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R Software Module

rwasp_variancereduction.wasp

Title produced by software

Variance Reduction Matrix

Date of computation

Sun, 18 Dec 2011 13:57:08 -0500

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/18/t13242346470qhvkl58j7bxzq5.htm/, Retrieved Sun, 05 May 2024 18:05:22 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=157133, Retrieved Sun, 05 May 2024 18:05:22 +0000

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-     [Univariate Data Series] [] [2008-12-08 19:22:39] [d2d412c7f4d35ffbf5ee5ee89db327d4]
- RMP   [Variance Reduction Matrix] [WS IX-aantal over...] [2011-12-06 09:34:20] [7c680a04865e75aa8ab422cdbfd97ac3]
- R  D      [Variance Reduction Matrix] [Paper VRM] [2011-12-18 18:57:08] [3e388c05c22237d436c48535c44f60bb] [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	'Gertrude Mary Cox' @ cox.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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157133&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157133&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157133&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	'Gertrude Mary Cox' @ cox.wessa.net

Variance Reduction Matrix
V(Y[t],d=0,D=0)	13049498496525	Range	13297704	Trim Var.	8743171331180.42
V(Y[t],d=1,D=0)	9488010982192.28	Range	17735416	Trim Var.	4392248692077.81
V(Y[t],d=2,D=0)	16339056138979.1	Range	25807117	Trim Var.	5790480013100.58
V(Y[t],d=3,D=0)	42580262524008.3	Range	49468523	Trim Var.	14132627664191.7
V(Y[t],d=0,D=1)	2128747303865.81	Range	11954416	Trim Var.	568772950846.057
V(Y[t],d=1,D=1)	4446147896994.54	Range	16799895	Trim Var.	1406437377615.38
V(Y[t],d=2,D=1)	12991749407003.9	Range	31824794	Trim Var.	3841067920133.64
V(Y[t],d=3,D=1)	42211635906245.8	Range	49575634	Trim Var.	14878035888168.4
V(Y[t],d=0,D=2)	6098706820521.66	Range	16613088	Trim Var.	1655794123526.67
V(Y[t],d=1,D=2)	12684559295074.5	Range	29446607	Trim Var.	3580984128337.55
V(Y[t],d=2,D=2)	37075529836322.6	Range	41586925	Trim Var.	9320257281851.63
V(Y[t],d=3,D=2)	121974309299475	Range	78978059	Trim Var.	41150854335194.1

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 13049498496525 & Range & 13297704 & Trim Var. & 8743171331180.42 \tabularnewline
V(Y[t],d=1,D=0) & 9488010982192.28 & Range & 17735416 & Trim Var. & 4392248692077.81 \tabularnewline
V(Y[t],d=2,D=0) & 16339056138979.1 & Range & 25807117 & Trim Var. & 5790480013100.58 \tabularnewline
V(Y[t],d=3,D=0) & 42580262524008.3 & Range & 49468523 & Trim Var. & 14132627664191.7 \tabularnewline
V(Y[t],d=0,D=1) & 2128747303865.81 & Range & 11954416 & Trim Var. & 568772950846.057 \tabularnewline
V(Y[t],d=1,D=1) & 4446147896994.54 & Range & 16799895 & Trim Var. & 1406437377615.38 \tabularnewline
V(Y[t],d=2,D=1) & 12991749407003.9 & Range & 31824794 & Trim Var. & 3841067920133.64 \tabularnewline
V(Y[t],d=3,D=1) & 42211635906245.8 & Range & 49575634 & Trim Var. & 14878035888168.4 \tabularnewline
V(Y[t],d=0,D=2) & 6098706820521.66 & Range & 16613088 & Trim Var. & 1655794123526.67 \tabularnewline
V(Y[t],d=1,D=2) & 12684559295074.5 & Range & 29446607 & Trim Var. & 3580984128337.55 \tabularnewline
V(Y[t],d=2,D=2) & 37075529836322.6 & Range & 41586925 & Trim Var. & 9320257281851.63 \tabularnewline
V(Y[t],d=3,D=2) & 121974309299475 & Range & 78978059 & Trim Var. & 41150854335194.1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157133&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]13049498496525[/C][C]Range[/C][C]13297704[/C][C]Trim Var.[/C][C]8743171331180.42[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]9488010982192.28[/C][C]Range[/C][C]17735416[/C][C]Trim Var.[/C][C]4392248692077.81[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]16339056138979.1[/C][C]Range[/C][C]25807117[/C][C]Trim Var.[/C][C]5790480013100.58[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]42580262524008.3[/C][C]Range[/C][C]49468523[/C][C]Trim Var.[/C][C]14132627664191.7[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]2128747303865.81[/C][C]Range[/C][C]11954416[/C][C]Trim Var.[/C][C]568772950846.057[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]4446147896994.54[/C][C]Range[/C][C]16799895[/C][C]Trim Var.[/C][C]1406437377615.38[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]12991749407003.9[/C][C]Range[/C][C]31824794[/C][C]Trim Var.[/C][C]3841067920133.64[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]42211635906245.8[/C][C]Range[/C][C]49575634[/C][C]Trim Var.[/C][C]14878035888168.4[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]6098706820521.66[/C][C]Range[/C][C]16613088[/C][C]Trim Var.[/C][C]1655794123526.67[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]12684559295074.5[/C][C]Range[/C][C]29446607[/C][C]Trim Var.[/C][C]3580984128337.55[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]37075529836322.6[/C][C]Range[/C][C]41586925[/C][C]Trim Var.[/C][C]9320257281851.63[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]121974309299475[/C][C]Range[/C][C]78978059[/C][C]Trim Var.[/C][C]41150854335194.1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157133&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157133&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)	13049498496525	Range	13297704	Trim Var.	8743171331180.42
V(Y[t],d=1,D=0)	9488010982192.28	Range	17735416	Trim Var.	4392248692077.81
V(Y[t],d=2,D=0)	16339056138979.1	Range	25807117	Trim Var.	5790480013100.58
V(Y[t],d=3,D=0)	42580262524008.3	Range	49468523	Trim Var.	14132627664191.7
V(Y[t],d=0,D=1)	2128747303865.81	Range	11954416	Trim Var.	568772950846.057
V(Y[t],d=1,D=1)	4446147896994.54	Range	16799895	Trim Var.	1406437377615.38
V(Y[t],d=2,D=1)	12991749407003.9	Range	31824794	Trim Var.	3841067920133.64
V(Y[t],d=3,D=1)	42211635906245.8	Range	49575634	Trim Var.	14878035888168.4
V(Y[t],d=0,D=2)	6098706820521.66	Range	16613088	Trim Var.	1655794123526.67
V(Y[t],d=1,D=2)	12684559295074.5	Range	29446607	Trim Var.	3580984128337.55
V(Y[t],d=2,D=2)	37075529836322.6	Range	41586925	Trim Var.	9320257281851.63
V(Y[t],d=3,D=2)	121974309299475	Range	78978059	Trim Var.	41150854335194.1

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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