Description Usage Arguments Details Value References
This function estimates the signal proportion and the signal density by using the marginal distribution of Y, followed by a profile likelihood based approach. It returns the vector of estimated local false discovery rates and the corresponding rejection set at a prespecified level for the false discovery rate.
1 |
y |
The observed vector of z-scores. |
x |
The n\times p data matrix, where n must be equal to thelength of y. If you are interested in the intercept, you must add a column of 1's to x. |
blambda |
The tolerance threshold while implementing a quasi-Newton approach for estimating the signal proportion. Default is set to 1e-6/length(y). We recommend not changing it unless absolutely sure. |
level |
The level at which the false discovery rate is to be controlled. Should be a scalar in [0,1]. Default set to 0.05. |
Note that the marginal distribution of Y based on the aforementioned model is same as that in a standard two-groups model (Efron 2008, see References). Fixing \barπ = \mathbf{E}[π(X)], the signal density φ_1(\cdot) is estimated using the Rmosek optimization suite. The primary idea is to approximate the mixing distribution G(\cdot) using \max\{100,√{n}\} many components, each having a suitable Gaussian distribution. The signal proportion is then estimated using the BFGS algorithm. Finally, the algorithm chooses the best value of \barπ based on a profile likelihood approach.
This function returns a list consisting of the following:
p |
The estimated prior probabilities, i.e., \hatπ(\cdot) evaluated at the data points. |
b |
The estimates for the coefficient vector in the logistic function. |
f1y |
The vector of estimated signal density evaluated at the data points. |
kwo |
This is a list with four items - i. atoms: The vector of means for the Gaussian distributions used to approximate G(\cdot), ii. probs: The vector of probabilities for each Gaussian component used to approximate G(\cdot), iii. f1y: Same as f1y above, iv. ll: The average of the logarithmic values of f1y. |
localfdr |
The vector of estimated local false discovery rates evaluated at the data points. |
den |
The vector of estimated conditional densities evaluated at the data points. |
ll |
The log-likelihood evaluated at the estimated optima. |
rejset |
The vector of 1s and 0s where 1 indicates that the corresponding hypothesis is to be rejected. |
pi0 |
The average of the entries of the vector p. |
ll_list |
The vector of profile log-likelihoods corresponding to a pre-determined set of grid points for \barπ. The highest element of this vector is the output in ll. |
Deb, N., Saha, S., Guntuboyina, A. and Sen, B., 2018. Two-component Mixture Model in the Presence of Covariates. arXiv preprint arXiv:1810.07897.
Koenker, R. and Mizera, I., 2014. Convex optimization, shape constraints, compound decisions, and empirical Bayes rules. Journal of the American Statistical Association, 109(506), pp.674-685.
Efron, B., 2008. Microarrays, empirical Bayes and the two-groups model. Statistical science, pp.1-22.
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.