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Overview
| Comment: | Corrected use of bandwidth, adjusted a test to take care of pecularities of the kernels |
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| Timelines: | family | ancestors | descendants | both | trunk |
| Files: | files | file ages | folders |
| SHA1: |
991cdf14aaf67dff84df63b03494827a |
| User & Date: | markus 2014-01-20 05:17:53 |
Context
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2014-01-21
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| 17:28 | Ticket [861f53ff24]. Added proper initialization to CreateNonce when falling back to md5 (no dev/urandom). Bumped version to 1.3.3. check-in: 8175173735 user: andreask tags: trunk | |
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2014-01-20
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| 05:17 | Corrected use of bandwidth, adjusted a test to take care of pecularities of the kernels check-in: 991cdf14aa user: markus tags: trunk | |
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2014-01-18
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| 14:20 | Added three test cases for the kernel density estimation. Resulted in a few small corrections (deal with missing values) check-in: 2456e0d413 user: markus tags: trunk | |
Changes
Changes to modules/math/ChangeLog.
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2014-01-18 Arjen Markus <[email protected]> * statistics.tcl: Added stat_kernel.tcl * stat_kernel.tcl: Implements a straightforward kernel density estimation procedure * statistics.man: Describe the kernel denstity estimation procedure, moved the description of several tests to the general section * statistics.test: Added three tests for the kernel density estimation (note: one result is a bit troublesome) * pkgIndex.tcl: Bumped version of statistics package to 0.9 |
> > > > |
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2014-01-19 Arjen Markus <[email protected]> * stat_kernel.tcl: Corrected use of bandwidth * statistics.test: Added margin per kernel - not quite satisfactory in the case of the uniform kernel 2014-01-18 Arjen Markus <[email protected]> * statistics.tcl: Added stat_kernel.tcl * stat_kernel.tcl: Implements a straightforward kernel density estimation procedure * statistics.man: Describe the kernel denstity estimation procedure, moved the description of several tests to the general section * statistics.test: Added three tests for the kernel density estimation (note: one result is a bit troublesome) * pkgIndex.tcl: Bumped version of statistics package to 0.9 |
Changes to modules/math/stat_kernel.tcl.
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lappend xvalue [expr {$xb + $i * $dx}]
}
#
# Construct the density function
#
set density {}
set scale [expr {$opt(-bandwidth)}]
foreach x $xvalue {
set sum 0.0
foreach d $data w $weight {
if { $d != {} } {
set kvalue [$opt(-kernel) [expr {$scale * ($x-$d)}]]
set sum [expr {$sum + $w * $kvalue}]
}
................................................................................
}
lappend density [expr {$sum * $scale}]
}
#
# Return the result
#
return [list $xvalue $density [list $xbegin $xend $mean $stdev $scale]]
}
# gaussian, uniform, triangular, epanechnikov, biweight, cosine, logistic --
# The Gaussian kernel
#
# Arguments:
# x (Scaled) argument
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lappend xvalue [expr {$xb + $i * $dx}]
}
#
# Construct the density function
#
set density {}
set scale [expr {1.0/$opt(-bandwidth)}]
foreach x $xvalue {
set sum 0.0
foreach d $data w $weight {
if { $d != {} } {
set kvalue [$opt(-kernel) [expr {$scale * ($x-$d)}]]
set sum [expr {$sum + $w * $kvalue}]
}
................................................................................
}
lappend density [expr {$sum * $scale}]
}
#
# Return the result
#
return [list $xvalue $density [list $xbegin $xend $mean $stdev $opt(-bandwidth)]]
}
# gaussian, uniform, triangular, epanechnikov, biweight, cosine, logistic --
# The Gaussian kernel
#
# Arguments:
# x (Scaled) argument
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Changes to modules/math/statistics.test.
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test "spearman-rank-extended-1.0" "Test extended Spearman rank correlation procedure" -match tolerant -body {
::math::statistics::spearman-rank-extended {106 86 100 101 99 103 97 113 112 110} \
{ 7 0 27 50 28 29 20 12 6 17}
} -result {-0.175757575758 10 -0.456397284}
#
# Note: for the uniform kernel the sum is roughly 0.92. It would appear from a visual
# investigation that the sides may influence this, as well as the default bandwidth.
# Leave it for now.
#
test "kernel-density-1.0" "Test various kernel functions" -body {
set data {1 2 3 4 5 6 7 8 9 10}
set roughlyOne {}
foreach kernel {gaussian uniform triangular epanechnikov biweight cosine logistic} {
set result [::math::statistics::kernel-density $data -kernel $kernel]
set sum 0.0
set xbegin [lindex $result 2 0]
set xend [lindex $result 2 1]
set number [llength [lindex $result 0]]
set dx [expr {($xend-$xbegin) / $number}]
................................................................................
# Integral should be roughly one
#
set sum 0.0
foreach v [lindex $result 1] {
set sum [expr {$sum + $dx * $v}]
}
lappend roughlyOne [expr {abs($sum-1.0) < 0.01}]
}
return $roughlyOne
} -result {1 0 1 1 1 1 1}
test "kernel-density-1.1" "Test various options - just that they have effect" -body {
set subResults {}
set data {1 2 3 4 5 6 7 8 9 10}
set result [::math::statistics::kernel-density $data -number 20]
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test "spearman-rank-extended-1.0" "Test extended Spearman rank correlation procedure" -match tolerant -body {
::math::statistics::spearman-rank-extended {106 86 100 101 99 103 97 113 112 110} \
{ 7 0 27 50 28 29 20 12 6 17}
} -result {-0.175757575758 10 -0.456397284}
#
# Note: for the uniform and the logistic kernel the sum deviates more from 1 than for the others.
# For the logistic kernel this is because the density function is very widespread. For the
# uniform kernel the reason is not quite clear. Hence the margin per kernel.
#
test "kernel-density-1.0" "Test various kernel functions" -body {
set data {1 2 3 4 5 6 7 8 9 10}
set roughlyOne {}
foreach kernel {gaussian uniform triangular epanechnikov biweight cosine logistic} \
margin {0.01 0.02 0.01 0.01 0.01 0.01 0.05 } {
set result [::math::statistics::kernel-density $data -kernel $kernel]
set sum 0.0
set xbegin [lindex $result 2 0]
set xend [lindex $result 2 1]
set number [llength [lindex $result 0]]
set dx [expr {($xend-$xbegin) / $number}]
................................................................................
# Integral should be roughly one
#
set sum 0.0
foreach v [lindex $result 1] {
set sum [expr {$sum + $dx * $v}]
}
lappend roughlyOne [expr {abs($sum-1.0) < $margin}]
}
return $roughlyOne
} -result {1 1 1 1 1 1 1}
test "kernel-density-1.1" "Test various options - just that they have effect" -body {
set subResults {}
set data {1 2 3 4 5 6 7 8 9 10}
set result [::math::statistics::kernel-density $data -number 20]
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