# deconv: A function to compute Empirical Bayes estimates using... In deconvolveR: Empirical Bayes Estimation Strategies

## Description

A function to compute Empirical Bayes estimates using deconvolution

## Usage

 1 2 3 deconv(tau, X, y, Q, P, n = 40, family = c("Poisson", "Normal", "Binomial"), ignoreZero = TRUE, deltaAt = NULL, c0 = 1, scale = TRUE, pDegree = 5, aStart = 1, ...) 

## Arguments

 tau a vector of (implicitly m) discrete support points for θ X the vector of sample values: a vector of counts for Poisson, a vector of z-scores for Normal, a 2-d matrix with rows consisting of pairs, (trial size n_i, number of successes X_i) for Binomial. See details below y the multinomial counts. See details below Q the Q matrix, implies y and P are supplied as well; see details below P the P matrix, implies Q and y are supplied as well; see details below n the number of support points for X. Applies only to Poisson and Normal. In the former, implies that support of X is 1 to n or 0 to n-1 depending on the ignoreZero parameter below. In the latter, the range of X is divided into n bins to construct the multinomial sufficient statistic y (y_k = number of X in bin K) described in the references below family the exponential family, one of c("Poisson", "Normal", "Binomial") with "Poisson", the default ignoreZero if the zero values should be ignored (default = TRUE). Applies to Poisson only and has the effect of adjusting P for the truncation at zero deltaAt the theta value where a delta function is desired (default NULL). Applies to Normal only if non-null c0 the regularization parameter (default 1) scale if the Q matrix should be scaled so that the spline basis has mean 0 and columns sum of squares to be one, (default TRUE) pDegree the degree of the splines to use (default 5). In notation used in the references below, p = pDegree + 1 aStart the starting values for the non-linear optimization, default is a vector of 1s ... further args to function nlm

## Value

a list of 9 items consisting of

 mle the maximum likelihood estimate \hat{α} Q the m by p matrix Q P the n by m matrix P S the ratio of artificial to genuine information per the reference below, where it was referred to as R(α) cov the covariance matrix for the mle cov.g the covariance matrix for the g mat an m by 6 matrix containing columns for theta, g, std. error of g, G (the cdf of g), std. error of G, and the bias of g loglik the negative log-likelihood function for the data taking a p-vector argument statsFunction a function to compute the statistics returned above

## Details

The data X is always required with two exceptions. In the Poisson case, y alone may be specified and X omitted, in which case the sample space of the observations $X$ is assumed to be 1, 2, .., length(y). The second exception is for experimentation with other exponential families besides the three implemented here: y, P and Q can be specified together.

## References

Bradley Efron. Empirical Bayes Deconvolution Estimates. Biometrika 103(1), 1-20, ISSN 0006-3444. doi:10.1093/biomet/asv068. http://biomet.oxfordjournals.org/content/103/1/1.full.pdf+html

Bradley Efron and Trevor Hastie. Computer Age Statistical Inference. Cambridge University Press. ISBN 978-1-1-7-14989-2. Chapter 21.

## Examples

 1 2 3 4 5 6 7 set.seed(238923) ## for reproducibility N <- 1000 theta <- rchisq(N, df = 10) X <- rpois(n = N, lambda = theta) tau <- seq(1, 32) result <- deconv(tau = tau, X = X, ignoreZero = FALSE) print(result\$stats) 

deconvolveR documentation built on May 29, 2017, 3:06 p.m.