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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

Fri, 09 Dec 2011 06:54:01 -0500

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/2011/Dec/09/t1323431746qykfikqkkynxrgp.htm/, Retrieved Thu, 02 May 2024 16:51:19 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=153278, Retrieved Thu, 02 May 2024 16:51:19 +0000

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No (this computation is public)

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Estimated Impact

129

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

-     [Variance Reduction Matrix] [] [2011-12-09 11:37:33] [f2faabc3a2466a29562900bc59f67898]
- R  D    [Variance Reduction Matrix] [] [2011-12-09 11:54:01] [5988e21ec0676b551e455a86717edc1d] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	0 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

\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 & 0 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=153278&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]0 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=153278&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=153278&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	0 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Variance Reduction Matrix
V(Y[t],d=0,D=0)	33262261.4338983	Range	25303	Trim Var.	22354803.5345912
V(Y[t],d=1,D=0)	36719122.345412	Range	29984	Trim Var.	17015228.6835994
V(Y[t],d=2,D=0)	97440433.0904416	Range	56102	Trim Var.	45679967.1191554
V(Y[t],d=3,D=0)	315477893.097744	Range	91105	Trim Var.	161758899.758431
V(Y[t],d=0,D=1)	11549377.1702128	Range	13003	Trim Var.	7282611.17770035
V(Y[t],d=1,D=1)	7080542.84458834	Range	12056	Trim Var.	4087757.67804878
V(Y[t],d=2,D=1)	21495507.0628019	Range	22955	Trim Var.	12528558.3358974
V(Y[t],d=3,D=1)	75460528.2707071	Range	41164	Trim Var.	41026793.3009447
V(Y[t],d=0,D=2)	36352483.8571429	Range	23794	Trim Var.	24608063.3538306
V(Y[t],d=1,D=2)	15099799.3647059	Range	18193	Trim Var.	8583192.72903226
V(Y[t],d=2,D=2)	43444030.7139037	Range	34184	Trim Var.	22128078.1195402
V(Y[t],d=3,D=2)	153205440.75	Range	63377	Trim Var.	78240900.6871921

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 33262261.4338983 & Range & 25303 & Trim Var. & 22354803.5345912 \tabularnewline
V(Y[t],d=1,D=0) & 36719122.345412 & Range & 29984 & Trim Var. & 17015228.6835994 \tabularnewline
V(Y[t],d=2,D=0) & 97440433.0904416 & Range & 56102 & Trim Var. & 45679967.1191554 \tabularnewline
V(Y[t],d=3,D=0) & 315477893.097744 & Range & 91105 & Trim Var. & 161758899.758431 \tabularnewline
V(Y[t],d=0,D=1) & 11549377.1702128 & Range & 13003 & Trim Var. & 7282611.17770035 \tabularnewline
V(Y[t],d=1,D=1) & 7080542.84458834 & Range & 12056 & Trim Var. & 4087757.67804878 \tabularnewline
V(Y[t],d=2,D=1) & 21495507.0628019 & Range & 22955 & Trim Var. & 12528558.3358974 \tabularnewline
V(Y[t],d=3,D=1) & 75460528.2707071 & Range & 41164 & Trim Var. & 41026793.3009447 \tabularnewline
V(Y[t],d=0,D=2) & 36352483.8571429 & Range & 23794 & Trim Var. & 24608063.3538306 \tabularnewline
V(Y[t],d=1,D=2) & 15099799.3647059 & Range & 18193 & Trim Var. & 8583192.72903226 \tabularnewline
V(Y[t],d=2,D=2) & 43444030.7139037 & Range & 34184 & Trim Var. & 22128078.1195402 \tabularnewline
V(Y[t],d=3,D=2) & 153205440.75 & Range & 63377 & Trim Var. & 78240900.6871921 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=153278&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]33262261.4338983[/C][C]Range[/C][C]25303[/C][C]Trim Var.[/C][C]22354803.5345912[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]36719122.345412[/C][C]Range[/C][C]29984[/C][C]Trim Var.[/C][C]17015228.6835994[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]97440433.0904416[/C][C]Range[/C][C]56102[/C][C]Trim Var.[/C][C]45679967.1191554[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]315477893.097744[/C][C]Range[/C][C]91105[/C][C]Trim Var.[/C][C]161758899.758431[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]11549377.1702128[/C][C]Range[/C][C]13003[/C][C]Trim Var.[/C][C]7282611.17770035[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]7080542.84458834[/C][C]Range[/C][C]12056[/C][C]Trim Var.[/C][C]4087757.67804878[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]21495507.0628019[/C][C]Range[/C][C]22955[/C][C]Trim Var.[/C][C]12528558.3358974[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]75460528.2707071[/C][C]Range[/C][C]41164[/C][C]Trim Var.[/C][C]41026793.3009447[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]36352483.8571429[/C][C]Range[/C][C]23794[/C][C]Trim Var.[/C][C]24608063.3538306[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]15099799.3647059[/C][C]Range[/C][C]18193[/C][C]Trim Var.[/C][C]8583192.72903226[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]43444030.7139037[/C][C]Range[/C][C]34184[/C][C]Trim Var.[/C][C]22128078.1195402[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]153205440.75[/C][C]Range[/C][C]63377[/C][C]Trim Var.[/C][C]78240900.6871921[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=153278&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=153278&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)	33262261.4338983	Range	25303	Trim Var.	22354803.5345912
V(Y[t],d=1,D=0)	36719122.345412	Range	29984	Trim Var.	17015228.6835994
V(Y[t],d=2,D=0)	97440433.0904416	Range	56102	Trim Var.	45679967.1191554
V(Y[t],d=3,D=0)	315477893.097744	Range	91105	Trim Var.	161758899.758431
V(Y[t],d=0,D=1)	11549377.1702128	Range	13003	Trim Var.	7282611.17770035
V(Y[t],d=1,D=1)	7080542.84458834	Range	12056	Trim Var.	4087757.67804878
V(Y[t],d=2,D=1)	21495507.0628019	Range	22955	Trim Var.	12528558.3358974
V(Y[t],d=3,D=1)	75460528.2707071	Range	41164	Trim Var.	41026793.3009447
V(Y[t],d=0,D=2)	36352483.8571429	Range	23794	Trim Var.	24608063.3538306
V(Y[t],d=1,D=2)	15099799.3647059	Range	18193	Trim Var.	8583192.72903226
V(Y[t],d=2,D=2)	43444030.7139037	Range	34184	Trim Var.	22128078.1195402
V(Y[t],d=3,D=2)	153205440.75	Range	63377	Trim Var.	78240900.6871921

Figure 1

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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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