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Is considering a specific distribution necessary before computing an average?

The mean (average) is a descriptive statistic, just like the variance (standard deviation), skewness, or the coefficients of a linear regression, etc. They are just the mathematical results of ...
jginestet's user avatar
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1 vote

Is considering a specific distribution necessary before computing an average?

You do not need to know the distribution of the average to use it. Suppose the observations are assumed to be independent and identically distributed. In that case, the estimated expected value of the ...
Xiaochuan Lu's user avatar
1 vote

Variance of marginal posterior distribution

While this is probably true for most relevant examples an easy counterexample exist in that $\theta$ and $\phi$ can be independent in both prior and likelihood. I have constructed a realistic example ...
Lukas Lohse's user avatar
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2 votes
Accepted

Help developing intuition behind sufficient statistics (Casella & Berger)

One can visualize this explanation along a temporal axis The random variable $\mathbf X$ is generated by a distribution $\mathbb P_\theta(\mathbf x)$ with unknown parameter $\theta$ and its observed ...
Xi'an's user avatar
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1 vote

Help developing intuition behind sufficient statistics (Casella & Berger)

What is a sufficient statistic? What is its objective? To understand that, consider a (Polish) measurable space $(\mathscr X,\mathfrak A ) $ let $\mathfrak P$ be a collection of probability measures ...
User1865345's user avatar
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1 vote
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Regression with dependent observations of only one individual

My Y variable will likely be binary (agrees/disagrees) or on a Likert scale (1-5) I'd recommend the Likert scale since it's more informative. For analysis you can use an ordinal logistic model. https:...
Lukas Lohse's user avatar
  • 2,862
0 votes

Asymptotically Normally Distributed

This is answered, but here's another explanation which might shed some more light. What is an estimator $\hat{\theta}_n$? It's just a function you calculate from the sample, i.e. $\hat{\theta}_n = h(...
Abhishek Divekar's user avatar
6 votes

Isn't it problematic to look at the data to decide to use a parametric vs. non-parametric test?

Incredible answers. To summarize some elements of a statistical philosophy that avoids problems of model uncertainty / forking paths: Pre-specify flexible but powerful methods that are less likely ...
Frank Harrell's user avatar
4 votes

Isn't it problematic to look at the data to decide to use a parametric vs. non-parametric test?

In the end, what matters is what the data sampled from nature tells about the questions we have about nature. When data supplies us at with novel questions that we want the same data to answer us, ...
Sextus Empiricus's user avatar
6 votes

Isn't it problematic to look at the data to decide to use a parametric vs. non-parametric test?

Nicely, in some answers and comments there are already links to some stuff I have written. I will try to give a message in a nutshell here. Yes, you are right. There is a problem. One nice way to show ...
Christian Hennig's user avatar
8 votes

Isn't it problematic to look at the data to decide to use a parametric vs. non-parametric test?

I want to make a distinction that doesn't seem to have come up in previous answers. There is a difference between examining the results of several complete analyses (estimates, p-values, confidence ...
Ben Bolker's user avatar
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10 votes

Isn't it problematic to look at the data to decide to use a parametric vs. non-parametric test?

Isn't it an example of the forking paths problem? Yes. There are a number of posts on site that address this issue, (and related issues of various aspects of model selection such as deciding whether ...
Glen_b's user avatar
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9 votes
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Derivative of the Score Function in Fisher Information

This is an interesting confusion --- it comes from the fact that the MLE for a fixed set of data has a zero score (under standard regularity conditions) but data randomly generated from a simulation ...
Ben's user avatar
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7 votes

Derivative of the Score Function in Fisher Information

Another possible confusion comes from the distinction between the estimator $\hat\theta$ and the value it has in the current dataset. Let's write $\dot \ell(\theta)$ for the score function. It's true ...
Thomas Lumley's user avatar
8 votes

Derivative of the Score Function in Fisher Information

Under mild regularity conditions, the expected value of the scores is zero. I.e., these are the first-order partial derivatives that have an expectation of zero (sum to zero) at the MLE. Thus, ...
Marjolein Fokkema's user avatar
1 vote

How to calculate the statistic for ctree function?

Function ctree does not use $\chi^2$ tests, it uses conditional inference tests. These are implemented in package libcoin, ...
Marjolein Fokkema's user avatar
20 votes

Isn't it problematic to look at the data to decide to use a parametric vs. non-parametric test?

I strongly agree with Stephan Kolassa, but I do think there is an exception: Suppose you carefully consider in advance what test or model you want to use. You justify your choices of assumptions and ...
Frans Rodenburg's user avatar
26 votes
Accepted

Isn't it problematic to look at the data to decide to use a parametric vs. non-parametric test?

Abso-****ing-lutely yes. Ideally, one would decide on the entire analysis before seeing the first shred of data, by leveraging pilot data (which is not used in the "real" analysis). My ...
Stephan Kolassa's user avatar
1 vote
Accepted

How to find the average and SE of a un unknown PDF from a set on sample values already combined into several bins?

Here is a very approximate solution. First, take a guess at the median. Looks like it's about 280, but that's just eyeballing it. You could calculate it assuming a uniform distribution within the ...
Peter Flom's user avatar
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