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R Software Module

rwasp_variancereduction.wasp

Title produced by software

Variance Reduction Matrix

Date of computation

Wed, 29 Dec 2010 12:13:40 +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/t1293625027idipfww8gvokm8v.htm/, Retrieved Fri, 03 May 2024 07:41:35 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116743, Retrieved Fri, 03 May 2024 07:41:35 +0000

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Estimated Impact

147

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

-     [Variance Reduction Matrix] [] [2010-12-15 19:36:01] [9f0fea5f96e3630b8f903250153d0968]
-   PD    [Variance Reduction Matrix] [Variance Reductio...] [2010-12-29 12:13:40] [be9b1effb945c5b0652fb49bcca5faef] [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	2 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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116743&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116743&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116743&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Variance Reduction Matrix
V(Y[t],d=0,D=0)	111235287.378838	Range	45888	Trim Var.	73988293.4595075
V(Y[t],d=1,D=0)	24061739.3254199	Range	27844	Trim Var.	15011610.0274510
V(Y[t],d=2,D=0)	52992198.4694578	Range	39364	Trim Var.	32321045.7343660
V(Y[t],d=3,D=0)	147402277.090463	Range	65306	Trim Var.	88436153.7049662
V(Y[t],d=0,D=1)	53575355.0090779	Range	42474	Trim Var.	28798276.0561578
V(Y[t],d=1,D=1)	46012278.8884005	Range	35590	Trim Var.	28276705.5919753
V(Y[t],d=2,D=1)	99451945.6459426	Range	53356	Trim Var.	60798663.5037975
V(Y[t],d=3,D=1)	280030147.836823	Range	84570	Trim Var.	154921116.291464
V(Y[t],d=0,D=2)	124428698.948276	Range	62599	Trim Var.	74051771.9928405
V(Y[t],d=1,D=2)	144506081.381983	Range	61138	Trim Var.	85832801.5905673
V(Y[t],d=2,D=2)	310317662.015321	Range	92564	Trim Var.	186962131.288947
V(Y[t],d=3,D=2)	872827987.42353	Range	151953	Trim Var.	531537182.999279

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 111235287.378838 & Range & 45888 & Trim Var. & 73988293.4595075 \tabularnewline
V(Y[t],d=1,D=0) & 24061739.3254199 & Range & 27844 & Trim Var. & 15011610.0274510 \tabularnewline
V(Y[t],d=2,D=0) & 52992198.4694578 & Range & 39364 & Trim Var. & 32321045.7343660 \tabularnewline
V(Y[t],d=3,D=0) & 147402277.090463 & Range & 65306 & Trim Var. & 88436153.7049662 \tabularnewline
V(Y[t],d=0,D=1) & 53575355.0090779 & Range & 42474 & Trim Var. & 28798276.0561578 \tabularnewline
V(Y[t],d=1,D=1) & 46012278.8884005 & Range & 35590 & Trim Var. & 28276705.5919753 \tabularnewline
V(Y[t],d=2,D=1) & 99451945.6459426 & Range & 53356 & Trim Var. & 60798663.5037975 \tabularnewline
V(Y[t],d=3,D=1) & 280030147.836823 & Range & 84570 & Trim Var. & 154921116.291464 \tabularnewline
V(Y[t],d=0,D=2) & 124428698.948276 & Range & 62599 & Trim Var. & 74051771.9928405 \tabularnewline
V(Y[t],d=1,D=2) & 144506081.381983 & Range & 61138 & Trim Var. & 85832801.5905673 \tabularnewline
V(Y[t],d=2,D=2) & 310317662.015321 & Range & 92564 & Trim Var. & 186962131.288947 \tabularnewline
V(Y[t],d=3,D=2) & 872827987.42353 & Range & 151953 & Trim Var. & 531537182.999279 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116743&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]111235287.378838[/C][C]Range[/C][C]45888[/C][C]Trim Var.[/C][C]73988293.4595075[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]24061739.3254199[/C][C]Range[/C][C]27844[/C][C]Trim Var.[/C][C]15011610.0274510[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]52992198.4694578[/C][C]Range[/C][C]39364[/C][C]Trim Var.[/C][C]32321045.7343660[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]147402277.090463[/C][C]Range[/C][C]65306[/C][C]Trim Var.[/C][C]88436153.7049662[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]53575355.0090779[/C][C]Range[/C][C]42474[/C][C]Trim Var.[/C][C]28798276.0561578[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]46012278.8884005[/C][C]Range[/C][C]35590[/C][C]Trim Var.[/C][C]28276705.5919753[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]99451945.6459426[/C][C]Range[/C][C]53356[/C][C]Trim Var.[/C][C]60798663.5037975[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]280030147.836823[/C][C]Range[/C][C]84570[/C][C]Trim Var.[/C][C]154921116.291464[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]124428698.948276[/C][C]Range[/C][C]62599[/C][C]Trim Var.[/C][C]74051771.9928405[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]144506081.381983[/C][C]Range[/C][C]61138[/C][C]Trim Var.[/C][C]85832801.5905673[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]310317662.015321[/C][C]Range[/C][C]92564[/C][C]Trim Var.[/C][C]186962131.288947[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]872827987.42353[/C][C]Range[/C][C]151953[/C][C]Trim Var.[/C][C]531537182.999279[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116743&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116743&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)	111235287.378838	Range	45888	Trim Var.	73988293.4595075
V(Y[t],d=1,D=0)	24061739.3254199	Range	27844	Trim Var.	15011610.0274510
V(Y[t],d=2,D=0)	52992198.4694578	Range	39364	Trim Var.	32321045.7343660
V(Y[t],d=3,D=0)	147402277.090463	Range	65306	Trim Var.	88436153.7049662
V(Y[t],d=0,D=1)	53575355.0090779	Range	42474	Trim Var.	28798276.0561578
V(Y[t],d=1,D=1)	46012278.8884005	Range	35590	Trim Var.	28276705.5919753
V(Y[t],d=2,D=1)	99451945.6459426	Range	53356	Trim Var.	60798663.5037975
V(Y[t],d=3,D=1)	280030147.836823	Range	84570	Trim Var.	154921116.291464
V(Y[t],d=0,D=2)	124428698.948276	Range	62599	Trim Var.	74051771.9928405
V(Y[t],d=1,D=2)	144506081.381983	Range	61138	Trim Var.	85832801.5905673
V(Y[t],d=2,D=2)	310317662.015321	Range	92564	Trim Var.	186962131.288947
V(Y[t],d=3,D=2)	872827987.42353	Range	151953	Trim Var.	531537182.999279

Figure 1

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Postscript link

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Parameters (Session):

par1 = 4 ;

Parameters (R input):

par1 = 4 ;

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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