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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 computationFri, 24 Dec 2010 15:43:32 +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/24/t1293206116tirqcov98dklwsq.htm/, Retrieved Tue, 30 Apr 2024 05:34:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115161, Retrieved Tue, 30 Apr 2024 05:34:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact105

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Variance Reduction Matrix] [] [2010-12-24 15:43:32] [95610e892c4b5c84ff80f4c898567a9d] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1.35
1.91
1.31
1.19
1.3
1.14
1.1
1.02
1.11
1.18
1.24
1.36
1.29
1.73
1.41
1.15
1.31
1.15
1.08
1.1
1.14
1.24
1.33
1.49
1.38
1.96
1.36
1.24
1.35
1.23
1.09
1.08
1.33
1.35
1.38
1.5
1.47
2.09
1.52
1.29
1.52
1.27
1.35
1.29
1.41
1.39
1.45
1.53
1.45
2.11
1.53
1.38
1.54
1.35
1.29
1.33
1.47
1.47
1.54
1.59
1.5
2
1.51
1.4
1.62
1.44
1.29
1.28
1.4
1.39
1.46
1.49

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=115161&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=115161&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115161&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)0.0506547535211267Range1.09Trim Var.0.023074503968254
V(Y[t],d=1,D=0)0.0646303420523139Range1.26Trim Var.0.026984229390681
V(Y[t],d=2,D=0)0.179091118012422Range1.98Trim Var.0.0792712057112639
V(Y[t],d=3,D=0)0.551132651321398Range3.65Trim Var.0.226039016393443
V(Y[t],d=0,D=1)0.0070647175141243Range0.44Trim Var.0.00402292103424179
V(Y[t],d=1,D=1)0.00934091174751607Range0.56Trim Var.0.00474528301886792
V(Y[t],d=2,D=1)0.0289864488808227Range0.84Trim Var.0.0148339366515837
V(Y[t],d=3,D=1)0.098234022556391Range1.66Trim Var.0.0526828235294118
V(Y[t],d=0,D=2)0.0178808510638298Range0.73Trim Var.0.00949994192799071
V(Y[t],d=1,D=2)0.0312664199814986Range0.87Trim Var.0.015569512195122
V(Y[t],d=2,D=2)0.100429806763285Range1.66Trim Var.0.0526789102564103
V(Y[t],d=3,D=2)0.338366363636364Range2.88Trim Var.0.178112280701754

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 0.0506547535211267 & Range & 1.09 & Trim Var. & 0.023074503968254 \tabularnewline
V(Y[t],d=1,D=0) & 0.0646303420523139 & Range & 1.26 & Trim Var. & 0.026984229390681 \tabularnewline
V(Y[t],d=2,D=0) & 0.179091118012422 & Range & 1.98 & Trim Var. & 0.0792712057112639 \tabularnewline
V(Y[t],d=3,D=0) & 0.551132651321398 & Range & 3.65 & Trim Var. & 0.226039016393443 \tabularnewline
V(Y[t],d=0,D=1) & 0.0070647175141243 & Range & 0.44 & Trim Var. & 0.00402292103424179 \tabularnewline
V(Y[t],d=1,D=1) & 0.00934091174751607 & Range & 0.56 & Trim Var. & 0.00474528301886792 \tabularnewline
V(Y[t],d=2,D=1) & 0.0289864488808227 & Range & 0.84 & Trim Var. & 0.0148339366515837 \tabularnewline
V(Y[t],d=3,D=1) & 0.098234022556391 & Range & 1.66 & Trim Var. & 0.0526828235294118 \tabularnewline
V(Y[t],d=0,D=2) & 0.0178808510638298 & Range & 0.73 & Trim Var. & 0.00949994192799071 \tabularnewline
V(Y[t],d=1,D=2) & 0.0312664199814986 & Range & 0.87 & Trim Var. & 0.015569512195122 \tabularnewline
V(Y[t],d=2,D=2) & 0.100429806763285 & Range & 1.66 & Trim Var. & 0.0526789102564103 \tabularnewline
V(Y[t],d=3,D=2) & 0.338366363636364 & Range & 2.88 & Trim Var. & 0.178112280701754 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115161&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]0.0506547535211267[/C][C]Range[/C][C]1.09[/C][C]Trim Var.[/C][C]0.023074503968254[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.0646303420523139[/C][C]Range[/C][C]1.26[/C][C]Trim Var.[/C][C]0.026984229390681[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]0.179091118012422[/C][C]Range[/C][C]1.98[/C][C]Trim Var.[/C][C]0.0792712057112639[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]0.551132651321398[/C][C]Range[/C][C]3.65[/C][C]Trim Var.[/C][C]0.226039016393443[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]0.0070647175141243[/C][C]Range[/C][C]0.44[/C][C]Trim Var.[/C][C]0.00402292103424179[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]0.00934091174751607[/C][C]Range[/C][C]0.56[/C][C]Trim Var.[/C][C]0.00474528301886792[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]0.0289864488808227[/C][C]Range[/C][C]0.84[/C][C]Trim Var.[/C][C]0.0148339366515837[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]0.098234022556391[/C][C]Range[/C][C]1.66[/C][C]Trim Var.[/C][C]0.0526828235294118[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]0.0178808510638298[/C][C]Range[/C][C]0.73[/C][C]Trim Var.[/C][C]0.00949994192799071[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]0.0312664199814986[/C][C]Range[/C][C]0.87[/C][C]Trim Var.[/C][C]0.015569512195122[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]0.100429806763285[/C][C]Range[/C][C]1.66[/C][C]Trim Var.[/C][C]0.0526789102564103[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]0.338366363636364[/C][C]Range[/C][C]2.88[/C][C]Trim Var.[/C][C]0.178112280701754[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115161&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115161&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)0.0506547535211267Range1.09Trim Var.0.023074503968254
V(Y[t],d=1,D=0)0.0646303420523139Range1.26Trim Var.0.026984229390681
V(Y[t],d=2,D=0)0.179091118012422Range1.98Trim Var.0.0792712057112639
V(Y[t],d=3,D=0)0.551132651321398Range3.65Trim Var.0.226039016393443
V(Y[t],d=0,D=1)0.0070647175141243Range0.44Trim Var.0.00402292103424179
V(Y[t],d=1,D=1)0.00934091174751607Range0.56Trim Var.0.00474528301886792
V(Y[t],d=2,D=1)0.0289864488808227Range0.84Trim Var.0.0148339366515837
V(Y[t],d=3,D=1)0.098234022556391Range1.66Trim Var.0.0526828235294118
V(Y[t],d=0,D=2)0.0178808510638298Range0.73Trim Var.0.00949994192799071
V(Y[t],d=1,D=2)0.0312664199814986Range0.87Trim Var.0.015569512195122
V(Y[t],d=2,D=2)0.100429806763285Range1.66Trim Var.0.0526789102564103
V(Y[t],d=3,D=2)0.338366363636364Range2.88Trim Var.0.178112280701754


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()