kdens {PPMiss}

Kernel density estimator

Description

The probability density function F' is estimated using a kernel density approach. More specifically, first y_i = \hat{f}(x_i^\ast) is estimated using T = 512 (default for the function density) equally spaced points x_i^\ast, 1 \leq i \leq T, in the interval [x_{(1)} - 3b, x_{(n)} + 3b], where b is the bandwidth for the Gaussian kernel density estimator, chosen by applying the Silverman's rule of thumb (the default procedure in density). A cubic spline interpolation (the default method for spline) is then applied to the pairs \{(x_i^\ast, y_i)\}_{i=1}^T to obtain \hat F_n'(x) for all x \in [x_{(1)} - 3b, x_{(n)} + 3b].

Usage

kdens(x)

Arguments

x

the data from which the estimate is to be computed.

Value

a function that approximates the probability density function.

Examples

# creating a time series
trunc = 50000
cks <- arfima.coefs(d = 0.25, trunc = trunc)
eps <- rnorm(trunc+1000)
x <- sapply(1:1000, function(t) sum(cks*rev(eps[t:(t+trunc)])))

# kernel density function
dfun <- kdens(x)

# plot
curve(dfun, from = min(x), to = max(x))