5
votes
Cramer-Rao bound for biased estimators
how does the bound help us for biased estimators since if the estimator is biased then it's variance is not equal to its mean squared error
If you are using the squared error loss then we may use the ...
- 71.9k
3
votes
Summary output of binomial GLMM shows significant effects, but graph shows overlapping CI error bars?
Interpreting this type of plot takes some care, for a few reasons.
First, the simple relationship between 95% confidence intervals (CI) and $p < 0.05$ only holds for comparisons of the CI against ...
- 86.8k
3
votes
Cramer-Rao bound for biased estimators
The thing about unbiased estimators is that they are not always the best estimator in terms of minimized error. Often, you should choose to use a biased estimator. Nonetheless, one should still care ...
- 151
3
votes
Accepted
How to calculate confidence intervals for very small sample point estimates (percentages) for a large positive distribution?
Yes, these are correct 'exact' confidence intervals; they are described by Ulm (1990).
Very briefly, he showed that for a Poisson mean $\lambda$ given an observation $x,$ the boundaries $(\lambda_L, \...
- 2,081
3
votes
Interpretation of Maximum Likelihood Value
This is not a complete answer, but two possible initial aveneues for an answer.
There are two key concepts which I think are worth considering.
Each LL value is obtained by re-sampling the original ...
- 266
3
votes
Why are my odds ratio confidence intervals so wide?
The sample odds ratio is very large (20). As such, you observe an extremely strong association between the two binary variables.
But this very large value would drastically change if a single ...
- 11.6k
2
votes
Interpretation of Maximum Likelihood Value
I can reproduce this when I consider (for example) a model with Gaussian noise. Then the loglikelihood can be expressed very easily; namely in terms of the sum of squared residuals $ \sum_{i=1}^n r_i^...
- 71.9k
2
votes
Statistical significance of correlations from confidence intervals... making my brain hurt a little
Yes, that means it is not significant at the 0.01 level.
No, that means you fail to reject the null. If p was less than 0.01 you would reject the null.
And you can test if the correlation is ...
- 110k
2
votes
Accepted
Confidence interval on ratio of estimates for exponential random variables
Note:
The CI is an interval for a population parameter not a sample estimate. The estimates will crop up in the endpoints of your interval
The (ordinary) F distribution for the ratio of estimates ...
- 278k
2
votes
Accepted
Using 95% confidence intervals for pairwise comparisons in mixed effects model
The point estimates and standard errors agree perfectly between the two methods, and the confidence limits calculated the two ways are very similar (probably due to the difference between z- based and ...
- 86.8k
1
vote
Accepted
Confidence Intervals around Backtransformed Log-linear Regression
I indeed arrive at an expression that looks different.
From
$$ \sqrt{n}(e^{\hat{\beta}_1} - e^{\beta_1}) \to^d \mathcal{N}(0, e^{2\beta_1}\sigma^2) $$
we obtain, plugging in the estimator for $\beta_1$...
- 31.8k
1
vote
Overlapping confidence intervals of two proportions
I hesitate to say it applies to all types of confidence intervals, there could be some odd cases. But it generally applies (although it can get tricky).
Why?
Well, a p-value of x (say, 0.05) would ...
- 110k
1
vote
Difference between F-test and confidence intervals on variance estimates
If the data from the first sample gives a very tight estimate for variance, $\sigma^2_x$, whilst data from the second sample gives a very wide estimate for second variance, $\sigma^2_y$, then even ...
- 458
1
vote
Calculate WEIGHTED confidence interval for a linear fit
This https://stats.stackexchange.com/a/52712/341520 is a fantastic answer which basically solves your problem, but you have to express the model with linear algebra, which immensely improves notation ...
- 2,197
1
vote
non-central F-statistic confidence intervals seem inconsistent with ANOVA p-values
You are on the right track in that the central $F$ distribution assumes $H_0$ whereas the non-central one assumes $H_A$, but what you are doing with the latter does not make a lot of sense.
To ...
- 2,081
1
vote
Accepted
Model most likely coordinates of target using Bayesian
the best position
You could say that the best position is the position where we have the largest probability of a goal. That is
$$p(goal|x,y)$$
With a Bayesian approach you would compute
$$p(goal|x,y,...
- 71.9k
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