R: Parzen's Kernel Mode Estimator

parzen {modeest} | R Documentation

## Parzen's Kernel Mode Estimator

### Description

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

### Usage

      parzen(x,
             bw = NULL,
             kernel = "gaussian",
             abc = FALSE,
             par = shorth(x),
             optim.method = "BFGS",
             ...)

### Arguments

`x` | numeric. Vector of observations.
`bw` | numeric. The smoothing bandwidth to be used.
`kernel` | character. The kernel to be used. Available kernels are `"biweight"`, `"cosine"`, `"eddy"`, `"epanechnikov"`, `"gaussian"`, `"optcosine"`, `"rectangular"`, `"triangular"`, `"uniform"`. See `density.default` for more details on some of these kernels.
`abc` | logical. If `FALSE` (the default), the kernel density estimate is maximised using `optim`.
`par` | numeric. The initial value used in `optim`.
`optim.method` | character. If `abc = FALSE`, the method used in `optim`.
`...` | if `abc = FALSE`, further arguments to be passed to `optim`.

### Details

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

### Value

`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.

### Note

The user should preferentially call `parzen` through `mlv(x, method = "kernel", ...)` or `mlv(x, method = "parzen", ...)`. This returns an object of class `mlv`.

Presently, `parzen` is quite slow.

### Author(s)

P. Poncet

### 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.

### See Also

`mlv`, `naive`

### 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
    M <- mlv(x, method = "kernel", kernel = "gaussian", bw = 0.3, par = shorth(x))
    print(M)
    plot(M)

[Package modeest version 2.1 Index]