tttjjj/elt_bench huggingface dataset:
In response to the specific question about whether to use McNemar's test for PPV and NPV the answer is no because you don't have the same population compared in each test. It is also not appropriate to use simple comparison of proportions test because populations are not independent either. I will keep an eye open for a suitable test for this situation...
Can you please provide a citation for the 15 estimate?  Once upon a time someone I was working with tried and I found one that recommended 10 based on simulation (and a correction for unequal proportions and number of predictors).
That's a nice example, so +1 for it. However, as you already pointed out, it does not really help in convincing others to use BMA. Actually, I run it and it even took some time to convince me that BMA is better here than the classical approach: the best model is not the true model (the best model only includes x2 and x3) and the parameters for model2 aren't that much off, at least for the relevant parameters. However, it shows some significant parameters x5 and x6 that shouldn't be there and BMA does a great job in telling you that this is not significant, so this is a plus for BMA.
Maybe you can get the information from here http://stackoverflow.com/questions/1407957/netflix-prize-dataset
I actually ran a multiple regression to see the VIF values, but can I use them? My data is far from normally distibuted, so im sticking with the poisson option in the generalized linear model.
(+1) I would add that it is folly to invoke the CLT in this context. If, for instance, the duration of one task on the critical path dominated the length of the project, then the CLT is useless and attempting to apply its formula would lead to overoptimistic estimates.  For the last quarter century, *simulation* has been the standard practice for estimating variation in project duration, because the (clear, explicit) dependencies among tasks can create total duration distributions that cannot be calculated or approximated in any other way.
For Monte Carlo sampling of posterior predictive distributions under the Gaussian error model, the algorithm is: (1) sample model parameters, including $\\sigma$ (e.g., by MCMC); (2) sample from a Gaussian with mean $\\mathrm{E}[Y|X]$ and standard deviation $\\sigma$. Predictive intervals can be constructed from the empirical cdf generated by *that* sampling algorithm.
Pardon, I ment $cos$. Pearson $r$ is cosine. The formula is correct. Please _read_ details under the link.
@TuncJamgocyan It sounds like you want to test correlation?
Why not? Think about it. When we call a estimator "unbiased", we mean that on average, its estimate is equal to the true value of theta. However, there can still be a lot of variation around the true value, so that the error of the estimate is high.
The James-Stein estimator is a biased estimator with lower MSE than OLS, for example.
8 countries and 10 years doesn't give a large amount of observations. The small sample size might be an issue. What type of panel regression do you use?
Are you sure, that the Student distribution has maximum entropy? Could you post reference?
Further to my comment, your expected 90 respondents *do not make a random sample of the population*.  The random sample are the 100 you selected.  Ten (10) are missing due to a systematic bias in your methods.
There is no difference between variance and covariance: all covariances can be obtained as (linear combinations) of variances and variances, of course, are just particular examples of covariances.  (Mathematicians call this relationship [polarization](http://en.wikipedia.org/wiki/Polarization_identity).)
Can you clarify what your actual goal is? If I got you correctly, it is to somehow find the different components that lead to the signal. You are in a sense seeking a different representation of the signal which lets you see what is going on more easily. Am I correct?
@Heta Thanks, very nice of you to come back to let me know!
What is "the right answer" & how do you know it?
Can you write some crash-introduction of what you want to do (including Eigenstrat step)? People are rather lazy, and are much more prone to answer questions that don't require too much googling just to be understood.
For simplicity in this case, $p_i$ is known.
Can you make this reply more self-contained, e.g. by providing a brief overview of the slides/references you linked to?
Thank you @whuber for pointing that out. I have updated my question for the sake of clarification.
but that's the thing: in the absence of further constraints the optimal solution is not necessarely unique.
What are the characteristics you want to fit here - and how many days/different types of outcomes are there? It would be reasonably straightforward to use GEE for repeated measures (outcome yes/no, for different types of outcomes on different days clustered among different people; a working assumption is that outcomes nearby in time are more correlated than those far apart) but it depends on what the characteristics are.
@B_Miner I was referencing ARMA for errors in time series regression not for NN or SVM.
It's a relationship between two probability distributions so you can't really say "information content increases", but you can say the two RVs are more dependent on one another.  For more detail, yes please post a new question.
Nick, many thanks; this is very helpful. I'll look at these papers, and beta regression, too.
@Chris: Could be. I can't say. I don't know enough about the theory behind it.
This seems like a math question, not a statistics one. In statistics, we would want (indeed, require) many more points than the mathematical minimum. There's nothing really about regression here - it's more the minimum points to define certain curves in various spaces.
This is exactly what I needed! Fast and sufficiently accurate!
1) for the probability mass function. 2) $a\\ge 0$, yes. (Question edited to report this clarifications)
I am not very familiar with data imputation. I have some variables that have very few non missing values. Something like 20 available samples over a dataset with 13000 samples. Does data imputation work well also with this kind of variables? This is why I was thinking to perform lasso using only the covariance matrix.  From what I know lasso does not work very well with categorical variables and that group lasso is a better approach for this kind of problem but your answer seems to contradict this point. Are you sure that lasso can be used also on categorical data?
Actually I don't want to partition the forecast into different factors. What I want is to generate three models (each one with different inferences for the coefficients), in order to compare their RSS. I'm a freshman with ARIMA models, and didn't understand how to use what you said to do this.
**Wilcoxon sign-rank test** is a 2-related-samples test which tests H0 that the difference between the two variables is symmetric about 0. **Sign test** tests H0 that this difference has median 0.
To help you a bit more, whenever you read about the sum of independent random variables, you should think immediately about characteristic functions, or in the discrete case, about probability generating functions. This will give you a short and elegant solution for your problem. By the way, Raikov's Theorem gives an even stronger statement for your specific problem.
Thanks for adding the tag; Please read the [tag wiki info](http://stats.stackexchange.com/tags/self-study/info) for that tag.  What do you know about distributions of means?
You may find the following thread helpful: [when-should-you-center-your-data-when-should-you-standardize](http://stats.stackexchange.com/questions/29781/).
That's a good point - using non-orthodox notation can signal that you don't know what you are doing (even if you do).
@whuber, thanks! I've been a lurker for a while, but a sudden increase in free time means I can finally (try to) give back a bit!
Because $X_1X_2\\cdots X_{n-1}$ is a random variable and (assuming all the $X_i$ are independent) it is independent of $X_n$, the answer is obtained inductively: nothing new is needed. Lest this seem too mysterious, the technique is no different than pointing out that since you can add two numbers with a calculator, you can add $n$ numbers with the same calculator just by repeated addition.
The only error that *matters* is one that affects the analysis you will be doing with the distribution.  Perhaps you could tell us what that analysis will be.  As an extreme (but realistic) example, suppose you're simulating the maximum of $n$ iid standard normals in order to estimate the 95th percentile.  You could replace the standard normal distribution (with cdf $\\Phi$) by $0$ for all values less than $\\Phi^{-1}((0.95-\\varepsilon)^{1/n})$, with $\\varepsilon$ small, without making an appreciable error in the results.  That's a *really* bad approximation to the Normal, but it works here.
I don't think testing for independence is possible unless you have some idea of what form the dependence might take (time series, panel, spatial, etc). If you randomly assign an order and test for independence once, then the test will have correct size, but it generally will not have any power. For example, if you take a stationary time series with dependence and then randomly reorder it, the observations will become independent asymptotically, and the test with random ordering has asymptotic power equal to size.
I may be missing something, but IMHO, permbinom() does not perform a permutation of its input (a re-arrangement of the input values), hence permtest() does not perform a permutation test. I think permbinom's random swapping of the input 1s and 0s with probability .5 gives you exactly what just calling rbinom(n, size=1, prob=.5) itself gives you: the probability for a 1 is .5 for each element, same for a 0 - regardless of the input vector. Your solution seems equivalent to the original one - it's a MC simulation with given priors. Sorry if I'm totally off base here, I'm by no means an expert.
Because the mapping $(U,V)\\to(X,Y)$ simply folds the unit square in half along the diagonal, the joint distribution of $(X,Y)$ is uniform on the upper triangle $0\\le X\\le 1$, $0\\le Y\\le 1$, $X\\le Y$.
One thing to realize about linear regression is that regressing $Y$ on $X$ is *not* the same as regressing $X$ on $Y$, see [here](http://stats.stackexchange.com/questions/22718/regressing-x-on-y-or-y-on-x/22721#22721).
@MichaelMayer You said they *could* be highly correlated and they certainly could. But need they be? That is, could you have a large change in a coefficient by adding a variable that is *not* highly correlated with the other independent variable? Sure, just so long as there is an interaction. This in fact happens; one case: Trying to predict whether a person has HIV. Individual variable 1 = sex (male, female, other) IV 2 = sexuality (straight, gay/lesbian, bi, other) Adding that second variable changes the first coefficient a LOT.
Are you using or have access to Stata 13?
Sweet. Never heard of it. I'll definitely look into it. Maybe that's what I'm after, after all :)
(I'm one person, & the down-voter.) `+0` can do **two completely different things**. If you manually code $x_1$ & $x_2$ dummies for `cyl`  as 0 or 1, then using it *will* force the intercept to zero & fit the two-parameter model $\\operatorname{E}Y= \\beta_1 x_1 + \\beta_2 x_2$. But if R's been told that `cyl_factor`'s categorical it gets clever & fits the three-parameter model you describe. So "removing the intercept" is ambiguous. Now I know all this & you know all this, but IMO the answer's unclear - potentially misleading - for someone who doesn't.
Thanks Guillermo.  I did suspect that they treated the Spearman's rank correlation as Pearson's correlation and calculated the difference of two Pearson's correlations.

However, it seems to me it is not the correct way to do it, and so I am making a post here.
Thanks for the pointer on Latex
I don't know much about SAS but did you have a look at [quantreg](http://support.sas.com/rnd/app/papers/quantreg.pdf)?
@anna It would depend on how you coded your contrast (or how your software did it for you). You could perhaps add all this information to your question to make it more interesting and attract more attention to it. A little more context could also be useful (what's XECI?)
When $x$ is fixed (and not random), $x'\\beta$ is the projection of $y$ onto the space generated by the columns of $x$. This geometric characterization makes the claim obvious in this situation.  Using statistical intuition, we can also characterize $x'\\beta$ as the fit to $y$.  Even when the problem is overparameterized (*i.e.*, $x$ has deficient rank), there is no problem because the extra parameters don't change the fit.  I cannot see a way easily to generalize to *random* $x$, partly because there is no inherent relationship among the ranks of $x$ and $\\mathbb{E}(x'x)$.
Is there any way apart from SEM to do this. Could I regress equation 2 to 4 individually and get the predicted value which I could then use to estimate the new beta's from regression equation 1?
I found a general formula for the mgf for gamma distributions but i'm not sure how to apply the transformation to it.
"If R is broken you call....?" Brian Ripley :-) (+1 for this well argued response)
@ndoogan To clarify, my advice is not "use beta regression when your response is a proportion" but rather "if your response can only take values in $(0,1)$ _such as_ proportions/percentages then beta regression is typical"
thank you very much, I have added more information above to specify   my doubts
@Chris check this out about interpreting overlapping CIs http://pubs.amstat.org/doi/abs/10.1198/000313001317097960
Also the original question is also around the confusion of using SE or SD interchangeably while they are two different things
But how it's help, would you please explain more ?
thank you for your answer; although the example dataset is tiny, the real dataset has 100 subjects measured on 6 dates
"I'm a little confused, can anyone help" is not a very specific question. Are you asking whether the usual computations for intraclass correlation are still valid in the case of unequal cluster sizes?
As currently worded your question is in the abstract until at the end you refer to bedrooms.  This perhaps suggests that $y$ is housing rents and $X$ includes various attributes of housing including number of bedrooms, but it would be helpful to clarify this in the question.
Do you have any other prior beliefs for $\\tau_i$, or any assumptions about how it should be modeled? I can't quite suss out why there are two sources of variance.
I've edited the response to reflect this.
If you just look at the likelihood, you get the answer you gave. But one must also take the sampling scheme into account. Rather like the MSE in anova.
I know a more standard way to obtain something similar to model2: introduce a second stratification variable-group and apply the model ($\\beta$,$\\beta_{group}$) to the total_data. The likelihood ratio test would be to test against H0:$\\beta_{group}=0$. Is this the same as the method I described above?
Thanks suncoolsu and Rolando2 for your replies. The micro-organisms are different mutants of the same spp. The data samples are technical triplicates for each mutant at a log phase of growth, monitored for the prodcution of a specific chemical. Unfortunately, the 3rd replicate for control was lost during experiment.
Than you for you response. I am not sure if I explained what I did clearly. My data follows Negative Binomial distribution, Negative Binomial is a mixture of Gamma and Poisson. The underlying Gamma distribution is what I am interested in, which is also what I meant by latent variable. My another post explained how I got the estimate of mean and variance of the Gamma distribution. http://math.stackexchange.com/questions/752964/can-i-estimate-variance-of-gamma-from-negative-binomial-distributed-data-given
An explanation about the down vote could warn unsuspecting readers (and the clueless author) about what is wrong with this answer…
I don't see anything wrong about your work. I am not very comfortable about assuming the missing value as the mean, because you are practically changing 5% of your data (It might be alright, I am just pointing out it might be risky). Another note that is worth mentioning is that your test is not "absolutely" significant, you have to mention it was significant at 5% only, because the p value is less than 0.05.
You remove the items with the highest "alpha if item removed" not lowest...
I will reformulate. I was trying to solve it with R, but I think I'm missing a fundamental concept here which is why I'm not getting the results I'm expecting.
Thanks. The link looks promising
And do you know what p-values are in general - if not see [here](http://stats.stackexchange.com/questions/31) or [here](http://en.wikipedia.org/wiki/P-value).
Probably asking this in the Quantitative Finance forum will be more effective: https://quant.stackexchange.com/
I have seen this link earlier..I am getting this "Error in boxcox.default(y ~ x) : response variable must be positive" error when I am using boxcox..
A lot of exercises like this are really more designed (in my experience) to emphasize or test recognition of the pmf.  So  we'd assume that $p(x;\\pi)$ is some slight specialization of a standard pmf, perhaps by a simple transform of the random variable, try to figure out which one it is, then get the sample space from the definition of the (standard) pmf.  In this case, the random variable $x$ can be easily transformed to another random variable, let us say $y$, for which $p(y;\\pi)$ is a well-known distribution, and everything else follows from that.
@Macro, $X_1$ is the first draw from $N$ independent draws; $Y_1$ is the first order statistic (you might prefer to write $X_{(1)}$ instead). I made the notation more precise in response to your other comments.
$m_{i}(t)$ is a time dependent covariate, for simplicity you can consider a proportional relationship with time.
**NO** - leave it negative! $e^x$ is still positive when $x<0$.
Ok, I see that the question is not well defined, thank you for the comment. So maybe the only way how to improve the question is to compare only two pixels in an image. But as you mentioned @whuber, definition of similarity is still controversial.
BTW: I _never_ said that GEE does not estimate $\\sigma^2_\\alpha$. Are you trolling?
@Marjan the jackknife may not properly reflect uncertainty caused by variable selection.  The bootstrap properly shows more variability in which variables are labeled "significant".  If you want to do a "relative validation" you can show that predictive discrimination is good after correcting for overfitting.  This does not require dealing with the baseline hazard, but is validating relative log hazard estimates.  The `validate` function in the R `rms` package in conjunction with the `cph` function will do that.  The only stepwise algorithm implemented in `validate` is backwards stepdown.
@RayKoopman: It was an arbitrary decision based on my reading of the writeup. It is not necessarily correct, and neither this analysis nor the experiment itself are especially rigorous.
$E[X]$ is a number; $E[X\\mid Y]$ is a random variable -- a function of $Y$ -- whose expectation happens to be the same number as $E[X]$. So it is not clear what you mean when you write $E[X\\mid Y] < \\infty$.
Per your comment above: "...it can be argued that missing data correlate with projects with(in) certain characteristics **(categories)** and, thus, is not MCAR." <- Those categories.
I've made an edit to explicitly discuss the case of non-symmetry; I deliberately didn't consider the case where the mean doesn't exist (such as the Cauchy), since it's far from cases where one would contemplate the midrange.
I believe this best answers feelfree's question, although others have suggested other possible solutions, this one addresses the L1 need.
Ponder this: it is always possible to raise the $R^2$ in a model to $1.00$ by throwing in enough independent "explanatory" variables, whether or not they are related to the response (dependent) variable.  What effect do you suppose the addition of such variables would have on predictive performance?
I usually just write a matlab function to evaluate the loss for a particular set of penalties and then minimize it using the Nelder-Mead simplex algorithm.  I don't know of any libraries that has this built in.
@roland Yes I've seen that post, i specifically want the mathematical function though. How would you suggest i change my question to make that more clear?
I agree with whuber. There will be absolutely no impact if (1) the sample is weighted to scale back to 200K, and (2) the subsample is representative of the full sample.
Do I have to accept that with my kind of data I cannot use such packages?
It's not satisfactory...
Large testing organisations that use IRT also have to worry about consistency between offering of the test. Consistency of the latent  variable(s) is important but is attainable.
+1, I also changed my `model` to `fit` to parallel your answer.
I may be completely wrong here, but all the example outputs seems like simple counting operations (additionally the word "assumptions" confuses me). Do you want to extract statistical measures or do you want to e.g. extract the combination of variable values which "cause" certain injuries and hence allow prediction?
Aha - at last - someone with a sense of humour :)
@miguelmalvarez A correctly classified point won't turn into a support vector, it would have already been one if it was critical. Resampling *wrongly* classified training instances may change the decision boundary, not the the other way around.
Above the first 3D plot - should that say "The mean is the point..."?
What is the size and structure of your data?
(+1) Good idea.
Are you perhaps typing or reading the formula incorrectly?  As written here, it does not involve the "sum of $s$ and $s_c$": it involves their *difference*.  (The server for your reference is so slow that I could not review the slides to check and it's unlikely most other readers would succeed in doing that, either.)
@BenBolker, thank you for your excellent explanation of these issues. I'll add this check to RLRsim ASAP.
Because it can affect the interpretation, it might be worth noting that the units of inflation are not percent, but rather are per unit time.  Given that a percent is just another way of expressing a number (*e.g.*, $50\\% = 0.50$), one is led to ask *what is the change relative to*?  What is the alternative regression to which the log-log regression is to be compared?
@phx 	
Are you able to write down the $H_0$ hypothesis for the main effects tests ? (in the non-balanced case). Yes I mean simultaneous confidence intervals. With a balanced design, detecting a significant difference for at least one comparison should be equivalent to get a significant result for the corresponding ANOVA test. In the non-balanced case, multiple comparisons are always easy to interpret, whereas ANOVA is diffuclt, and the confidence intervals provide much more information than an ANOVA table. Moreover sometimes you are not interested in all pairwise comparisons.
Check [wikipedia](http://en.wikipedia.org/wiki/Validity_(statistics))  and then come back and clarify your question.  It might be that you mean reliability.
I think it should be. It follows from the definition of entropy.
I'd suggest thinking about what the possible states are, and what classes of transitions between them there are. If stock started at S and is above s, then would X be S less the sum of the demands since the last restock. If X is less than s, then the next day it is S and we can make an a priori argument about the probability of that happening.
yeah but.... this one isn't true... it mostly depends on how you parameterize the time variable $t$... i guess if you go back far enough, but come on...
They say it is possible to say _trochotomising_ [as well](http://www.drbilllong.com/Words/Thrix.html).
If Marco's answer is going in the right direction (I wasn't sure what you meant by law) you may be able to Kolmogorov-Smirnov test versus various distributions and see which one has the best fit.