Package 'asus'

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)

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