whuber

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bio	website	quantdec.com
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Consultant (environmental and spatial stats a specialty), expert witness, and teacher.

	57,400 reputation	bio	website	quantdec.com	visits	member for	2 years, 9 months
388190 badges		location	Northeastern US		seen	6 mins ago

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May 19	comment	Finding conditions on unspecified CDF that permit a solution to an equation I have no problem finding solutions by perturbing the uniform and exponential cases. As you have begun to see, conditions on $F'$ are of a wholly different nature than conditions on $F$ and have little to do with conditions involving moments of the distribution.
May 19	comment	Decomposition of the sum of two random variables @Xi'an I agree with you: the first part of this answer is wrong (-1). It implicitly confuses estimation with mathematical solution. Given just the sample, there are many possible estimands for $Y$, but this does not preclude the existence of good estimators of $Y$, perhaps obtained through deconvolution.
May 19	comment	AIC vs BIC vs MDL When comparing two values of AIC for two values of $K$, you are looking at $LL_0 - LL_1 - K_0 + K_1$. When comparing two values of $BIC$ you are looking at $LL_0 - LL_1 - \log(N)(K_0 - K_1)/2$. Thus the two will not necessarily be optimal for the same values of $K$.
May 19	comment	Finding conditions on unspecified CDF that permit a solution to an equation You are right : if $F$ is twice - differentiable on $[ 0, \overline {\alpha}] $, then necessarily $F' $ is defined and continuous in a neighborhood of $0$, whence $F' $ is bounded at zero and the limit of $xF' (x) $ as $x\to 0 $ must be $0$ anyway. But don't hope for sharper conditions. I trust that the figures might help you gain some intuition concerning how little can be said about $F$.
May 19	comment	AIC vs BIC vs MDL (1) What you seem to be missing is that when you change $K$, you change $LL$. (2) What do you mean by "MDL"?
May 19	comment	Order values of $x_1$ to achieve desired correlation with $x_2$. This is a tiny generalization of the question at stats.stackexchange.com/questions/3961/…, whose answer applies to this generalization.
May 19	comment	Should you ever standardise binary variables? Since it's your own implementation, then nobody else has any basis to give you an objective answer! You need to examine how your software treats the data in order to decide whether prior standardization make sense.
May 19	comment	Curve smoothness - local adjacency That second line is mysterious: what do three ordered pairs have to do with "time series" or curves? If we ignore that line, we are still led to wonder how your "curve" is given. Is it provided as a set of regularly spaced discrete data? Irregularly spaced data? Terms in an orthogonal expansion (such as Fourier series)? Something else? And are these data considered mathematically accurate or are they measurements whose variation has to be considered? To what do the data correspond: points in time, averages over time intervals, something else? All these dictate the possible answers.
May 19	comment	pdf of multivariate normal distribution Obviously there is more relevant information. You still need to explain what $F_{ml}$ means for instance. Users interested in answering this question accurately would also want to know how the random variables $y$ and $x$ are "combined" into $z$ and what "deviation scores" might mean. As far as the form of the multivariate Normal PDF goes, that's documented extensively on this site and is readily available on Wikipedia, among other places.
May 19	comment	Want to evaluate how uniform my data is? @gung (and Nick): the comments seem to read at cross-purposes with the question. Although the O.P. uses "uniform," I don't think they intend a uniform distribution of color. The way in which they use it suggests they are looking for something you would consider to be a "cluster" or multivariate distribution with relatively small variances in all components. "Monochromatic" might be a more accurate word for what they describe. If I am correct, this question asks for a way to measure the degree to which an image can be considered monochromatic.
May 19	comment	Measuring the presence of a correlation Your example of the data indicates there may be more records (up to 35) than users (10). That suggests there are multiple records per user. Is this the case and if so, do you have information about the user corresponding to each record?
May 19	comment	How to create the class range given 1 as the middle class, 3 as the highest value and 0.65 as the lowest value? Levius, the difficulties in understanding this question (which I share with @Nick) may stem from from the lack of context. The question jumps right into the middle of something without explanation. You spend a couple of screens explaining something that is not working without telling us the basic things needed in order to help you. What kind of data do you have? What are you trying to accomplish with them? What specifically do you mean by "the class interval"?
May 18	comment	Confidence interval for the difference between $X_1$ and $X_2$ or $X_3$ What do the data look like?
May 18	comment	pdf of multivariate normal distribution This question cannot make sense to those without access to the book. To make this an answerable question, please either (a) provide a link to those pages in the book or (b) an image of those pages or (c) a synopsis of the relevant material from those pages.
May 18	comment	Minimum enclosing Gaussian You have the same problem: any "enclosing" Gaussian that has a spread wider than one of the original components eventually will have a relative error of 100% in the tails.
May 18	comment	Is it fair to say that time-series violates IID? (1) Presumably "IDD" means "IID". (2) You seem to have confused your x's and y's. Of course there's no probability distributions for the x's: they are the dates. I will vote to close this question until it can be edited to make sense.
May 18	comment	Should you ever standardise binary variables? When you're doing logistic regression, the software will almost surely perform the standardization under the hood anyway (to achieve better numerical properties). Thus it's a good idea to keep the binary indicator expressed in a meaningful way. Standardizing it doesn't sound either good or useful.
May 17	comment	Why will a statistic be significant with sufficiently large samples unless the population effect is exactly zero? Yep, that's the problem with universal statements: there's always some blaggard who will come along with a counterexample just to ruin your fun :-).
May 17	comment	Minimum enclosing Gaussian It might be worth noticing that the solution cannot look like the illustration: the "enclosing" Gaussian must have a standard deviation no greater than the smaller of the SDs of the components--otherwise, the tails of the components will eventually be too large. This suggests that such an enclosing Gaussian will rarely be a decent approximation in any sense, unless both components are very similar to each other in shape and location.
May 17	comment	Why will a statistic be significant with sufficiently large samples unless the population effect is exactly zero? It's wise to be cautious about issuing extreme or universal statements, like something is "always false," because such statements are usually (always? :-) incorrect. In this case, you seem implicitly to assume that $H_0$ is simple. Composite null hypotheses frequently are true and have abundant, convincing evidence in support. But how has the conversation turned into whether the null is true, when the question concerns when it is false?