nonpar_mstep {hhsmm}

the M step function of the EM algorithm

Description

The M step function of the EM algorithm for the mixture of splines nonparametric density estimator

Usage

nonpar_mstep(x, wt, control = list(K = 5, lambda0 = 0.5))

Arguments

x

the observation matrix

wt

the state probabilities matrix (number of observations times number of states)

control

the parameters to control the M-step function. The simillar name is chosen with that of dnonpar, to be used in ... argument of the hhsmmfit function. Here, it contains the following items:

• K the degrees of freedom for the B-spline, default is K=5

• lambda0 the initial value of the smoothing parameter, default is lambda0=0.5

Value

list of emission (nonparametric mixture of splines) parameters: (coef)

Author(s)

Morteza Amini, [e-mail], Reza Salehian, [e-mail]

References

Langrock, R., Kneib, T., Sohn, A., & DeRuiter, S. L. (2015). Nonparametric inference in hidden Markov models using P-splines. Biometrics, 71(2), 520-528.

Examples

x <- rmvnorm(100, rep(0, 2), matrix(c(4, 2, 2, 3), 2, 2))
wt <- matrix(rep(1, 100), 100, 1)
emission = nonpar_mstep(x, wt)
coef <- emission$coef[[1]]
x_axis <- seq(min(x[, 1]), max(x[, 1]), length.out = 100)
y_axis <- seq(min(x[, 2]), max(x[, 2]), length.out = 100)
f1 <- function(x, y) { 
  data = matrix(c(x, y), ncol = 2)
  tmpmodel = list(parms.emission = emission)
	 dnonpar(data, 1, tmpmodel)
}
z1 <- outer(x_axis, y_axis, f1)
f2 <- function(x, y) { 
  data = matrix(c(x, y), ncol = 2)
  dmvnorm(data, rep(0, 2), matrix(c(4, 2, 2, 3), 2, 2))
}
z2 <- outer(x_axis, y_axis, f2)
par(mfrow = c(1, 2))
persp(x_axis, y_axis, z1, theta = -60, phi = 45, col = rainbow(50))
persp(x_axis, y_axis, z2, theta = -60, phi = 45, col = rainbow(50))