# manyMeans: Selective inference for many normal means In selectiveInference: Tools for Post-Selection Inference

## Description

Computes p-values and confidence intervals for the largest k among many normal means

## Usage

 `1` ```manyMeans(y, alpha=0.1, bh.q=NULL, k=NULL, sigma=1, verbose=FALSE) ```

## Arguments

 `y` Vector of outcomes (length n) `alpha` Significance level for confidence intervals (target is miscoverage alpha/2 in each tail) `bh.q` q parameter for BH(q) procedure `k` Number of means to consider `sigma` Estimate of error standard deviation `verbose` Print out progress along the way? Default is FALSE

## Details

This function compute p-values and confidence intervals for the largest k among many normal means. One can specify a fixed number of means k to consider, or choose the number to consider via the BH rule.

## Value

 `mu.hat` Vector of length n containing the estimated signal sizes. If a sample element is not selected, then its signal size estimate is 0 `selected.set` Indices of the vector y of the sample elements that were selected by the procedure (either BH(q) or top-K). Labelled "Selind" in output table. `pv` P-values for selected signals `ci` Confidence intervals `method` Method used to choose number of means `sigma` Value of error standard deviation (sigma) used `bh.q` BH q-value used `k` Desired number of means `threshold` Computed cutoff `call` The call to manyMeans

## Author(s)

Ryan Tibshirani, Rob Tibshirani, Jonathan Taylor, Joshua Loftus, Stephen Reid

## References

Stephen Reid, Jonathan Taylor, and Rob Tibshirani (2014). Post-selection point and interval estimation of signal sizes in Gaussian samples. arXiv:1405.3340.

## Examples

 ```1 2 3 4 5 6``` ```set.seed(12345) n = 100 mu = c(rep(3,floor(n/5)), rep(0,n-floor(n/5))) y = mu + rnorm(n) out = manyMeans(y, bh.q=0.1) out ```

### Example output

```Loading required package: glmnet
Loading required package: Matrix
Loading required package: foreach
Loaded glmnet 2.0-16

Loading required package: intervals

Attaching package: 'intervals'

The following object is masked from 'package:Matrix':

expand

Loading required package: survival

Call:
manyMeans(y = y, bh.q = 0.1)

Standard deviation of noise sigma = 1.000

SelInd  MuHat P-value LowConfPt UpConfPt
1  3.555   0.002     1.765    5.230
2  3.687   0.001     1.923    5.354
3  2.743   0.019     0.741    4.530
4  2.247   0.054     0.245    4.174
5  3.577   0.002     1.791    5.250
7  3.603   0.001     1.822    5.275
8  2.515   0.032     0.485    4.359
9  2.504   0.033     0.473    4.351
11  2.734   0.020     0.730    4.523
12  4.817   0.000     3.158    6.462
13  3.320   0.004     1.474    5.015
14  3.484   0.002     1.679    5.165
16  3.800   0.001     2.055    5.462
18  2.434   0.038     0.405    4.302
19  4.113   0.000     2.409    5.766
20  3.238   0.005     1.372    4.942
42 -1.963   0.086    -3.995   -0.055
60 -1.901   0.095    -3.959   -0.021
74  1.870   0.099     0.004    3.940
84  2.133   0.066     0.162    4.100
```

selectiveInference documentation built on Sept. 7, 2019, 9:02 a.m.