Discrete optimal kernel

Discrete optimal kernel

discrete_optimal(x, z, h, k)

Arguments

x

the target point at which the density is calculated

z

the vector of observations

h

the bandwidth (or smoothing parameter), which should match the condition (3 / 5) * (1 - 1 / k)) < h < 1

k

the integer (positive) parameter that defined the support of the kernel function

Value

Returns the value of the associated kernel function according to the target x and the bandwidth h.

Examples

discrete_optimal(x = 25, z = 1:50, h = 0.9, k = 20)
#>  [1] 0.00000000 0.00000000 0.00000000 0.00000000 0.01871809 0.01956892
#>  [7] 0.02037611 0.02113967 0.02185959 0.02253589 0.02316855 0.02375758
#> [13] 0.02430298 0.02480475 0.02526288 0.02567739 0.02604826 0.02637550
#> [19] 0.02665910 0.02689908 0.02709542 0.02724813 0.02735721 0.02742266
#> [25] 0.02744448 0.02742266 0.02735721 0.02724813 0.02709542 0.02689908
#> [31] 0.02665910 0.02637550 0.02604826 0.02567739 0.02526288 0.02480475
#> [37] 0.02430298 0.02375758 0.02316855 0.02253589 0.02185959 0.02113967
#> [43] 0.02037611 0.01956892 0.01871809 0.00000000 0.00000000 0.00000000
#> [49] 0.00000000 0.00000000