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1answer
67 views

How can be profile plots in EVT interpreted and what is the theoretical nature of it?

I have two question about profile log-likelihood. One is of theoretical nature and one is about a plot in R. I illustrate the two questions in a application of profile-likelihood in EVT. I use the ...
3
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1answer
58 views

Inconsistency in Two stage Maximum Likelihood Estimation

I want to maximize a log-likelihood function (L) that is a function of parameters $\beta_i$ for $i=1,..,k$ and $\alpha_1, \alpha_2$. Ideally, I want to perform the estimation of all parameters in one ...
2
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0answers
54 views

SAS profile-likelihood confidence intervals and p-values - why is there a discrepancy?

Using Firth's penalized likelihood method in logistic regression, why can you get a p-value of <.05 when the confidence interval for the estimate includes 1? code: ...
12
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3answers
585 views

What is the relationship between profile likelihood and confidence intervals?

To make this chart I generated random samples of different size from a normal distribution with mean=0 and sd=1. Confidence intervals were then calculated using alpha cutoffs ranging from .001 to .999 ...
2
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1answer
150 views

Is this a nested model and can I use the likelihood ratio test?

I have a data set, total_data and I applied a model to it. For instance, the model has one parameter $\beta$, and I calculated the log-likelihood of the fitted model (using maximum likelihood method). ...
3
votes
1answer
110 views

Likelihood analysis for exponential distribution

Assume a collection of independent exponential random variables $y_{1}, \ldots, y_{n}$ with means $\mu_{1}, \ldots, \mu_{n}$; where $\mu_{i} = \beta_{0}+\beta_{1}x_{i}$. How can I find the profile ...
3
votes
1answer
426 views

Profile likelihood confidence intervals

The theory behind profile likelihood (PL) confidence intervals (CIs) is clear to me. (See here, for example). SAS is surprisingly quick in calculating the PL CIs for all the covariates in a given ...
1
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1answer
43 views

Help me figure out the profile likehihood given this covariance function

I'm taking a spatial stats class, and I'm on the road so I can't ask the prof for help. Would appreciate help understanding what is going on here. The problem is set up with $Y = X_s'\beta + e$ ...
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0answers
47 views

References about profiled deviance components

I have read the excellent slides "Assessing the precision of estimates of variance components" from Douglas Bates. I'm looking for some references about these profiled deviance components (for ...
7
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2answers
758 views

How can I estimate 95% confidence intervals using profiling for parameters estimated by maximising a log-likelihood function using optim in R?

How can I estimate 95% confidence intervals using profiling for parameters estimated by maximising a log-likelihood function using optim in R? I know I can asymptotically estimate the covariance ...
5
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1answer
461 views

What is the exact definition of profile likelihood?

Does anyone here know the exact definition of Profile Likelihood? Or does it have one?
1
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0answers
142 views

A little confusion on Profile likelihood

As we all know, profile likelihood is an effective method for the estimation of conditional parametric model. But I still don't know exactly why it works. Profile likelihood was thoroughly studied by ...
0
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1answer
209 views

Profile likelihood of N in binomial model

Let $(n_1,...,n_k)$ be a sample from a Binomial$(N,p)$ where both parameters are unknown. In many cases, the profile likelihood of $N$ is asymptotic in the sense that it never decays to $0$. An ...
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0answers
68 views

“On/off problem” resources

I need to study in depth the on/off problem with different approaches: frequentist, bayesian - frequentist hybrid, profile likelihood. The on/off problem is a counting experiment where you observe ...
13
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2answers
556 views

Hessian of profile likelihood used for standard error estimation

This question is motivated by this one. I looked up two sources and this is what I found. A. van der Vaart, Assymptotic Statistics: It is rarely possible to compute a profile likelihood ...
12
votes
1answer
710 views

What are the disadvantages of the profile likelihood?

Consider a vector of parameters $(\theta_1, \theta_2)$, with $\theta_1$ the parameter of interest, and $\theta_2$ a nuisance parameter. If $L(\theta_1, \theta_2 ; x)$ is the likelihood constructed ...