Questions tagged [empirical-likelihood]
19 questions
28
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3 answers
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 that the likelihood of the observed data is…
Sameer
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5
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1 answer
Maximum likelihood as minimizing the dissimilarity between the empirical distriution and the model distribution
I am reading Ian Goodfellow "Deep Learning" book. At page 128 it says
One way to interpret maximum likelihood estimation is to view it as
minimizing the dissimilarity between the empirical distribution
$\hat{p}_{\text{data}}$, defined by the…
robertspierre
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5
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2 answers
Empirical PDF from Empirical CDF
Suppose I do an experiment $N$ times and get a vector $X$ of results. Let $C_X(y)$ be the empirical cumulative distribution function of $X$. Suppose $X$ is sorted so that $x_1 \leq x_2 \cdots \leq x_N$. Approximately,
$$C_X(y)=0\textrm{ if }y…
Lars Ericson
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4
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Understand the empirical likelihood
When I read the talk notes by Owen about empirical likelihood,
http://www.ms.uky.edu/~mai/sta709/Owen2005.pdf
I am confused about the solve of solution when I read the page 24.
Let's say we want to get the maximum value of $\sum_{i=1}^n \log(n w_i)$…
Fly_back
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3
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2 answers
Empirical Likelihood estimation in R
I'm new to Empirical Likelihood Estimation.
I'm trying to find an example of how to find the empirical likelihood estimate of a univariate mean $\mu$ using the emplik software package in R.
Any help or reference is greatly appreciated.
userK
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3
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1 answer
Use MLEs to choose the 'most likely' from a set of distributions?
Would it be valid to choose a probability distribution for assumptions based on the actual maximum likelihood of various distributions derived from MLE estimates?
For example, suppose I find MLE estimates of a normal distribution $[ \mu , \sigma^2…
HairyPotatoCat
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JuliaOpt Empirical Likelihood Estimation
I am trying to perform an empirical likelihood estimation in a regression setting using JuliaOpt (Convex or JuMP) and ran into difficulties using either API.
The problem:
Empirical likelihood for regression can be written as a maximization problem…
Vincent
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1
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Maximum Likelihood question
I need to obtain the functional (i.e.: statistic obtained from the empirical distribution function) associated to the most powerful test to contrast $H_0: f_o$ vs. $H_1: f_1$, using a sample of size $n$.
In particular, my problem is that I don’t…
sets
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0 answers
Can use pseudo maximum likelihood method with mixed continuous and discret data in copula
For copula models there are different estimation ways. One of them, is Pseudo maximum likelihood method. In this method, the margins are estimated using empirical cumulative density function. Then copula parameters is estimated using maxim…
Alice
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How to kernalize a logistic loss based regularized ERM optimization problem?
Given $\{\mathbf{x}_i,y_i\}, i=1,\ldots,m$, consider the following optimization problem:
$\min\limits_{\mathbf{w},b} \sum\limits_{i=1}^{m}\log(1+\exp(-y_i(\mathbf{w^Tx_i} + b)))$ $+\lambda|| \mathbf{w}||^2_2$
Solving the above optimization problem…
Sandhya Tripathi
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vote
0 answers
Given two empirical distribution A and B, how to setup a hypothesis test to test if a new data point is from distribution A?
I have two empirical distribution A and B (i.e. two continuous datasets in $\mathcal{R}$) and I am trying to set up a hypothesis test to test if a new data point is from distribution A. Naturally this calls for a likelihood ratio test. I was…
Jim He
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Calculate p-values based on many distributions without knowing which the test statistic is from
I have many (20) normal distributions of the probability of a certain event occurring. Each of these 20 has n>1000.I have an observed proportion from a separate sample that I want to compare to calculate a p-value. However, I don't know which of…
Ethan
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Standard Deviations of Detrended Data vs Original Data
I'am interested to know the opinion on this matter.
I have Data of a Financial Security. The goal is to view the Standard Deviations levels of the data to possibly see patterns of behavior of the Financial Security
As Financial Market theory states…
0
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0 answers
Why empirical likelihood ratio can be larger than some quantile of $\chi^2_1$, if EL is said to be maximised when $p_i = \frac{1}{n}$?
If EL is defined as $\prod_{i=1}^n p_i$ and empirical likelihood ratio is defined as $R(F) = -2 \log \{L(\hat{F})/L(F_n)\}$. If $R(F)\ge c$, then we can reject the $H_0: \mu = \mu_0$. If EL is maximised when $p_i = \frac{1}{n}$, then why the ratio…
user18942
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0
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Paper that proposes an algorithm for a optimal stoping rule based on an empirical distribution
Can you suggest me a paper that proposes an optimal stoping rule based on an empirical distribution?
I am looking for some like this:
I observe a random variable $x$ for a given time (this is usually the variable we need to build the rule and it is…
DanielTheRocketMan
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