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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_variancereduction.wasp

Title produced by software

Variance Reduction Matrix

Date of computation

Sun, 26 Dec 2010 22:38:21 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/26/t1293402979rkb9efgmqwjejqi.htm/, Retrieved Mon, 06 May 2024 23:55:36 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115827, Retrieved Mon, 06 May 2024 23:55:36 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

100

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Variance Reduction Matrix] [paper VRM] [2010-12-26 22:38:21] [4c854bb223ec27caaa7bcfc5e77b0dbd] [Current]

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Dataseries X:

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Histogram

Boxplots

5.2
7.9
8.7
8.9
15.3
15.4
18.1
19.7
13
12.6
6.2
3.5
3.4
0
9.5
8.9
10.4
13.2
18.9
19
16.3
10.6
5.8
3.6
2.6
5
7.3
9.2
15.7
16.8
18.4
18.1
14.6
7.8
7.6
3.8
5.6
2.2
6.8
11.8
14.9
16.7
16.7
15.9
13.6
9.2
2.8
2.5
4.8
2.8
7.8
9
12.9
16.4
21.8
17.8
13.5
10
10.4
5.5
4
6.8
5.7
9.1
13.6
15
20.9
20.4
14
13.7
7.1
0.8
2.1
1.3
3.9
10.7
11.1
16.4
17.1
17.3
12.9
10.9
5.3
0.7
-0.2
6.5
8.6
8.5
13.3
16.2
17.5
21.2
14.8
10.3
7.3
5.1
4.4
6.2
7.7
9.3
15.6
16.3
16.6
17.4
15.3
9.7
3.7
4.6
5.4
3.1
7.9
10.1
15
15.6
19.7
18.1
17.7
10.7
6.2
4.2
4
5.9
7.1
10.5
15.1
16.8
15.3
18.4
16.1
11.3
7.9
5.6
3.4
4.8
6.5
8.5
15.1
15.7
18.7
19.2
12.9
14.4
6.2
3.3
4.6
7.2
7.8
9.9
13.6
17.1
17.8
18.6
14.7
10.5
8.6
4.4
2.3
2.8
8.8
10.7
13.9
19.3
19.5
20.4
15.3
7.9
8.3
4.5
3.2
5
6.6
11.1
12.8
16.3
17.4
18.9
15.8
11.7
6.4
2.9
4.7
2.4
7.2
10.7
13.4
18.5
18.3
16.8
16.6
14.1
6.1
3.5
1.7
2.3
4.5
9.3
14.2
17.3
23
16.3
18.4
14.2
9.1
5.9
7.2
6.8
8
14.3
14.6
17.5
17.2
17.2
14.1
10.5
6.8
4.1
6.5
6.1
6.3
9.3
16.4
16.1
18
17.6
14
10.5
6.9
2.8
0.7
3.6
6.7
12.5
14.4
16.5
18.7
19.4
15.8
11.3
9.7
2.9

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115827&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115827&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115827&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

Variance Reduction Matrix
V(Y[t],d=0,D=0)	31.543009762901	Range	23.2	Trim Var.	24.8563789836348
V(Y[t],d=1,D=0)	12.6454952357512	Range	17.7	Trim Var.	8.649437058488
V(Y[t],d=2,D=0)	16.0723662376343	Range	25.3	Trim Var.	10.084940546707
V(Y[t],d=3,D=0)	46.0345934348852	Range	44.2	Trim Var.	28.5401745061564
V(Y[t],d=0,D=1)	5.76540439755777	Range	15.5	Trim Var.	3.24206582633053
V(Y[t],d=1,D=1)	9.78484113679778	Range	15.9	Trim Var.	6.21556455152904
V(Y[t],d=2,D=1)	28.7771059980334	Range	27.8	Trim Var.	18.5728929609379
V(Y[t],d=3,D=1)	93.099107142857	Range	47.3	Trim Var.	60.1728960199005
V(Y[t],d=0,D=2)	16.7707174849268	Range	23.8	Trim Var.	9.60477655440414
V(Y[t],d=1,D=2)	28.8078469897848	Range	28.9	Trim Var.	17.223718156304
V(Y[t],d=2,D=2)	85.4021868281339	Range	51.6	Trim Var.	54.6701297993019
V(Y[t],d=3,D=2)	277.201504119054	Range	90.2	Trim Var.	176.27768309663

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 31.543009762901 & Range & 23.2 & Trim Var. & 24.8563789836348 \tabularnewline
V(Y[t],d=1,D=0) & 12.6454952357512 & Range & 17.7 & Trim Var. & 8.649437058488 \tabularnewline
V(Y[t],d=2,D=0) & 16.0723662376343 & Range & 25.3 & Trim Var. & 10.084940546707 \tabularnewline
V(Y[t],d=3,D=0) & 46.0345934348852 & Range & 44.2 & Trim Var. & 28.5401745061564 \tabularnewline
V(Y[t],d=0,D=1) & 5.76540439755777 & Range & 15.5 & Trim Var. & 3.24206582633053 \tabularnewline
V(Y[t],d=1,D=1) & 9.78484113679778 & Range & 15.9 & Trim Var. & 6.21556455152904 \tabularnewline
V(Y[t],d=2,D=1) & 28.7771059980334 & Range & 27.8 & Trim Var. & 18.5728929609379 \tabularnewline
V(Y[t],d=3,D=1) & 93.099107142857 & Range & 47.3 & Trim Var. & 60.1728960199005 \tabularnewline
V(Y[t],d=0,D=2) & 16.7707174849268 & Range & 23.8 & Trim Var. & 9.60477655440414 \tabularnewline
V(Y[t],d=1,D=2) & 28.8078469897848 & Range & 28.9 & Trim Var. & 17.223718156304 \tabularnewline
V(Y[t],d=2,D=2) & 85.4021868281339 & Range & 51.6 & Trim Var. & 54.6701297993019 \tabularnewline
V(Y[t],d=3,D=2) & 277.201504119054 & Range & 90.2 & Trim Var. & 176.27768309663 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115827&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]31.543009762901[/C][C]Range[/C][C]23.2[/C][C]Trim Var.[/C][C]24.8563789836348[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]12.6454952357512[/C][C]Range[/C][C]17.7[/C][C]Trim Var.[/C][C]8.649437058488[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]16.0723662376343[/C][C]Range[/C][C]25.3[/C][C]Trim Var.[/C][C]10.084940546707[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]46.0345934348852[/C][C]Range[/C][C]44.2[/C][C]Trim Var.[/C][C]28.5401745061564[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]5.76540439755777[/C][C]Range[/C][C]15.5[/C][C]Trim Var.[/C][C]3.24206582633053[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]9.78484113679778[/C][C]Range[/C][C]15.9[/C][C]Trim Var.[/C][C]6.21556455152904[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]28.7771059980334[/C][C]Range[/C][C]27.8[/C][C]Trim Var.[/C][C]18.5728929609379[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]93.099107142857[/C][C]Range[/C][C]47.3[/C][C]Trim Var.[/C][C]60.1728960199005[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]16.7707174849268[/C][C]Range[/C][C]23.8[/C][C]Trim Var.[/C][C]9.60477655440414[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]28.8078469897848[/C][C]Range[/C][C]28.9[/C][C]Trim Var.[/C][C]17.223718156304[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]85.4021868281339[/C][C]Range[/C][C]51.6[/C][C]Trim Var.[/C][C]54.6701297993019[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]277.201504119054[/C][C]Range[/C][C]90.2[/C][C]Trim Var.[/C][C]176.27768309663[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115827&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115827&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Variance Reduction Matrix
V(Y[t],d=0,D=0)	31.543009762901	Range	23.2	Trim Var.	24.8563789836348
V(Y[t],d=1,D=0)	12.6454952357512	Range	17.7	Trim Var.	8.649437058488
V(Y[t],d=2,D=0)	16.0723662376343	Range	25.3	Trim Var.	10.084940546707
V(Y[t],d=3,D=0)	46.0345934348852	Range	44.2	Trim Var.	28.5401745061564
V(Y[t],d=0,D=1)	5.76540439755777	Range	15.5	Trim Var.	3.24206582633053
V(Y[t],d=1,D=1)	9.78484113679778	Range	15.9	Trim Var.	6.21556455152904
V(Y[t],d=2,D=1)	28.7771059980334	Range	27.8	Trim Var.	18.5728929609379
V(Y[t],d=3,D=1)	93.099107142857	Range	47.3	Trim Var.	60.1728960199005
V(Y[t],d=0,D=2)	16.7707174849268	Range	23.8	Trim Var.	9.60477655440414
V(Y[t],d=1,D=2)	28.8078469897848	Range	28.9	Trim Var.	17.223718156304
V(Y[t],d=2,D=2)	85.4021868281339	Range	51.6	Trim Var.	54.6701297993019
V(Y[t],d=3,D=2)	277.201504119054	Range	90.2	Trim Var.	176.27768309663

Figure 1

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = 12 ;

R code (references can be found in the software module):

par1 <- as.numeric(par1)
n <- length(x)
sx <- sort(x)
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Variance Reduction Matrix',6,TRUE)
a<-table.row.end(a)
for (bigd in 0:2) {
for (smalld in 0:3) {
mylabel <- 'V(Y[t],d='
mylabel <- paste(mylabel,as.character(smalld),sep='')
mylabel <- paste(mylabel,',D=',sep='')
mylabel <- paste(mylabel,as.character(bigd),sep='')
mylabel <- paste(mylabel,')',sep='')
a<-table.row.start(a)
a<-table.element(a,mylabel,header=TRUE)
myx <- x
if (smalld > 0) myx <- diff(myx,lag=1,differences=smalld)
if (bigd > 0) myx <- diff(myx,lag=par1,differences=bigd)
a<-table.element(a,var(myx))
a<-table.element(a,'Range',header=TRUE)
a<-table.element(a,max(myx)-min(myx))
a<-table.element(a,'Trim Var.',header=TRUE)
smyx <- sort(myx)
sn <- length(smyx)
a<-table.element(a,var(smyx[smyx>quantile(smyx,0.05) & smyxa<-table.row.end(a)
}
}
a<-table.end(a)
table.save(a,file='mytable.tab')
bitmap(file='pic0.png')
op <- par(mfrow=c(2,2))
plot(x,type='l',xlab='time',ylab='value',main='d=0, D=0')
plot(diff(x,lag=1,differences=1),type='l',xlab='time',ylab='value',main='d=1, D=0')
plot(diff(x,lag=par1,differences=1),type='l',xlab='time',ylab='value',main='d=0, D=1')
plot(diff(diff(x,lag=1,differences=1),lag=par1,differences=1),type='l',xlab='time',ylab='value',main='d=1, D=1')
par(op)
dev.off()

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Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code