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zScore for variance Ratio Test

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mrFendel 2023-04-13 03:38:10 +03:00
parent 2b83560da8
commit a68ebef26d
1 changed files with 32 additions and 10 deletions
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kmath-stat/src/commonMain/kotlin/space/kscience/kmath/series/VarianceRatio.kt
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@ -5,26 +5,48 @@
package space.kscience.kmath.series
import space.kscience.kmath.distributions.NormalDistribution
import space.kscience.kmath.operations.DoubleBufferOps.Companion.map
import space.kscience.kmath.operations.DoubleField.pow
import space.kscience.kmath.operations.algebra
import space.kscience.kmath.operations.bufferAlgebra
import space.kscience.kmath.operations.fold
fun varianceRatio(series: Series<Double>, shift: Int): Double {
val mean = series.fold(0.0) {acc, value -> acc + value} / series.size
// TODO: add p-value
public data class VarianceRatioTestResult(val varianceRatio: Double, val zScore: Double)
public fun varianceRatioTest(series: Series<Double>, shift: Int, homoscedastic: Boolean): VarianceRatioTestResult {
val sum = { x: Double, y: Double -> x + y }
val mean = series.fold(0.0, sum) / series.size
val demeanedSquares = series.map { power(it - mean, 2) }
val variance = demeanedSquares.fold(0.0) {acc, value -> acc + value}
val variance = demeanedSquares.fold(0.0, sum)
with(Double.algebra.bufferAlgebra.seriesAlgebra()) {
val seriesAgg = series
for (i in -1..-shift + 1) {
seriesAgg.shiftOp(i) { v1, v2 -> v1 + v2 }
for (i in -1..-shift + 1) { series.shiftOp(i) { v1, v2 -> v1 + v2 } }
val demeanedSquaresAgg = series.map { power(it - shift * mean, 2) }
val varianceAgg = demeanedSquaresAgg.fold(0.0, sum)
val varianceRatio =
varianceAgg * (series.size - 1) / variance / (series.size - shift + 1) / (1 - shift / series.size)
// calculating asymptotic variance
var phi: Double
if (homoscedastic) { // under homoscedastic null hypothesis
phi = 2 * (2 * shift - 1.0) * (shift - 1.0) / (3 * shift * series.size)
} else { // under homoscedastic null hypothesis
phi = 0.0
for (j in 1..<shift) {
val shiftedProd = demeanedSquares.shiftOp(j) { v1, v2 -> v1 * v2 }
val delta = series.size * shiftedProd.fold(0.0, sum) / variance.pow(2)
phi += delta * 4 * (shift - j) * (shift - j) / shift / shift // TODO: refactor with square
}
}
val demeanedSquaresAgg = seriesAgg.map { power(it - shift * mean, 2) }
val varianceAgg = demeanedSquaresAgg.fold(0.0) { acc, value -> acc + value }
return varianceAgg * (series.size - 1) / variance / (series.size - shift + 1) / (1 - shift / series.size)
val zScore = (varianceRatio - 1) / phi.pow(0.5)
return VarianceRatioTestResult(varianceRatio, zScore)
}
}