Type: Package
Title: Adaptive SURE Thresholding Using Side Information
Version: 1.5.0
Description: Provides the ASUS procedure for estimating a high dimensional sparse parameter in the presence of auxiliary data that encode side information on sparsity. It is a robust data combination procedure in the sense that even when pooling non-informative auxiliary data ASUS would be at least as efficient as competing soft thresholding based methods that do not use auxiliary data. For more information, please see the paper Adaptive Sparse Estimation with Side Information by Banerjee, Mukherjee and Sun (JASA 2020).
License: GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
Encoding: UTF-8
URL: https://github.com/trambakbanerjee/asus#asus
Imports: wavethresh, stats, utils
RoxygenNote: 7.2.3
Suggests: knitr, rmarkdown
VignetteBuilder: knitr
NeedsCompilation: no
Packaged: 2023-08-24 15:45:11 UTC; Trambak Banerjee
Author: Trambak Banerjee [aut, cre], Gourab Mukherjee [aut], Wenguang Sun [aut]
Maintainer: Trambak Banerjee <trambak@ku.edu>
Repository: CRAN
Date/Publication: 2023-08-24 16:20:14 UTC

Adaptive SURE thresholding with side information (asus)

Description

ASUS procedure for shrinkage estimation of a high dimensional sparse parameter.

Usage

asus(d, v.d, s, k = 2, m = 50)

Arguments

d

an n vector of primary observations

v.d

an n vector of variances for each component of d

s

an n vector of side information

k

number of groups. Default is k=2

m

partitions the support of |s| into m equidistant points. Default is m=50

Details

Estimates a sparse high dimensional vector using the ASUS procedure described in Banerjee et al. (2017). If k = 1 then ASUS is the SureShrink estimator. The current implementation of ASUS estimates the grouping thresholds based on the magnitude of |s|. See the reference for more details.

Value

  1. est - an n vector holding the estimates

  2. mse - estimate of risk

  3. tau - k-1 vector of grouping parameters if k>=2

  4. t - k vector of thresholding parameters

  5. size - k vector of group sizes

References

Banerjee. T, Mukherjee. G and Sun. W. Adaptive Sparse Estimation with Side Information. Journal of the American Statistical Association 115, no. 532 (2020): 2053-2067.

See Also

sureshrink,ejs,sureshrink.mse

Examples

library(asus)
set.seed(42)
d<-rnorm(10,2,1)
v.d<- rep(1,10)
set.seed(42)
s<-rnorm(10,3,0.1)
asus.out<-asus(d,v.d,s)

Risk of asus with pre-defined grouping thresholds

Description

Estimates the risk of asus when there are k(>2) groups with pre-defined grouping thresholds

Usage

asus.cuts(d, v.d, s, cutpoints)

Arguments

d

an n vector of primary observations

v.d

an n vector of variances for each component of d

s

an n vector of side information

cutpoints

k-1 pre-defined grouping thresholds for k groups. k must be bigger than 2.

Details

Estimates the risk of asus when there are k(>2) groups with k pre-defined grouping thresholds. This function is called when asus executes.

Value

mse - estimate of risk

References

Banerjee. T, Mukherjee. G and Sun. W. Adaptive Sparse Estimation with Side Information. Journal of the American Statistical Association 115, no. 532 (2020): 2053-2067.

See Also

asus,sureshrink,ejs,sureshrink.mse

Examples

library(asus)
set.seed(42)
d<-rnorm(10)
v.d<- rep(1,10)
set.seed(42)
s<-rnorm(10)
out<-asus.cuts(d,v.d,s,c(0.1,0.5,1))

Extended James-Stein (ejs) estimator

Description

Extended James-Stein estimator of a high dimensional sparse parameter.

Usage

ejs(d, v.d)

Arguments

d

an n vector of observations

v.d

an n vector of variances for each component of d

Details

Extended James-Stein estimator of mean from Brown (2008) and equation (7.3) in Xie et al. (2012)

Value

est - an n vector holding the estimates

References

  1. Brown, L.D. (2008). In-Season Prediction of Batting Averages: A Field Test of Empirical Bayes and Bayes Methodologies. The Annals of Applied Statistics, 2, 113-152

  2. Xie, X. C., Kou, S. C., and Brown, L. D. (2012). SURE Estimates for a Heteroscedastic Hierarchical Model. Journal of the American Statistical Association, 107, 1465-1479.

See Also

sureshrink,asus

Examples

library(asus)
set.seed(42)
d<-rnorm(10,2,1)
v.d<- rep(1,10)
theta.hat<-ejs(d,v.d)

Soft Thresholding estimator

Description

Soft thresholds the input signal y with the threshold value thld

Usage

softTh(y, thld)

Arguments

y

1D signal to be thresholded

thld

numeric threshold value

Value

a numeric vector of thresholded values of the same length as y.

References

Donoho, David L. "De-noising by soft-thresholding." IEEE transactions on information theory 41, no. 3 (1995): 613-627.

Examples

library(asus)
set.seed(42)
y<-rnorm(10,2,1)
thld<- 3
x<-softTh(y,thld)

SureShrink estimator

Description

SureShrink estimator of a high dimensional sparse parameter from Donoho and Johnstone (1995)

Usage

sureshrink(d, v.d)

Arguments

d

an n vector of observations

v.d

an n vector of variances for each component of d

Details

Estimates a threshold t by minimizing the SURE function and then soft thresholds d using t.

Value

  1. est - an n vector holding the estimates

  2. t - estimated threshold

References

David L Donoho and Iain M Johnstone. Adapting to unknown smoothness via wavelet shrinkage. Journal of the american statistical association, 90(432):1200-1224, 1995

See Also

sureshrink.mse

Examples

library(asus)
set.seed(42)
d<-rnorm(10,2,1)
v.d<- rep(1,10)
theta.hat<-sureshrink(d,v.d)

SURE estimate of risk

Description

Stein's Unbiased Risk Estimate for the sureshrink estimator

Usage

sureshrink.mse(d, v.d, type = 1, t = 0)

Arguments

d

an n vector of observations

v.d

an n vector of variances for each component of d

type

set type=1 if you want the thresholding parameter t to be estimated. Otherwise set type = 0 in which case you must provide t. Default is type = 1

t

soft thresholding parameter. If type = 1, then t is estimated whereas if type = 0 then you must provide t. Default is t = 0 (and type = 1)

Details

Estimates the risk of the surehsrink estimator of Donoho and Johnstone (1995).

Value

  1. sure.est - SURE estimate of risk

  2. t - estimated threshold (meaningless if type = 0)

References

  1. Charles M Stein. Estimation of the mean of a multivariate normal distribution. The annals of Statistics, pages 1135-1151, 1981

  2. David L Donoho and Iain M Johnstone. Adapting to unknown smoothness via wavelet shrinkage. Journal of the american statistical association, 90(432):1200-1224, 1995

See Also

sureshrink,asus

Examples

library(asus)
set.seed(42)
d<-rnorm(10,2,1)
v.d<- rep(1,10)
mse<-sureshrink.mse(d,v.d)