An R package forfamilialinference. Briefly, this package provides tests for hypotheses ofthe form
[ \mathrm{H}_0:\mu(\lambda)=\mu_0\text{ for some}\lambda\in\Lambda\quad\text{vs.}\quad\mathrm{H}_1:\mu(\lambda)\neq\mu_0\text{for all}\lambda\in\Lambda,](https://latex.codecogs.com/png.image?%5Cdpi%7B110%7D&space;%5Cbg_white&space;%0A%5Cmathrm%7BH%7D_0%3A%5Cmu%28%5Clambda%29%3D%5Cmu_0%5Ctext%7B%20for%20some%20%7D%5Clambda%5Cin%5CLambda%5Cquad%5Ctext%7Bvs.%7D%5Cquad%5Cmathrm%7BH%7D_1%3A%5Cmu%28%5Clambda%29%5Cneq%5Cmu_0%5Ctext%7B%20for%20all%20%7D%5Clambda%5Cin%5CLambda%2C%0A” _0:()=_0_1:()_0, “)
where is a family of centers,e.g., that induced by the Huber loss function with parameter
. In contrast to classic statisticaltests such as the
or sign tests for the mean or median, familialtests do not depend on a single (sometimes arbitrarily chosen)center.
Presently,familial supports tests of the Huber familyof centers, which includes the mean and median. Testing is carried outusing a Bayesian approach whereby the posterior probabilities of thecompeting hypotheses and
are from the Bayesianbootstrap. One- and two-sample tests are supported, as are directionaltests. Methods for visualizing output are provided.
To install the latest stable version from CRAN, run the followingcode:
install.packages('familial')To install the latest development version from GitHub, run thefollowing code:
devtools::install_github('ryan-thompson/familial')Thecenter.test() function performs a test of centers,with the default being the Huber family of centers.
library(familial)set.seed(1)# One-sample test with point nullx<- MASS::galaxiescenter.test(x,mu =21000)## -----------------------------------------------## familial test of centers with huber family## -----------------------------------------------## mu = 21000 ## posterior probabilities: ## H0 H1 ## 0.542 0.458 ## optimal decision: indeterminate# One-sample test with interval nullcenter.test(x,mu =c(20500,21500))## -----------------------------------------------## familial test of centers with huber family## -----------------------------------------------## mu = 20500 21500 ## posterior probabilities: ## H0 H1 ## 0.959 0.041 ## optimal decision: H0# Two-sample testx<- MASS::cabbages[MASS::cabbages$Cult=='c39','HeadWt']y<- MASS::cabbages[MASS::cabbages$Cult=='c52','HeadWt']center.test(x, y)## -----------------------------------------------## familial test of centers with huber family## -----------------------------------------------## mu = 0 ## posterior probabilities: ## H0 H1 ## 0.008 0.992 ## optimal decision: H1# Two-sample paired directional testx<- MASS::anorexia[MASS::anorexia$Treat=='FT','Postwt']y<- MASS::anorexia[MASS::anorexia$Treat=='FT','Prewt']center.test(x, y,paired = T,alternative ='greater')## -----------------------------------------------## familial test of centers with huber family## -----------------------------------------------## mu = 0 ## posterior probabilities: ## H0 H1 ## 0.006 0.994 ## optimal decision: H1See the packagevignetteorreferencemanual.