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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 computationWed, 15 Dec 2010 14:04:09 +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/15/t1292424693r07tqnduga077mn.htm/, Retrieved Fri, 03 May 2024 10:29:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=110439, Retrieved Fri, 03 May 2024 10:29:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact138

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] [paper1] [2010-12-15 14:04:09] [65e95fe5923d75db266bc83cb8a34c47] [Current]
- RMP     [(Partial) Autocorrelation Function] [autocorrelatie go...] [2010-12-19 13:20:23] [ca50229b6b451ac8f5a30a9e3154d674]
- RMP     [Spectral Analysis] [Spectral analysis...] [2010-12-19 13:53:16] [ca50229b6b451ac8f5a30a9e3154d674]
- RMP     [Spectral Analysis] [Spectral analysis...] [2010-12-19 13:54:31] [ca50229b6b451ac8f5a30a9e3154d674]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
10570
10297
10635
10872
10296
10383
10431
10574
10653
10805
10872
10625
10407
10463
10556
10646
10702
11353
11346
11451
11964
12574
13031
13812
14544
14931
14886
16005
17064
15168
16050
15839
15137
14954
15648
15305
15579
16348
15928
16171
15937
15713
15594
15683
16438
17032
17696
17745
19394
20148
20108
18584
18441
18391
19178
18079
18483
19644
19195
19650
20830
23595
22937
21814
21928
21777
21383
21467
22052
22680
24320
24977
25204

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110439&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110439&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110439&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Variance Reduction Matrix
V(Y[t],d=0,D=0)18753698.9577626Range14908Trim Var.14518362.7971154
V(Y[t],d=1,D=0)491649.964788732Range4661Trim Var.196683.252976190
V(Y[t],d=2,D=0)942330.298189135Range6201Trim Var.390094.264720942
V(Y[t],d=3,D=0)2664951.91076605Range10741Trim Var.1093284.34399788
V(Y[t],d=0,D=1)2747494.81693989Range7489Trim Var.1737487.36066763
V(Y[t],d=1,D=1)819689.528531073Range4636Trim Var.488034.187281621
V(Y[t],d=2,D=1)1962920.47691409Range6986Trim Var.1148194.90130624
V(Y[t],d=3,D=1)6174116.9646098Range12624Trim Var.3762064.78280543
V(Y[t],d=0,D=2)9130286.8494898Range13445Trim Var.5633930.51605759
V(Y[t],d=1,D=2)2562283.77127660Range7330Trim Var.1593443.74680604
V(Y[t],d=2,D=2)6399113.0120259Range12624Trim Var.3807666.39878049
V(Y[t],d=3,D=2)21106313.6159420Range21239Trim Var.12933493.6352564

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 18753698.9577626 & Range & 14908 & Trim Var. & 14518362.7971154 \tabularnewline
V(Y[t],d=1,D=0) & 491649.964788732 & Range & 4661 & Trim Var. & 196683.252976190 \tabularnewline
V(Y[t],d=2,D=0) & 942330.298189135 & Range & 6201 & Trim Var. & 390094.264720942 \tabularnewline
V(Y[t],d=3,D=0) & 2664951.91076605 & Range & 10741 & Trim Var. & 1093284.34399788 \tabularnewline
V(Y[t],d=0,D=1) & 2747494.81693989 & Range & 7489 & Trim Var. & 1737487.36066763 \tabularnewline
V(Y[t],d=1,D=1) & 819689.528531073 & Range & 4636 & Trim Var. & 488034.187281621 \tabularnewline
V(Y[t],d=2,D=1) & 1962920.47691409 & Range & 6986 & Trim Var. & 1148194.90130624 \tabularnewline
V(Y[t],d=3,D=1) & 6174116.9646098 & Range & 12624 & Trim Var. & 3762064.78280543 \tabularnewline
V(Y[t],d=0,D=2) & 9130286.8494898 & Range & 13445 & Trim Var. & 5633930.51605759 \tabularnewline
V(Y[t],d=1,D=2) & 2562283.77127660 & Range & 7330 & Trim Var. & 1593443.74680604 \tabularnewline
V(Y[t],d=2,D=2) & 6399113.0120259 & Range & 12624 & Trim Var. & 3807666.39878049 \tabularnewline
V(Y[t],d=3,D=2) & 21106313.6159420 & Range & 21239 & Trim Var. & 12933493.6352564 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110439&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]18753698.9577626[/C][C]Range[/C][C]14908[/C][C]Trim Var.[/C][C]14518362.7971154[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]491649.964788732[/C][C]Range[/C][C]4661[/C][C]Trim Var.[/C][C]196683.252976190[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]942330.298189135[/C][C]Range[/C][C]6201[/C][C]Trim Var.[/C][C]390094.264720942[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]2664951.91076605[/C][C]Range[/C][C]10741[/C][C]Trim Var.[/C][C]1093284.34399788[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]2747494.81693989[/C][C]Range[/C][C]7489[/C][C]Trim Var.[/C][C]1737487.36066763[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]819689.528531073[/C][C]Range[/C][C]4636[/C][C]Trim Var.[/C][C]488034.187281621[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]1962920.47691409[/C][C]Range[/C][C]6986[/C][C]Trim Var.[/C][C]1148194.90130624[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]6174116.9646098[/C][C]Range[/C][C]12624[/C][C]Trim Var.[/C][C]3762064.78280543[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]9130286.8494898[/C][C]Range[/C][C]13445[/C][C]Trim Var.[/C][C]5633930.51605759[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]2562283.77127660[/C][C]Range[/C][C]7330[/C][C]Trim Var.[/C][C]1593443.74680604[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]6399113.0120259[/C][C]Range[/C][C]12624[/C][C]Trim Var.[/C][C]3807666.39878049[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]21106313.6159420[/C][C]Range[/C][C]21239[/C][C]Trim Var.[/C][C]12933493.6352564[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110439&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110439&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)18753698.9577626Range14908Trim Var.14518362.7971154
V(Y[t],d=1,D=0)491649.964788732Range4661Trim Var.196683.252976190
V(Y[t],d=2,D=0)942330.298189135Range6201Trim Var.390094.264720942
V(Y[t],d=3,D=0)2664951.91076605Range10741Trim Var.1093284.34399788
V(Y[t],d=0,D=1)2747494.81693989Range7489Trim Var.1737487.36066763
V(Y[t],d=1,D=1)819689.528531073Range4636Trim Var.488034.187281621
V(Y[t],d=2,D=1)1962920.47691409Range6986Trim Var.1148194.90130624
V(Y[t],d=3,D=1)6174116.9646098Range12624Trim Var.3762064.78280543
V(Y[t],d=0,D=2)9130286.8494898Range13445Trim Var.5633930.51605759
V(Y[t],d=1,D=2)2562283.77127660Range7330Trim Var.1593443.74680604
V(Y[t],d=2,D=2)6399113.0120259Range12624Trim Var.3807666.39878049
V(Y[t],d=3,D=2)21106313.6159420Range21239Trim Var.12933493.6352564


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()