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Author

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R Software Module

rwasp_variancereduction.wasp

Title produced by software

Variance Reduction Matrix

Date of computation

Wed, 29 Dec 2010 21:51:02 +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/29/t12936593678rlye0nmh1xdxzt.htm/, Retrieved Fri, 03 May 2024 03:54:35 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117146, Retrieved Fri, 03 May 2024 03:54:35 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

126

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

-     [(Partial) Autocorrelation Function] [(partial) autocor...] [2009-12-09 13:20:29] [f7fc9270f813d017f9fa5b506fdc7682]
- RMP   [Variance Reduction Matrix] [variance reductio...] [2009-12-09 14:08:41] [f7fc9270f813d017f9fa5b506fdc7682]
- R  D    [Variance Reduction Matrix] [] [2010-12-26 20:46:22] [c420bdd199bcbe079f7d532ca3855317]
-             [Variance Reduction Matrix] [VRM- NWWZ] [2010-12-29 21:51:02] [63a115f47699ab31b1a302b9539c58a2] [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	1 seconds
R Server	'Gwilym Jenkins' @ www.wessa.org

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117146&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117146&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117146&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	1 seconds
R Server	'Gwilym Jenkins' @ www.wessa.org

Variance Reduction Matrix
V(Y[t],d=0,D=0)	692473505.103024	Range	115276	Trim Var.	474024249.981877
V(Y[t],d=1,D=0)	156520608.398562	Range	65564	Trim Var.	71168106.1115556
V(Y[t],d=2,D=0)	239616391.288855	Range	81499	Trim Var.	120131649.282323
V(Y[t],d=3,D=0)	548743239.949178	Range	125171	Trim Var.	284406736.891429
V(Y[t],d=0,D=1)	491558112.0633	Range	90402	Trim Var.	354146162.387857
V(Y[t],d=1,D=1)	28335850.4581992	Range	33911	Trim Var.	14779877.7111694
V(Y[t],d=2,D=1)	58350973.5621366	Range	44005	Trim Var.	27902811.2674294
V(Y[t],d=3,D=1)	190331656.105746	Range	76554	Trim Var.	97131659.4146872
V(Y[t],d=0,D=2)	654905858.432132	Range	101436	Trim Var.	497623011.684535
V(Y[t],d=1,D=2)	74790462.8544111	Range	55325	Trim Var.	36685410.3580413
V(Y[t],d=2,D=2)	165809250.864721	Range	80924	Trim Var.	93475736.680403
V(Y[t],d=3,D=2)	536651970.034483	Range	137469	Trim Var.	297251159.494772

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 692473505.103024 & Range & 115276 & Trim Var. & 474024249.981877 \tabularnewline
V(Y[t],d=1,D=0) & 156520608.398562 & Range & 65564 & Trim Var. & 71168106.1115556 \tabularnewline
V(Y[t],d=2,D=0) & 239616391.288855 & Range & 81499 & Trim Var. & 120131649.282323 \tabularnewline
V(Y[t],d=3,D=0) & 548743239.949178 & Range & 125171 & Trim Var. & 284406736.891429 \tabularnewline
V(Y[t],d=0,D=1) & 491558112.0633 & Range & 90402 & Trim Var. & 354146162.387857 \tabularnewline
V(Y[t],d=1,D=1) & 28335850.4581992 & Range & 33911 & Trim Var. & 14779877.7111694 \tabularnewline
V(Y[t],d=2,D=1) & 58350973.5621366 & Range & 44005 & Trim Var. & 27902811.2674294 \tabularnewline
V(Y[t],d=3,D=1) & 190331656.105746 & Range & 76554 & Trim Var. & 97131659.4146872 \tabularnewline
V(Y[t],d=0,D=2) & 654905858.432132 & Range & 101436 & Trim Var. & 497623011.684535 \tabularnewline
V(Y[t],d=1,D=2) & 74790462.8544111 & Range & 55325 & Trim Var. & 36685410.3580413 \tabularnewline
V(Y[t],d=2,D=2) & 165809250.864721 & Range & 80924 & Trim Var. & 93475736.680403 \tabularnewline
V(Y[t],d=3,D=2) & 536651970.034483 & Range & 137469 & Trim Var. & 297251159.494772 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117146&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]692473505.103024[/C][C]Range[/C][C]115276[/C][C]Trim Var.[/C][C]474024249.981877[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]156520608.398562[/C][C]Range[/C][C]65564[/C][C]Trim Var.[/C][C]71168106.1115556[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]239616391.288855[/C][C]Range[/C][C]81499[/C][C]Trim Var.[/C][C]120131649.282323[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]548743239.949178[/C][C]Range[/C][C]125171[/C][C]Trim Var.[/C][C]284406736.891429[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]491558112.0633[/C][C]Range[/C][C]90402[/C][C]Trim Var.[/C][C]354146162.387857[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]28335850.4581992[/C][C]Range[/C][C]33911[/C][C]Trim Var.[/C][C]14779877.7111694[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]58350973.5621366[/C][C]Range[/C][C]44005[/C][C]Trim Var.[/C][C]27902811.2674294[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]190331656.105746[/C][C]Range[/C][C]76554[/C][C]Trim Var.[/C][C]97131659.4146872[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]654905858.432132[/C][C]Range[/C][C]101436[/C][C]Trim Var.[/C][C]497623011.684535[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]74790462.8544111[/C][C]Range[/C][C]55325[/C][C]Trim Var.[/C][C]36685410.3580413[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]165809250.864721[/C][C]Range[/C][C]80924[/C][C]Trim Var.[/C][C]93475736.680403[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]536651970.034483[/C][C]Range[/C][C]137469[/C][C]Trim Var.[/C][C]297251159.494772[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117146&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117146&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)	692473505.103024	Range	115276	Trim Var.	474024249.981877
V(Y[t],d=1,D=0)	156520608.398562	Range	65564	Trim Var.	71168106.1115556
V(Y[t],d=2,D=0)	239616391.288855	Range	81499	Trim Var.	120131649.282323
V(Y[t],d=3,D=0)	548743239.949178	Range	125171	Trim Var.	284406736.891429
V(Y[t],d=0,D=1)	491558112.0633	Range	90402	Trim Var.	354146162.387857
V(Y[t],d=1,D=1)	28335850.4581992	Range	33911	Trim Var.	14779877.7111694
V(Y[t],d=2,D=1)	58350973.5621366	Range	44005	Trim Var.	27902811.2674294
V(Y[t],d=3,D=1)	190331656.105746	Range	76554	Trim Var.	97131659.4146872
V(Y[t],d=0,D=2)	654905858.432132	Range	101436	Trim Var.	497623011.684535
V(Y[t],d=1,D=2)	74790462.8544111	Range	55325	Trim Var.	36685410.3580413
V(Y[t],d=2,D=2)	165809250.864721	Range	80924	Trim Var.	93475736.680403
V(Y[t],d=3,D=2)	536651970.034483	Range	137469	Trim Var.	297251159.494772

Figure 1

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Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = 12 ; par2 = ; par3 = ; par4 = ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;

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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