions/5747.
Excellent, thanks! I'll give it shot. As for how meaningful it will be, I'm not sure either. I have hunches that I want to confirm or deny though, and this should get me started on that path given that I'm comfortable enough with model validation to check the validity of my results.
Your idea is a form of *hierarchical sampling.* The problem has a spatial element to it, suggesting that results in one sector will be correlated with results in neighboring sectors.  For a practical review of traditional and more modern sampling designs (including adaptive sampling, some kinds of spatial sampling, and other methods of ["observational economy"](https://www.google.com/search?q=%22observational+economy)) see [Steven Thompson's *Sampling*](http://www.amazon.com/Sampling-Wiley-Series-Probability-Statistics/dp/0470402318/ref=dp_ob_title_bk).
I guess your SVM doesn't work at all, but don't know why ! also may be its better to normalized your data ...
From what I heard, the use of the quadratic loss is more due to historical reasons than from practical ones. Interesting question! :)
What if a model consists of two nominal variables, one continuous variable (all as fixed effects) and one grouping variable (random effect) with 3rd-order interactions and, moreover, number of measured subjects is equal to number of observations or records in the dataset? How should I cover this in the model?
This is very broad. It is especially difficult to answer unless people understand what you mean by "video modalities" and "credibility scores". I am not voting to close yet, nor promising to answer, but more detail and a more specific focus would do no harm.
What did you do to conclude the interaction was significant?
For an ARIMA model (p,d,q) You will need at least as many past observations as the maximum of p+d or q, i.e. it depends on the order of lagged terms in the model.
Two things must be clear to answer this question. 1. What exactly do you want to do based on the data of the campaign respondents? 2. How did you go about sampling the campaign respondents (clearly and in detail)?
Thanks for the reply Peter.  In fact, my events have to occur at the same time at both positions (X and Y).  If my question was slightly different, I wonder whether there would be a simple solution.  Imagine that I am not talking about errors, but two different types of event that can happen - event A and event B.  If there are two places that these events can happen, and they happen at the same time in each of these places (so vectors A and B are fixed), what is the likelihood of observing my particular pattern?  e.g.
how if i got some  value $k$,then what does it mean?
+1 false positive and negative rates are what's missing. But I think the last paragraph is irrelevant. The point with those properties (*not* the ones in the bullet points)  is that you can break it down to a more accurate percentage for your conditional calculation. i.e. you can figure out what proportion of white women have lupus in the US.
After some 2nd thought, I feel that my original confusion is still unresolved. Yes, gls can be used to demonstrate the correlation structure and mean squared rums, but the model underneath it is not exactly the same as the paired-t test (or one-way repeated-measures ANOVA in general), and such an assessment is further supported by the incorrect DFs and p-value from gls. In the contrast, my lme command with compound symmetry provides the same F, DFs, and p-value. The only thing I'm puzzled about is how the lme model is parameterized as stated in my original post. Any help out there?
@ttnphns the rule is that the `subs` in same class are similar with each other compared that from other class. The classification here is natural/biological (for example chromosomes - markers from same chromosomes are correlated/associated in contrast to that from other chromosome are not significantly correlated or are independent). So I know the classification but how I got this classification is biological, but outcome should follow statistical rule - from the same group should be associated compared to other group.
Pretty well posed question (+1 from me), I like the background context, it makes it easier to judge which assumptions are plausible to make.  I'll have a go at answering, post my answer at some point in the near future
I think even the simple case of x = N(0,1) and y = N(0,ysd^2) is interesting. Obviously as ysd approaches zero the product x*exp(y) approaches normality, but has the case of ysd >= 1 been studied?
Any references for "Sim" or "Johansen"?  Thanks!
The reason people are confused about the distinction is that our conventional terminology is ambiguous. Non-parametric tests also assume "an underlying distribution"--otherwise you would have no basis to apply any probability theory! Any clear and correct answer has to make two key points. (1) Statistical tests assume the data are described by some unknown distribution *within a specified set of distributions.* (2) In parametric settings those sets can be described in a natural, continuous manner using a *finite* number of real values (the "parameters").
Appreciate your answer! Does the "in-between" method that you've mentioned have an **implementation** as `R` function or package? Actually, I start **questioning** whether I really do need *distribution fitting* **at all**, as my ultimate goal is to perform full SEM analysis. Since I have chosen a *PLS-SEM* analysis, which "doesn't impose any distributional assumptions on the data" (Sanchez, 2013, p. 34). **References:** Sanchez, G. (2013). *PLS Path Modeling with R.* Retrieved from http://gastonsanchez.com/PLS_Path_Modeling_with_R.pdf.
There are several different models you could build based on this data. Using more than one predictor would rersult in a regression plane though, so the task seems to imply that you choose one. But the dataset itself does not necessitate a specific choice, so some clarification is indeed missing...
Adding a bit of explanation - you don't really have multiple outcomes, you have one outcome with multiple possible levels: No disease, psoriasis, cancer ...
I happens for the same reason it happens in ordinary multiple regression. See the diagram [here](http://en.wikipedia.org/wiki/Simpson%27s_paradox). There will be some collinearity among the variables, but it can be quite mild.
Tiniest of nits: the place of publication and publisher of Kendall's book was London: Griffin. You're citing the printer, I believe.
+1 nice complement to what's already here.  I should have brought in effect size myself, and I'm a *huge* fan of Abelson's *Statistics* *as* *Principled* *Argument* -- I'd give you another +1 for that if I could.
Bootstrapping (sampling with replacement) seems a more natural way of performing a large number of re-samplings, as it is more randomised than repeated cross-validation.  For bootstrapping the use of bagged enembles is a nice feature, with the out-of-bag error as a performance estimate.  There isn't a huge amount to choose between the two.
c4 and d2 are constants. Look for them here http://finzi.psych.upenn.edu/R/library/IQCC/html/00Index.html 
As for "in and out of control" processes, I think it is too elementary in SPC. Search for "in control" here as an example http://www.cheresources.com/spczz.shtml
UPDATE I found a way to do this by just doing a little C coding to munch on the data. C is so much easier than RTFM.
(-1) All the information you need is in the Wikipedia article you linked to.
I believe the Introduction to Probability and Statistics Using R is the closest one but still not the one I am looking for. Im editing the question in a second to give a reference of exactly what I am looking for, but unfortunately uses miniTab instead of R. The Art of R Programming seems more concerned with R than the fact of learning of statistics (correct me if I am wrong), and again the previous book concerns me about being rigorous enough on statistics for make assumptions of statistics background, which I, unfortunately lack. I will also summarize the main points.
It sounds like the OP has *matched* data, so it may be better to use the Wilcoxon matched-pairs `signrank` test, rather than a test that assumes independence over time.
@user41270: assume that you have a classifier that can tell signal from noise, but not with perfect accuracy and you have equal amount of signal and noise trials. What bias will result with the best accuracy?
I like the part about "My current working practice is to use R to prototype and use C when I need an extra boost of speed." - it sounds like the job description of my poor unworthy self and the C++ developers in the next office... and I think it really captures basically *any* situation involving R, C/C++ and an issue in statistical computation.
@Macro: I appreciate it. I posted my answer. Would you please check the random effect model. Should I adjust for other covariates that i'm interested? also, should we only look at students' baseline scores in this longitudinal study to calculate ICC?
(i) You don't need to remove the third row - the NA will cause the fit to ignore it. (ii) You can then extract the fitted value for the missing observation from the fit of the linear model, whether direct from the object or via the `fitted` function. (iii) It's best to specify the model in your call to `lm` or you're relying on the columns being in the right order.
Draw vectors from this multivariate normal as you usually would, and then check the Mahalanobis distance.
This is most commonly called the delta method in statistics.
If the variance is zero, the variable is constant. I am happy to admire the symmetry of every constant.
Hi Pocrastinator, I have a typo in my SUM function (see Daniel's comment). That's why boot can't work with AREA function. thanks.
Ah, I see your point.  Maybe the real problem description does have two actions, "left" and "right", and there are no transition probabilities, hence deterministic.  In that case, all those $0.5*V_k(s=2)$ statements etc. should be changed to just $V_k(s=2)$ if you choose "left" and $V_k(s=3)$ if you choose "right", and the value $V_k(s=1)$ is the maximum over choosing "left" and "right".
@Andy W: I've just added a link to what appears to be the relevant section of the Wikipedia article on ANOVA.
On this site, good keywords to use for searches are "errors in variables" and "deming regression."  In 2D, PCA *does* provide the fit you are looking for. (Proof: diagonalizing the variance-covariance matrix shows that the smallest eigenvalue is the smallest possible mean square distance which is achieved in the direction of the corresponding eigenvector. The best linear approximation must be orthogonal to that, which is the direction of the other eigenvector: the first principal component.) However, it does not compute useful adjunct statistics that can be afforded by other methods.
OK - I think this is the right conceptual answer - I hadn't appreciated the difference between the effect of the correlation across repeated measures on the within group power (improved) and between groups power (degraded).  Of course, given that this is a clinical trial, what I really care about is the power to detect a group x time interaction.  I believe I should be using in g*power the "repeated measures, within-between interaction" model, which does show increasing power with increasing correlation over the repeated measure.
@ttnphns We have several cells, and we know what tissue each cell belong to (label). Now we also have some measurements for each cell, and we want to see if we cluster cells using these measures, do we get cells of the same type in the same group?
Yes, in general, but what kind of t-test it is depends on the data: do your regressions involve independent responses or not?
Do you have any reference or source for the statement "*in small samples the MOM is superior to the ML estimation*" in the case of the GPD? (It relates to another question here - one of mine, as it happens.)
The y-axis is transformed according to the Normal cumulative density function, $F(y)=\\int_{-\\infty}^y \\exp(-t^2/2) dt / \\sqrt{2\\pi}$, as multiplied by $100$ to convert to percent. In the illustration it spans the range from (approximately) $y=-3$ to $y=3$, giving $F(y)$ ranging from about $0.3$% to $99.7$%.
Hi Cita and welcome to the site. Is this a homework question? If so, could you please add the `self-study` tag as we treat those kind of questions differently. Thank you.