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R Software Module

rwasp_variancereduction.wasp

Title produced by software

Variance Reduction Matrix

Date of computation

Wed, 29 Dec 2010 14:42:02 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/29/t1293633595dbm5tq90igbse89.htm/, Retrieved Fri, 03 May 2024 06:02:13 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116879, Retrieved Fri, 03 May 2024 06:02:13 +0000

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No (this computation is public)

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Estimated Impact

126

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

-     [Spectral Analysis] [Paper] [2010-12-29 14:04:15] [f9c71f724b8f3da7e2789afe36ffff39]
- RMPD    [Variance Reduction Matrix] [Paper: VRM (18t/m24)] [2010-12-29 14:42:02] [35c3410767ea63f72c8afa35bf7b6164] [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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116879&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116879&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116879&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Variance Reduction Matrix
V(Y[t],d=0,D=0)	111691755.052314	Range	49662	Trim Var.	67437838.6072709
V(Y[t],d=1,D=0)	47088819.5908903	Range	36008	Trim Var.	19273092.9402433
V(Y[t],d=2,D=0)	67142909.1065644	Range	41746	Trim Var.	31012939.1721311
V(Y[t],d=3,D=0)	151034364.879719	Range	59978	Trim Var.	61980273.639548
V(Y[t],d=0,D=1)	63231782.805377	Range	27358	Trim Var.	49572316.4397678
V(Y[t],d=1,D=1)	5745488.91984271	Range	12844	Trim Var.	2950460.86387632
V(Y[t],d=2,D=1)	12876123.9761905	Range	19943	Trim Var.	6306093.37960784
V(Y[t],d=3,D=1)	43302319.900974	Range	31808	Trim Var.	23709515.3877551
V(Y[t],d=0,D=2)	89491398.8445883	Range	30215	Trim Var.	71734971.3219512
V(Y[t],d=1,D=2)	13952124.6555556	Range	20672	Trim Var.	6465351.54871795
V(Y[t],d=2,D=2)	34115861.2545455	Range	28063	Trim Var.	17004582.8596491
V(Y[t],d=3,D=2)	114105115.773256	Range	52997	Trim Var.	56916170.4046942

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 111691755.052314 & Range & 49662 & Trim Var. & 67437838.6072709 \tabularnewline
V(Y[t],d=1,D=0) & 47088819.5908903 & Range & 36008 & Trim Var. & 19273092.9402433 \tabularnewline
V(Y[t],d=2,D=0) & 67142909.1065644 & Range & 41746 & Trim Var. & 31012939.1721311 \tabularnewline
V(Y[t],d=3,D=0) & 151034364.879719 & Range & 59978 & Trim Var. & 61980273.639548 \tabularnewline
V(Y[t],d=0,D=1) & 63231782.805377 & Range & 27358 & Trim Var. & 49572316.4397678 \tabularnewline
V(Y[t],d=1,D=1) & 5745488.91984271 & Range & 12844 & Trim Var. & 2950460.86387632 \tabularnewline
V(Y[t],d=2,D=1) & 12876123.9761905 & Range & 19943 & Trim Var. & 6306093.37960784 \tabularnewline
V(Y[t],d=3,D=1) & 43302319.900974 & Range & 31808 & Trim Var. & 23709515.3877551 \tabularnewline
V(Y[t],d=0,D=2) & 89491398.8445883 & Range & 30215 & Trim Var. & 71734971.3219512 \tabularnewline
V(Y[t],d=1,D=2) & 13952124.6555556 & Range & 20672 & Trim Var. & 6465351.54871795 \tabularnewline
V(Y[t],d=2,D=2) & 34115861.2545455 & Range & 28063 & Trim Var. & 17004582.8596491 \tabularnewline
V(Y[t],d=3,D=2) & 114105115.773256 & Range & 52997 & Trim Var. & 56916170.4046942 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116879&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]111691755.052314[/C][C]Range[/C][C]49662[/C][C]Trim Var.[/C][C]67437838.6072709[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]47088819.5908903[/C][C]Range[/C][C]36008[/C][C]Trim Var.[/C][C]19273092.9402433[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]67142909.1065644[/C][C]Range[/C][C]41746[/C][C]Trim Var.[/C][C]31012939.1721311[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]151034364.879719[/C][C]Range[/C][C]59978[/C][C]Trim Var.[/C][C]61980273.639548[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]63231782.805377[/C][C]Range[/C][C]27358[/C][C]Trim Var.[/C][C]49572316.4397678[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]5745488.91984271[/C][C]Range[/C][C]12844[/C][C]Trim Var.[/C][C]2950460.86387632[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]12876123.9761905[/C][C]Range[/C][C]19943[/C][C]Trim Var.[/C][C]6306093.37960784[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]43302319.900974[/C][C]Range[/C][C]31808[/C][C]Trim Var.[/C][C]23709515.3877551[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]89491398.8445883[/C][C]Range[/C][C]30215[/C][C]Trim Var.[/C][C]71734971.3219512[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]13952124.6555556[/C][C]Range[/C][C]20672[/C][C]Trim Var.[/C][C]6465351.54871795[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]34115861.2545455[/C][C]Range[/C][C]28063[/C][C]Trim Var.[/C][C]17004582.8596491[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]114105115.773256[/C][C]Range[/C][C]52997[/C][C]Trim Var.[/C][C]56916170.4046942[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116879&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116879&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)	111691755.052314	Range	49662	Trim Var.	67437838.6072709
V(Y[t],d=1,D=0)	47088819.5908903	Range	36008	Trim Var.	19273092.9402433
V(Y[t],d=2,D=0)	67142909.1065644	Range	41746	Trim Var.	31012939.1721311
V(Y[t],d=3,D=0)	151034364.879719	Range	59978	Trim Var.	61980273.639548
V(Y[t],d=0,D=1)	63231782.805377	Range	27358	Trim Var.	49572316.4397678
V(Y[t],d=1,D=1)	5745488.91984271	Range	12844	Trim Var.	2950460.86387632
V(Y[t],d=2,D=1)	12876123.9761905	Range	19943	Trim Var.	6306093.37960784
V(Y[t],d=3,D=1)	43302319.900974	Range	31808	Trim Var.	23709515.3877551
V(Y[t],d=0,D=2)	89491398.8445883	Range	30215	Trim Var.	71734971.3219512
V(Y[t],d=1,D=2)	13952124.6555556	Range	20672	Trim Var.	6465351.54871795
V(Y[t],d=2,D=2)	34115861.2545455	Range	28063	Trim Var.	17004582.8596491
V(Y[t],d=3,D=2)	114105115.773256	Range	52997	Trim Var.	56916170.4046942

Figure 1

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Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = 0.5 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 2 ; par7 = 1 ; par8 = 0 ; par9 = 1 ; par10 = FALSE ;

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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