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Jan 11, 2019 · Made up shrinkage estimator. If we use some kind of shrinkage estimator to combine individual and pooled averages, say \(\widehat \mu=w_i\bar x_i+(1-w_i)\bar x_\cdot\) where \(\bar x_\cdot\) denotes the overall mean, do we see the expected improvement? Let’s set \(w=.8\) just for fun.
Oct 15, 2010 · You could do a pooled estimate as follows. You can then use the pooled estimates to generate a combined confidence interval. Specifically, let: $\bar{x_1} \sim N(\mu,\frac{\sigma^2}{n_1})$ $\bar{x_2} \sim N(\mu,\frac{\sigma^2}{n_2})$ Using the confidence intervals for the two cases, you can re-construct the standard errors for the estimates and ...
- Sounds a lot like meta-analysis to me. Your assumption that the samples are from the same population means you can use fixed-effect meta-analysis (...
- This is not unlike a stratified sample. So, pooling the samples for a point estimate and standard error seems like a reasonable approach. The two s...
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Dec 20, 2018 · The idea of a shrinkage estimator is simple. However, think about how to choose the optimal value of delta? The solution to this problem was found by Ledoit and Wolf in this excellent paper....
- Vivek Palaniappan
Peter Ho Shrinkage estimators October 31, 2013 risk is just the average of the Bayes risks from the pcomponents, R( ; ) = E[Xp j=1 ( j j) 2]=p = Xp j=1 E[( j j) 2]=p; and so calculating the Bayes risk is similar to calculating the risk in the p = 1 problem. For ˝2(x) = ax, where a= 1 w= ˝2=(1 + ˝2), we have E[(aX )2] = E[(aX a + (1 a) )2]
What is a Shrinkage Estimator? A shrinkage estimator is a new estimate produced by shrinking a raw estimate (like the sample mean). For example, two extreme mean values can be combined to make one more centralized mean value; repeating this for all means in a sample will result in a revised sample mean that has “shrunk” towards the true ...
We show how a particular shrinkage estimator, the ridge regression estimator, can reduce variance and estimation error in cases where the predictors are highly collinear. We show how this estimator and other biased estimators can be viewed as solutions to penalized least-squares problems.
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How do you combine individual and pooled averages using shrinkage estimators?
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Nov 9, 2010 · What's the optimal way to combine the two measurements to form a final estimate of their true average size?
