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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 computationTue, 02 Dec 2008 11:04:59 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/02/t1228241156ofkh11gblwn76ol.htm/, Retrieved Tue, 28 May 2024 12:25:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28172, Retrieved Tue, 28 May 2024 12:25:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsBert Moons
Estimated Impact192

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F       [Variance Reduction Matrix] [Non Stationary Ti...] [2008-12-02 18:04:59] [1828943283e41f5e3270e2e73d6433b4] [Current]
Feedback Forum
2008-12-04 10:24:01 [Steven Vercammen] [reply] 
De variantie reductie matrix geeft de varianties weer na differentiatie, optimaal is dat de variantie zo klein mogelijk is omdat we dan zoveel mogelijk kunnen verklaren. De variantie is hier optimaal bij d=1 en D=0.
2008-12-07 11:26:10 [Steven Vanhooreweghe] [reply] 
Wat je hier doet is wel correct. Het is alleen spijtig dat je er geen uitleg bij hebt gegeven. Ook heb je alleen de VRM-methode gebruikt. Je had ook de ACF en de spectrale analyse kunnen doen.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
19,2
26,6
26,6
31,4
31,2
26,4
20,7
20,7
15
13,3
8,7
10,2
4,3
-0,1
-4,6
-3,9
-3,5
-3,4
-2,5
-1,1
0,3
-0,9
3,6
2,7
-0,2
-1
5,8
6,4
9,6
13,2
10,6
10,9
12,9
15,9
12,2
9,1
9
17,4
14,7
17
13,7
9,5
14,8
13,6
12,6
8,9
10,2
12,7
16
10,4
9,9
9,5
8,6
10
3,5
-4,2
-4,4
-1,5
-0,1
0,8

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=28172&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=28172&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28172&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)82.3145169491525Range36Trim Var.51.952793904209
V(Y[t],d=1,D=0)12.6338223261251Range16.1Trim Var.8.12208272859216
V(Y[t],d=2,D=0)22.5126588021779Range20.6Trim Var.15.6572699849170
V(Y[t],d=3,D=0)65.0663345864662Range35.7Trim Var.44.121137254902
V(Y[t],d=0,D=1)203.813293439716Range53.7Trim Var.135.182398373984
V(Y[t],d=1,D=1)34.9393154486586Range25.3Trim Var.20.8707195121951
V(Y[t],d=2,D=1)68.5172946859903Range34.9Trim Var.37.8053782051282
V(Y[t],d=3,D=1)205.408181818182Range58.7Trim Var.125.832199730094
V(Y[t],d=0,D=2)497.951642857143Range73.2Trim Var.389.762893145161
V(Y[t],d=1,D=2)110.773058823529Range39Trim Var.77.4078064516129
V(Y[t],d=2,D=2)240.807201426025Range68Trim Var.150.137574712644
V(Y[t],d=3,D=2)753.726534090909Range109.7Trim Var.508.629729064039

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 82.3145169491525 & Range & 36 & Trim Var. & 51.952793904209 \tabularnewline
V(Y[t],d=1,D=0) & 12.6338223261251 & Range & 16.1 & Trim Var. & 8.12208272859216 \tabularnewline
V(Y[t],d=2,D=0) & 22.5126588021779 & Range & 20.6 & Trim Var. & 15.6572699849170 \tabularnewline
V(Y[t],d=3,D=0) & 65.0663345864662 & Range & 35.7 & Trim Var. & 44.121137254902 \tabularnewline
V(Y[t],d=0,D=1) & 203.813293439716 & Range & 53.7 & Trim Var. & 135.182398373984 \tabularnewline
V(Y[t],d=1,D=1) & 34.9393154486586 & Range & 25.3 & Trim Var. & 20.8707195121951 \tabularnewline
V(Y[t],d=2,D=1) & 68.5172946859903 & Range & 34.9 & Trim Var. & 37.8053782051282 \tabularnewline
V(Y[t],d=3,D=1) & 205.408181818182 & Range & 58.7 & Trim Var. & 125.832199730094 \tabularnewline
V(Y[t],d=0,D=2) & 497.951642857143 & Range & 73.2 & Trim Var. & 389.762893145161 \tabularnewline
V(Y[t],d=1,D=2) & 110.773058823529 & Range & 39 & Trim Var. & 77.4078064516129 \tabularnewline
V(Y[t],d=2,D=2) & 240.807201426025 & Range & 68 & Trim Var. & 150.137574712644 \tabularnewline
V(Y[t],d=3,D=2) & 753.726534090909 & Range & 109.7 & Trim Var. & 508.629729064039 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28172&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]82.3145169491525[/C][C]Range[/C][C]36[/C][C]Trim Var.[/C][C]51.952793904209[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]12.6338223261251[/C][C]Range[/C][C]16.1[/C][C]Trim Var.[/C][C]8.12208272859216[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]22.5126588021779[/C][C]Range[/C][C]20.6[/C][C]Trim Var.[/C][C]15.6572699849170[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]65.0663345864662[/C][C]Range[/C][C]35.7[/C][C]Trim Var.[/C][C]44.121137254902[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]203.813293439716[/C][C]Range[/C][C]53.7[/C][C]Trim Var.[/C][C]135.182398373984[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]34.9393154486586[/C][C]Range[/C][C]25.3[/C][C]Trim Var.[/C][C]20.8707195121951[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]68.5172946859903[/C][C]Range[/C][C]34.9[/C][C]Trim Var.[/C][C]37.8053782051282[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]205.408181818182[/C][C]Range[/C][C]58.7[/C][C]Trim Var.[/C][C]125.832199730094[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]497.951642857143[/C][C]Range[/C][C]73.2[/C][C]Trim Var.[/C][C]389.762893145161[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]110.773058823529[/C][C]Range[/C][C]39[/C][C]Trim Var.[/C][C]77.4078064516129[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]240.807201426025[/C][C]Range[/C][C]68[/C][C]Trim Var.[/C][C]150.137574712644[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]753.726534090909[/C][C]Range[/C][C]109.7[/C][C]Trim Var.[/C][C]508.629729064039[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28172&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28172&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)82.3145169491525Range36Trim Var.51.952793904209
V(Y[t],d=1,D=0)12.6338223261251Range16.1Trim Var.8.12208272859216
V(Y[t],d=2,D=0)22.5126588021779Range20.6Trim Var.15.6572699849170
V(Y[t],d=3,D=0)65.0663345864662Range35.7Trim Var.44.121137254902
V(Y[t],d=0,D=1)203.813293439716Range53.7Trim Var.135.182398373984
V(Y[t],d=1,D=1)34.9393154486586Range25.3Trim Var.20.8707195121951
V(Y[t],d=2,D=1)68.5172946859903Range34.9Trim Var.37.8053782051282
V(Y[t],d=3,D=1)205.408181818182Range58.7Trim Var.125.832199730094
V(Y[t],d=0,D=2)497.951642857143Range73.2Trim Var.389.762893145161
V(Y[t],d=1,D=2)110.773058823529Range39Trim Var.77.4078064516129
V(Y[t],d=2,D=2)240.807201426025Range68Trim Var.150.137574712644
V(Y[t],d=3,D=2)753.726534090909Range109.7Trim Var.508.629729064039


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(x,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')