type one overall

setting: row<-40 col<-100 num<-5 str<-0 times<-100

1. largest beta

• get estimated beta, and its largest signal
• get noise by deleting true signals from estimated beta, and then get the largest signal of noise
• run n times
• regard 5% largest value of noise as cutoff, and find out the percent of signals in estimated beta lager than cutoff

1. str<-rep(0,5)

## [1] 0.05 0.05

2. str<-seq(0.1,0.5,0.1)

## [1] "reg"
##     0.1  0.2  0.3  0.4  0.5
## 5  0.14 0.27 0.50 0.49 0.46
## 10 0.11 0.33 0.39 0.35 0.37
## 15 0.20 0.32 0.19 0.27 0.53
## 20 0.19 0.33 0.35 0.43 0.48
## 25 0.25 0.44 0.33 0.31 0.30
## [1] "smo"
##     0.1  0.2  0.3  0.4  0.5
## 5  0.12 0.36 0.76 0.99 1.00
## 10 0.09 0.24 0.48 0.94 1.00
## 15 0.14 0.24 0.65 0.74 0.82
## 20 0.16 0.55 0.46 0.74 0.68
## 25 0.14 0.38 0.47 0.84 0.53
## [1] "smo-reg"
##      0.1   0.2  0.3  0.4  0.5
## 5  -0.02  0.09 0.26 0.50 0.54
## 10 -0.02 -0.09 0.09 0.59 0.63
## 15 -0.06 -0.08 0.46 0.47 0.29
## 20 -0.03  0.22 0.11 0.31 0.20
## 25 -0.11 -0.06 0.14 0.53 0.23

2. smallest MSE

• obtain true beta and estimated beta, then calculate MSE
• look beta equal to 0 as true noise beta and get estimated noise beta, calculate MSE with same method as last step
• find 5% smallest value in noise MSE as cutoff
• calculate power by deviding times with number of values that larger than cutoff in true MSE

1. str<-rep(0,5)

## [1] 0.12

2. str<-seq(0.1,0.5,0.1)

## [1] "reg"
##    0.1 0.2 0.3 0.4 0.5
## 5    0   0   0   0   0
## 10   0   0   0   0   0
## 15   0   0   0   0   0
## 20   0   0   0   0   0
## 25   0   0   0   0   0
## [1] "smo"
##     0.1  0.2  0.3  0.4  0.5
## 5  0.02 0.01 0.05 0.04 0.01
## 10 0.00 0.00 0.00 0.01 0.00
## 15 0.00 0.00 0.00 0.00 0.00
## 20 0.00 0.00 0.00 0.00 0.00
## 25 0.00 0.00 0.00 0.00 0.00
## [1] "smo-reg"
##     0.1  0.2  0.3  0.4  0.5
## 5  0.02 0.01 0.05 0.04 0.01
## 10 0.00 0.00 0.00 0.01 0.00
## 15 0.00 0.00 0.00 0.00 0.00
## 20 0.00 0.00 0.00 0.00 0.00
## 25 0.00 0.00 0.00 0.00 0.00