The empirical tag has no wiki summary.
2
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2answers
31 views
Convergence of empirical distribution parameters of a sequence of generated normal variables
I am generating a sequence of normal random variables (using the routines from boost C++ library). How fast would you expect the mean and the variance of the sequence converge to the actual variance?
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1
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1answer
74 views
Intuition behind Dvoretzky Kiefer Wolfowitz inequality
I've been reading about the Dvoretzky-Kiefer-Wolfowitz inequality, in the context of confidence bands on empirical distribution functions.
I think I understand the inequality at face value: that the ...
1
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1answer
91 views
Physical significance of heavy tail distributions
I have come across several usage of the term "heavy tail distributions", but unable to find some good resources in the Internet to answer few of my questions:
Compared to what the tail of the ...
7
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1answer
354 views
Empirical distribution alternative
BOUNTY:
The full bounty will be awarded to someone who provides a reference to any published paper which uses or mentions the estimator $\tilde{F}$ below.
Motivation:
This section is probably not ...
-1
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2answers
96 views
Estimation of Density Function from a Transformed CDF [closed]
Suppose I can observe $x_1,...,x_n$ as the realization of the random variables $X_1,..,X_n$. Using $x_1,...,x_n$, I can estimate the empirical cumulative distribution function (CDF), ...
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0answers
37 views
Defining Empirical Risk Minimization
I am reading Machine Learning - A probabilistic Perspective by Kevin Murphy and in chapter 6.5 the author discusses Empirical Risk Minimization, and provides the following definition:
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2
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1answer
135 views
Difference-in-difference with interaction terms
I am looking for an empirical paper that perform a difference-in-difference regression where the whole did regression (treated+post+post*treated) is interacted with a continuous variable (or a ...
1
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0answers
86 views
Empirical coverage probabilities of confidence intervals
Can someone tell me how the type of distribution is related to an empirical coverage probability? (for some distributions the Central-limit-theorem seems to be more easily satisfied)
14
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3answers
420 views
What are some illustrative applications of empirical likelihood?
I have heard of Owen's empirical likelihood, but until recently paid it no heed until I came across it in a paper of interest (Mengersen et al. 2012).
In my efforts to understand it, I have gleaned ...
0
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4answers
277 views
What is the proper way to estimate the CDF for a distribution from samples taken from that distribution?
Given $n$ samples from a (continuous) distribution X, the obvious thing to do is sort them, and distribute them equally across $[0,1]$ by taking $(x_{(k)}, (k-1/2)/n)$ as estimates of particular ...
0
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1answer
78 views
How to present a empirical study when using econometric models?
I've got a (probably easy) question in how to handle empirical studies, when there are a lot of effects involved. I have a whole bunch of variables and I'd like to analyze just a few of them. But the ...
4
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4answers
198 views
Which distribution to use with MCMC and empirical data?
In class, we've been learning a myriad of really interesting techniques to sample from a given distribution, filter online data, particle filters, etc.
My issue is that when I take some real-world ...
4
votes
1answer
826 views
How to use/interpret empirical distribution?
First of all I'd like to apologize for the vague title, I couldn't really formulate a better one just now, please feel free to change, or advice me to change, the title to make it better fit the core ...
1
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2answers
298 views
Interpolating the empirical cumulative function
The empirical cumulative distribution function of a random variable, given observations $x_\left( k \right) > x_\left( k-1 \right)$, $k \in \mathbb N$, $k \le n$, is defined as $F_{emp}(x_\left( k ...
15
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1answer
2k views
Empirical Relationship Between Mean, Median and Mode
For a unimodal distribution which is moderately skewed, we have the following empirical relationship between mean, mode and median:
(Mean-Mode) ~ 3(Mean-Median)
Could someone please explain how the ...
6
votes
1answer
935 views
Why Use the Cornish-Fisher Expansion Instead of Sample Quantile?
The Cornish-Fisher Expansion provides a way to estimate the quantiles of a distribution based on moments. (In this sense, I see it as a complement to the Edgeworth Expansion, which gives an estimate ...
