BGWM.covar.estim {Branching} | R Documentation |
Calculates a estimation of the covariance matrices of a multi-type Bienayme - Galton - Watson process from experimental observed data that can be modeled by this kind of process.
BGWM.covar.estim(sample, method=c("EE-m","MLE-m"), d, n, z0)
sample |
nonnegative integer matrix with d columns and dn rows, trajectory of the process with the number of individuals for every combination parent type - descendent type (observed data). |
method |
methods of estimation (EE-m with empirical estimation of the mean matrix, MLE-m with maximum likelihood estimation of the mean matrix). |
d |
positive integer, number of types. |
n |
positive integer, nth generation. |
z0 |
nonnegative integer vector of size d, initial population by type. |
This function estimates the covariance matrices of a BGWM process using two possible estimators from asymptotic results related with empirical estimator and maximum likelihood estimator of the mean matrix, they both require the so-called full sample associated with the process, ie, it is required to have the trajectory of the process with the number of individuals for every combination parent type - descendent type. For more details see Torres-Jimenez (2010) or Maaouia & Touati (2005).
A list
object with:
method |
method of estimation selected. |
V |
A |
Camilo Jose Torres-Jimenez cjtorresj@unal.edu.co
Torres-Jimenez, C. J. (2010), Relative frequencies and parameter estimation in multi-type Bienaym? - Galton - Watson processes, Master's Thesis, Master of Science in Statistics. Universidad Nacional de Colombia. Bogota, Colombia.
Maaouia, F. & Touati, A. (2005), 'Identification of Multitype Branching Processes', The Annals of Statistics 33(6), 2655-2694.
BGWM.mean
, BGWM.covar
, BGWM.mean.estim
, rBGWM
## Not run: ## Estimation of covariace matrices from simulated data # Variables and parameters d <- 3 n <- 30 N <- c(10,10,10) LeslieMatrix <- matrix( c(0.08, 1.06, 0.07, 0.99, 0, 0, 0, 0.98, 0), 3, 3 ) # offspring distributions from the Leslie matrix # (with independent distributions) Dists.pois <- data.frame( name=rep( "pois", d ), param1=LeslieMatrix[,1], param2=NA, stringsAsFactors=FALSE ) Dists.binom <- data.frame( name=rep( "binom", 2*d ), param1=rep( 1, 2*d ), param2=c(t(LeslieMatrix[,-1])), stringsAsFactors=FALSE ) Dists.i <- rbind(Dists.pois,Dists.binom) Dists.i <- Dists.i[c(1,4,5,2,6,7,3,8,9),] Dists.i # covariance matrices of the process from its offspring distributions V <- BGWM.covar(Dists.i,"independents",d) # generated trajectories of the process from its offspring distributions simulated.data <- rBGWM(Dists.i, "independents", d, n, N, TRUE, FALSE, FALSE)$o.c.s # estimation of covariance matrices using mean matrix empiric estimate # from generated trajectories of the process V.EE.m <- BGWM.covar.estim( simulated.data, "EE-m", d, n, N )$V # estimation of covariance matrices using mean matrix maximum likelihood # estimate from generated trajectories of the process V.MLE.m <- BGWM.covar.estim( simulated.data, "MLE-m", d, n, N )$V # Comparison of exact and estimated covariance matrices V V - V.EE.m V - V.MLE.m ## End(Not run)