# Tag Info

### 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 ...

### 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 ...

### 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 ...
Accepted

### 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 ...
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 ...
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 ...
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 $\beta_1$...
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 ...
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 ...
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 ...
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 ...
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,...

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