# EB_CS: Main function used in the paper (Du and Hu, 2020) In EBCHS: An Empirical Bayes Method for Chi-Squared Data

## Description

Give a sequence of chi-squared statistic values, the function computes the posterior mean, variance, and skewness of the noncentrality parameter given the data.

## Usage

 ```1 2 3 4 5 6 7``` ```EB_CS( x, df, qq = c(0.2, 0.4, 0.6, 0.8), method = c("LS", "PLS", "g_model"), mixture = FALSE ) ```

## Arguments

 `x` a sequence of chi-squared test statistics `df` the degrees of freedom `qq` the quantiles used in spline basis `method` LS: parametric least-squares; PLS: penalized least-squares; g-model: g-modeling `mixture` default is FALSE: there is no point mass at zero.

## Value

a list: posterior mean, variance, and skewness estimates

## References

Du and Hu (2020), An Empirical Bayes Method for Chi-Squared Data, Journal of American Statistical Association, forthcoming.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19``` ```p = 1000 k = 7 # the prior distribution for lambda alpha = 2 beta = 10 # lambda lambda = rep(0, p) pi_0 = 0.8 p_0 = floor(p*pi_0) p_1 = p-p_0 lambda[(p_0+1):p] = rgamma(p_1, shape = alpha, rate=1/beta) # Generate a Poisson RV J = sapply(1:p, function(x){rpois(1, lambda[x]/2)}) X = sapply(1:p, function(x){rchisq(1, k+2*J[x])}) qq_set = seq(0.01, 0.99, 0.01) out = EB_CS(X, k, qq=qq_set, method='LS', mixture = TRUE) E = out\$E_lambda V = out\$V_lambda S = out\$S_lambda ```

EBCHS documentation built on June 1, 2021, 9:08 a.m.