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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_variancereduction.wasp
Title produced by softwareVariance Reduction Matrix
Date of computationThu, 16 Dec 2010 21:35:06 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/16/t1292535308myq2b1v5wglag05.htm/, Retrieved Fri, 03 May 2024 09:27:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111300, Retrieved Fri, 03 May 2024 09:27:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact137

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [] [2008-12-08 19:22:39] [d2d412c7f4d35ffbf5ee5ee89db327d4]
- RMPD    [Variance Reduction Matrix] [] [2010-12-16 21:35:06] [40b262140b988d7b8204c4955f8b7651] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
-0.9
1.2
1.4
1.5
1.3
1.4
-0.4
1.9
1.6
1.4
1.3
1.6
1.7
1.5
1.4
1.7
1.9
2.0
2.3
2.0
2.2
2.5
2.8
2.7
2.7
3.0
3.0
2.3
2.4
2.3
2.1
2.2
1.9
1.5
1.4
1.4
1.2
1.1
1.1
1.8
1.5
1.5
1.4
1.4
1.5
1.7
1.7
1.7
1.5
1.7
1.4
1.3
1.3
1.2
1.2
1.3
1.2
1.2
1.1
0.9
1.2
1.0
1.3
0.8
1.2
1.3
1.0
1.3
1.3
1.5
1.6
1.6
1.1
1.7
1.4
1.8
1.6
1.7
1.8
1.7
1.7
1.4
1.2
1.4
1.3
1.4
1.7
1.5
1.5
1.4
1.4
1.5
1.2
1.3
1.3
1.6
1.5
1.4
1.6
1.2
1.4
1.8
1.8
1.9
2.1
2.4
2.4
2.4
1.9
2.4
2.2
2.7
2.4
2.3
2.0
2.0
2.2
1.8
1.7
1.6
1.4
1.2
1.1
1.0
1.3
1.1
0.7
1.1
1.1
1.2
1.4

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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=111300&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=111300&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111300&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk






Variance Reduction Matrix
V(Y[t],d=0,D=0)0.29504873752202Range3.9Trim Var.0.133025487256372
V(Y[t],d=1,D=0)0.158056648777579Range4.1Trim Var.0.0351659292035398
V(Y[t],d=2,D=0)0.389234496124031Range6.7Trim Var.0.0979206712433257
V(Y[t],d=3,D=0)1.25030511811024Range12.7Trim Var.0.341040211147337
V(Y[t],d=0,D=1)0.640535536248398Range4.6Trim Var.0.341641685769705
V(Y[t],d=1,D=1)0.305801100970592Range4.7Trim Var.0.111012820512821
V(Y[t],d=2,D=1)0.767260536398467Range7.8Trim Var.0.300479853479854
V(Y[t],d=3,D=1)2.49981109445277Range14.6Trim Var.1.00285287528006
V(Y[t],d=0,D=2)1.54990301534121Range6Trim Var.0.91860470324748
V(Y[t],d=1,D=2)0.77887870619946Range5.6Trim Var.0.349310797897754
V(Y[t],d=2,D=2)1.96408791208791Range9.6Trim Var.0.983599812996727
V(Y[t],d=3,D=2)6.41995519044063Range17.6Trim Var.2.98082178690874

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 0.29504873752202 & Range & 3.9 & Trim Var. & 0.133025487256372 \tabularnewline
V(Y[t],d=1,D=0) & 0.158056648777579 & Range & 4.1 & Trim Var. & 0.0351659292035398 \tabularnewline
V(Y[t],d=2,D=0) & 0.389234496124031 & Range & 6.7 & Trim Var. & 0.0979206712433257 \tabularnewline
V(Y[t],d=3,D=0) & 1.25030511811024 & Range & 12.7 & Trim Var. & 0.341040211147337 \tabularnewline
V(Y[t],d=0,D=1) & 0.640535536248398 & Range & 4.6 & Trim Var. & 0.341641685769705 \tabularnewline
V(Y[t],d=1,D=1) & 0.305801100970592 & Range & 4.7 & Trim Var. & 0.111012820512821 \tabularnewline
V(Y[t],d=2,D=1) & 0.767260536398467 & Range & 7.8 & Trim Var. & 0.300479853479854 \tabularnewline
V(Y[t],d=3,D=1) & 2.49981109445277 & Range & 14.6 & Trim Var. & 1.00285287528006 \tabularnewline
V(Y[t],d=0,D=2) & 1.54990301534121 & Range & 6 & Trim Var. & 0.91860470324748 \tabularnewline
V(Y[t],d=1,D=2) & 0.77887870619946 & Range & 5.6 & Trim Var. & 0.349310797897754 \tabularnewline
V(Y[t],d=2,D=2) & 1.96408791208791 & Range & 9.6 & Trim Var. & 0.983599812996727 \tabularnewline
V(Y[t],d=3,D=2) & 6.41995519044063 & Range & 17.6 & Trim Var. & 2.98082178690874 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111300&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]0.29504873752202[/C][C]Range[/C][C]3.9[/C][C]Trim Var.[/C][C]0.133025487256372[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.158056648777579[/C][C]Range[/C][C]4.1[/C][C]Trim Var.[/C][C]0.0351659292035398[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]0.389234496124031[/C][C]Range[/C][C]6.7[/C][C]Trim Var.[/C][C]0.0979206712433257[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]1.25030511811024[/C][C]Range[/C][C]12.7[/C][C]Trim Var.[/C][C]0.341040211147337[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]0.640535536248398[/C][C]Range[/C][C]4.6[/C][C]Trim Var.[/C][C]0.341641685769705[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]0.305801100970592[/C][C]Range[/C][C]4.7[/C][C]Trim Var.[/C][C]0.111012820512821[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]0.767260536398467[/C][C]Range[/C][C]7.8[/C][C]Trim Var.[/C][C]0.300479853479854[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]2.49981109445277[/C][C]Range[/C][C]14.6[/C][C]Trim Var.[/C][C]1.00285287528006[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]1.54990301534121[/C][C]Range[/C][C]6[/C][C]Trim Var.[/C][C]0.91860470324748[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]0.77887870619946[/C][C]Range[/C][C]5.6[/C][C]Trim Var.[/C][C]0.349310797897754[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]1.96408791208791[/C][C]Range[/C][C]9.6[/C][C]Trim Var.[/C][C]0.983599812996727[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]6.41995519044063[/C][C]Range[/C][C]17.6[/C][C]Trim Var.[/C][C]2.98082178690874[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111300&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111300&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Variance Reduction Matrix
V(Y[t],d=0,D=0)0.29504873752202Range3.9Trim Var.0.133025487256372
V(Y[t],d=1,D=0)0.158056648777579Range4.1Trim Var.0.0351659292035398
V(Y[t],d=2,D=0)0.389234496124031Range6.7Trim Var.0.0979206712433257
V(Y[t],d=3,D=0)1.25030511811024Range12.7Trim Var.0.341040211147337
V(Y[t],d=0,D=1)0.640535536248398Range4.6Trim Var.0.341641685769705
V(Y[t],d=1,D=1)0.305801100970592Range4.7Trim Var.0.111012820512821
V(Y[t],d=2,D=1)0.767260536398467Range7.8Trim Var.0.300479853479854
V(Y[t],d=3,D=1)2.49981109445277Range14.6Trim Var.1.00285287528006
V(Y[t],d=0,D=2)1.54990301534121Range6Trim Var.0.91860470324748
V(Y[t],d=1,D=2)0.77887870619946Range5.6Trim Var.0.349310797897754
V(Y[t],d=2,D=2)1.96408791208791Range9.6Trim Var.0.983599812996727
V(Y[t],d=3,D=2)6.41995519044063Range17.6Trim Var.2.98082178690874


Figures (Output of Computation)

Input Parameters & R Code

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()