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R Software Module

rwasp_variancereduction.wasp

Title produced by software

Variance Reduction Matrix

Date of computation

Fri, 24 Dec 2010 10:52:18 +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/24/t12931878516ssr45hpizrvfdp.htm/, Retrieved Tue, 30 Apr 2024 07:43:20 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114739, Retrieved Tue, 30 Apr 2024 07:43:20 +0000

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

-       [Variance Reduction Matrix] [] [2010-12-24 10:52:18] [3bdb54d050744f47368418ea7c7e8e96] [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	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114739&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114739&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114739&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Variance Reduction Matrix
V(Y[t],d=0,D=0)	874383.430509	Range	5009	Trim Var.	496166.749378882
V(Y[t],d=1,D=0)	968091.063461176	Range	5655	Trim Var.	523189.777173913
V(Y[t],d=2,D=0)	2524921.21906938	Range	9068	Trim Var.	1425563.81383648
V(Y[t],d=3,D=0)	8103262.49698254	Range	14665	Trim Var.	4708522.67685694
V(Y[t],d=0,D=1)	517693.75534645	Range	5111	Trim Var.	217365.958881432
V(Y[t],d=1,D=1)	648910.091984705	Range	4961	Trim Var.	295746.608289498
V(Y[t],d=2,D=1)	1594633.66794451	Range	8761	Trim Var.	718368.53957529
V(Y[t],d=3,D=1)	4778504.00110865	Range	13215	Trim Var.	2242393.6052558
V(Y[t],d=0,D=2)	1385831.49789082	Range	8210	Trim Var.	593306.49311408
V(Y[t],d=1,D=2)	1870648.5771261	Range	7677	Trim Var.	945063.351475341
V(Y[t],d=2,D=2)	4662750.00118835	Range	12265	Trim Var.	2452116.26912091
V(Y[t],d=3,D=2)	14157614.6732026	Range	23219	Trim Var.	7367722.39555603

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 874383.430509 & Range & 5009 & Trim Var. & 496166.749378882 \tabularnewline
V(Y[t],d=1,D=0) & 968091.063461176 & Range & 5655 & Trim Var. & 523189.777173913 \tabularnewline
V(Y[t],d=2,D=0) & 2524921.21906938 & Range & 9068 & Trim Var. & 1425563.81383648 \tabularnewline
V(Y[t],d=3,D=0) & 8103262.49698254 & Range & 14665 & Trim Var. & 4708522.67685694 \tabularnewline
V(Y[t],d=0,D=1) & 517693.75534645 & Range & 5111 & Trim Var. & 217365.958881432 \tabularnewline
V(Y[t],d=1,D=1) & 648910.091984705 & Range & 4961 & Trim Var. & 295746.608289498 \tabularnewline
V(Y[t],d=2,D=1) & 1594633.66794451 & Range & 8761 & Trim Var. & 718368.53957529 \tabularnewline
V(Y[t],d=3,D=1) & 4778504.00110865 & Range & 13215 & Trim Var. & 2242393.6052558 \tabularnewline
V(Y[t],d=0,D=2) & 1385831.49789082 & Range & 8210 & Trim Var. & 593306.49311408 \tabularnewline
V(Y[t],d=1,D=2) & 1870648.5771261 & Range & 7677 & Trim Var. & 945063.351475341 \tabularnewline
V(Y[t],d=2,D=2) & 4662750.00118835 & Range & 12265 & Trim Var. & 2452116.26912091 \tabularnewline
V(Y[t],d=3,D=2) & 14157614.6732026 & Range & 23219 & Trim Var. & 7367722.39555603 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114739&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]874383.430509[/C][C]Range[/C][C]5009[/C][C]Trim Var.[/C][C]496166.749378882[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]968091.063461176[/C][C]Range[/C][C]5655[/C][C]Trim Var.[/C][C]523189.777173913[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]2524921.21906938[/C][C]Range[/C][C]9068[/C][C]Trim Var.[/C][C]1425563.81383648[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]8103262.49698254[/C][C]Range[/C][C]14665[/C][C]Trim Var.[/C][C]4708522.67685694[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]517693.75534645[/C][C]Range[/C][C]5111[/C][C]Trim Var.[/C][C]217365.958881432[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]648910.091984705[/C][C]Range[/C][C]4961[/C][C]Trim Var.[/C][C]295746.608289498[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]1594633.66794451[/C][C]Range[/C][C]8761[/C][C]Trim Var.[/C][C]718368.53957529[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]4778504.00110865[/C][C]Range[/C][C]13215[/C][C]Trim Var.[/C][C]2242393.6052558[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]1385831.49789082[/C][C]Range[/C][C]8210[/C][C]Trim Var.[/C][C]593306.49311408[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]1870648.5771261[/C][C]Range[/C][C]7677[/C][C]Trim Var.[/C][C]945063.351475341[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]4662750.00118835[/C][C]Range[/C][C]12265[/C][C]Trim Var.[/C][C]2452116.26912091[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]14157614.6732026[/C][C]Range[/C][C]23219[/C][C]Trim Var.[/C][C]7367722.39555603[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114739&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114739&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)	874383.430509	Range	5009	Trim Var.	496166.749378882
V(Y[t],d=1,D=0)	968091.063461176	Range	5655	Trim Var.	523189.777173913
V(Y[t],d=2,D=0)	2524921.21906938	Range	9068	Trim Var.	1425563.81383648
V(Y[t],d=3,D=0)	8103262.49698254	Range	14665	Trim Var.	4708522.67685694
V(Y[t],d=0,D=1)	517693.75534645	Range	5111	Trim Var.	217365.958881432
V(Y[t],d=1,D=1)	648910.091984705	Range	4961	Trim Var.	295746.608289498
V(Y[t],d=2,D=1)	1594633.66794451	Range	8761	Trim Var.	718368.53957529
V(Y[t],d=3,D=1)	4778504.00110865	Range	13215	Trim Var.	2242393.6052558
V(Y[t],d=0,D=2)	1385831.49789082	Range	8210	Trim Var.	593306.49311408
V(Y[t],d=1,D=2)	1870648.5771261	Range	7677	Trim Var.	945063.351475341
V(Y[t],d=2,D=2)	4662750.00118835	Range	12265	Trim Var.	2452116.26912091
V(Y[t],d=3,D=2)	14157614.6732026	Range	23219	Trim Var.	7367722.39555603

Figure 1

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Postscript link

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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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Tree of Dependent Computations

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Input Parameters & R Code