parzen() R function from [modeest]

Parzen's Kernel mode estimator

Parzen's kernel mode estimator is the value maximizing the kernel density estimate.


parzen(
  x,
  bw = NULL,
  kernel = "gaussian",
  abc = FALSE,
  tolerance = .Machine$double.eps^0.25,
  ...
)

Arguments

x: numeric. Vector of observations.
bw: numeric. The smoothing bandwidth to be used.
kernel: character. The kernel to be used. For available kernels see densityfun in package statip.
abc: logical. If FALSE (the default), the kernel density estimate is maximised using optim.
tolerance: numeric. Desired accuracy in the optimize function.
...: If abc = FALSE, further arguments to be passed to optim.

Returns

parzen returns a numeric value, the mode estimate. If abc = TRUE, the x value maximizing the density estimate is returned. Otherwise, the optim

method is used to perform maximization, and the attributes: 'value', 'counts', 'convergence' and 'message', coming from the optim method, are added to the result.

Details

If kernel = "uniform", the naive mode estimate is returned.

Note

The user may call parzen through mlv(x, method = "kernel", ...) or mlv(x, method = "parzen", ...).

Presently, parzen is quite slow.

Examples


# Unimodal distribution 
x <- rlnorm(10000, meanlog = 3.4, sdlog = 0.2) 

## True mode 
lnormMode(meanlog = 3.4, sdlog = 0.2) 

## Estimate of the mode 
mlv(x, method = "kernel", kernel = "gaussian", bw = 0.3, par = shorth(x))

References

Parzen E. (1962). On estimation of a probability density function and mode. Ann. Math. Stat., 33 (3):1065--1076.
Konakov V.D. (1973). On the asymptotic normality of the mode of multidimensional distributions. Theory Probab. Appl., 18 :794-803.
Eddy W.F. (1980). Optimum kernel estimators of the mode. Ann. Statist., 8 (4):870-882.
Eddy W.F. (1982). The Asymptotic Distributions of Kernel Estimators of the Mode. Z. Wahrsch. Verw. Gebiete, 59 :279-290.
Romano J.P. (1988). On weak convergence and optimality of kernel density estimates of the mode. Ann. Statist., 16 (2):629-647.
Abraham C., Biau G. and Cadre B. (2003). Simple Estimation of the Mode of a Multivariate Density. Canad. J. Statist., 31 (1):23-34.
Abraham C., Biau G. and Cadre B. (2004). On the Asymptotic Properties of a Simple Estimate of the Mode. ESAIM Probab. Stat., 8 :1-11.

parzen function