Does single nearest neighbor

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Does single nearest neighbor imputation preserve
covariances?
Ronald E. McRoberts Northern Research
Station USDA Forest Service Saint Paul, Minnesota
USA
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A frequently noted feature of single neighbor
imputation or k-NN imputation with small k is
that covariances are either preserved or are
better preserved.
To what degree is this statement valid?
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Two kinds of covariances 1. Spatial covariance
for same variable 2. Covariance between
variables Two kinds of test data
sets 1. Reference set 2. Target set
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(No Transcript)
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FIA plot configuration
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FIA subplots relative to TM pixels
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Data ? 3 dates of Landsat TM/ETM
imagery ? 2,266 FIA plots (9,064 subplots) ---
Reference set ? Match FIA subplots to Landsat
pixels ? 4 variables - proportion forest
area - volume (m3/hectare) - basal area
(m2/hectare) - tree count (count/hectare) ? 15
AOIs of radius 10-km (350,000 pixels) ---
Target sets
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Spatial covariances
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Volume (ft3/acre) Reference set
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Density (trees/acre) Reference set
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Volume (ft3/acre) Target set AOI-1
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Volume (ft3/acre) Target set AOI-1(20 k radius
for plots)
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Volume (ft3/acre) Target set AOI-3
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Volume (ft3/acre) Target set AOI-3(20 k radius
for plots)
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Variances
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Proportion forest area Reference set
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Volume (ft3/acre) Reference set
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Basal area (ft2/acre) Reference set
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Density (trees/acre) Reference set
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Volume (ft3/acre) Target set AOI-1
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Volume (ft3/acre) Target set AOI-3
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Correlations
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Correlations (Plots/k-NN) Reference set
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Correlations (Plots/k-NN) Target set AOI-1
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Correlations (Plots/k-NN) Target set AOI-1
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Conclusions ? Spatial covariances - Tend to
be preserved in Reference set - May or may not
be preserved in Target sets ? Variances - Not
well-preserved in Reference set - Not preserved
in Target sets ? Correlations - Well-preserved
in Reference set - Not preserved in Target
sets ? Variances not preserved gt covariances
not preserved