| Type: | Package |
| Title: | Estimate Parameter of Bivariate Copula |
| Version: | 2.0 |
| Date: | 2016-03-07 |
| Author: | Yan Li, Yang Li, Yichen Qin, and Jun yan |
| Maintainer: | Yan Li <YanLi_stats@hotmail.com> |
| Description: | Implement an interval censor method to break ties when using data with ties to fitting a bivariate copula. |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| Depends: | copula |
| NeedsCompilation: | no |
| Packaged: | 2016-03-21 13:23:35 UTC; Leonhard |
| Repository: | CRAN |
| Date/Publication: | 2016-03-25 14:48:05 |
likelihood function
Description
likelihood function used in intervalFitb()
Usage
Newloglik2(param, x, copula)
Arguments
param |
Value of parameter in copula function |
x |
Inputted dataset |
copula |
Selected copula function |
Details
none
Value
result |
The result of log-likelihood function |
Note
It's a internal log-likelihood function used in optim function
Author(s)
Yan Li
References
none
See Also
none
Examples
library(copula)
## generate sample
data <- rCopula(50, claytonCopula(2))
## return the value of log-likelihood funcion for selected params
Newloglik2(param=2, data, claytonCopula(2))
Censor method to break ties
Description
Implement an interval censor method to break ties when using data with ties to fitting a bivariate copula.
Details
nothing
Author(s)
Yan Li, Yang Li, Yichen Qin, and Jun Yan
References
Yan Li, Yang Li, Yichen Qin, and Jun Yan. Statistical Inference for Copula Modeling(working paper)
Examples
library(copula)
## Generate sample and introduce ties
data <- rCopula(50, claytonCopula(2))
data[, 1] <- round(data[, 1], digit=1)
## Estimate parameter of clayton copula from the sample
intervalFitb(copula=claytonCopula(2), method="BFGS", data)
Using censor method to break ties
Description
Estimate the parameter of copula with interval censor method to break ties in data.
Usage
intervalFitb(copula, method, x, start, lower, upper, optim.control,
estimate.variance, hideWarnings, bound.eps)
Arguments
copula |
Type of copula to fit the data |
method |
Method used in the 'optim' function |
x |
Data with ties |
See Details for following inputs:
start |
Initial value used in 'optim' function |
lower, upper |
Bounds on the variables for the "L-BFGS-B" method or method "Brent" |
optim.control |
A list of control parameters |
estimate.variance |
Estimate variance |
hideWarnings |
Hide warnings in procedure of estimation |
bound.eps |
Minimum finite distance |
Details
Except the 'copula', 'x' and 'method', other inputs of the intervalFitb function has default value.
For method,
Method "BFGS" is a quasi-Newton method (also known as a variable metric algorithm), specifically that published simultaneously in 1970 by Broyden, Fletcher, Goldfarb and Shanno. This uses function values and gradients to build up a picture of the surface to be optimized.
Method "L-BFGS-B" is that of Byrd et. al. (1995) which allows box constraints, that is each variable can be given a lower and/or upper bound. The initial value must satisfy the constraints. This uses a limited-memory modification of the BFGS quasi-Newton method. If non-trivial bounds are supplied, this method will be selected, with a warning.
Method "Brent" is for one-dimensional problems only, using 'optimize' function. It can be useful in cases where optim() is used inside other functions where only method can be specified, such as in mle from package stats4.
Value
fit |
Estimation of parameter |
Note
The intervalFitb function only works for bivariate copula function.
Author(s)
Yan Li
References
None
Examples
library(copula)
## Generate sample and introduce ties
data <- rCopula(50, claytonCopula(2))
data[, 1] <- round(data[, 1], digit=1)
## Estimate parameter of clayton copula from the sample
intervalFitb(copula=claytonCopula(2), method="BFGS", data)