Discrete kernel for categorical data with k
unordered categories.
1  dkern(x, y, k, lambda)

x 
categorical data vector 
y 
postive integer defining a fixed category 
k 
positive integer giving the number of categories 
lambda 
smoothing parameter 
This kernel was introduced in Aitchison & Aitken (1976); see also Titterington (1980).
The setting lambda =1/k
corresponds to the extreme case 'maximal smoothing',
while lambda = 1
means ‘no smoothing’. Statistically sensible settings are
only 1/k
<= lambda
<=1
.
Jochen Einbeck (2006)
Aitchison, J. and Aitken, C.G.G. (1976). Multivariate binary discrimination by kernel method. Biometrika 63, 413420.
Titterington, D. M. (1980). A comparative study of kernelbased density estimates for categorical data. Technometrics, 22, 259268.
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