Fit compak smoother at values x using a sample of data

The function estimates the p.m.f. using the Conway-Maxwell-Poisson associated kernels (compak) smoother. Bandwidth can be specified as h or nu where nu= 1/h. If none is specified, one can be provided by using cross-validation or minimising Kullback-Leibler divergence.

compak_fitpmf(
  a.sample,
  x = NULL,
  h = NULL,
  nu = NULL,
  workers = 1L,
  bandwidth_optim = "KL",
  ...
)

Arguments

a.sample	numeric vector: the data sample from which estimate is to be computed.
x	Either NULL or a numeric vector: the points of the grid at which the density is to be estimated. If none is provided, the range of a.sample will be used.
h, nu	numeric: the bandwidth or smoothing parameter. Only one is needed and they are related by nu = 1/h. If neither h nor nu is provided, a bandwidth selection will be carried out.
workers	numeric; a positive integer to represent the number of cores used for parallel processing to evaluate the kde
bandwidth_optim	character; the type of bandwidth selection to be used. Possible values are "KL" (Kullback-Leibler divergence) and "CV" (cross-validation).
...	other arguments passed to bandwidth selection, such as interval.

Value

An object class 'compak' is a list containing the following components:

f.cmp

the estimated p.m.f. values

data

The data - same as input a.sample

h

The bandwidth used to compute the density estimate

nu

The dispersion used to compute the density estimate

x

The coordinates of the points where the density is estimated

bandwidth_optim

the type of bandwidth selection used - same as input

kernel.est

a list that contains the estimated kernel at each grid point

Examples

### Huang et, al (2020) Page 10
data(days)
fit.compak2 <- compak_fitpmf(days, 10:40, bandwidth_optim = "CV")
fit.compak2
#> 
#> Call: compak_fitpmf(a.sample = days, x = 10:40, bandwidth_optim = "CV")
#> 
#> Data: days
#> Bandwidth: 0.0251
#> Bandwidth selection: cross-validation
#> Kernel: Conway-Maxwell-Poisson
#> Range: [10, 40]
#> 
#> Parameter estimates
#> nu: 39.8985

### Huang et, al (2020) Page 9
# \donttest{
data(somites)
fit.compak <- compak_fitpmf(somites, 60:180, bandwidth_optim = "CV")
# }