MixSemiRob (version 1.1.0)

semimrBinFull: Semiparametric Mixture of Binomial Regression with a Degenerate Component with Constant Proportion and Time-Varying Success Probability (Backfitting)

Description

`semimrBinFull' implements the backfitting method (Cao and Yao, 2012) for semiparametric estimation of a mixture of binomial distributions with one degenerate component, with constant proportion and time-varying success probability \(p\).

Usage

semimrBinFull(t, x, N, tg = NULL, tune = 1, tol = 1e-02)

Value

A list containing the following elements:

pt

estimated time-varying success probabilities for the first component.

w

estimated constant proportion for the first component.

h

bandwidth for the kernel regression. The bandwidth calculation can be found in Section 4 of Cao and Yao (2012).

Arguments

t

a vector of time variable along which \(p(t)\) varies.

x

a vector of observed number of successes. The length of t and x must be the same.

N

a scalar, specifying the number of trials for the Binomial distribution.

tg

grid points of time used in the kernel regression for the estimation of \(p(t)\). Default is NULL, and 100 equally spaced grid points will automatically generated using the minimum and maximum values of t.

tune

a scalar, specifying the percentage of data included in local estimation. related to the bandwidth selection and local estimation. Default is 1.

tol

stopping criteria for the algorithm.

Details

The semiparametric mixture of binomial regression model is as follows: $$w \times (N,p(t))+(1-w)\times B(N,0),$$ where \(B(N,p)\) is the probability mass function of a binomial distribution with the number of trials \(N\) and the success probability \(p\). Here, the second component is a degenerate distribution with mass 1 on 0. The time-varying success probability \(p(t)\) for the binomial components are estimated by the kernel regression using a full iterative backfitting procedure with some bandwidth.

References

Cao, J. and Yao, W. (2012). Semiparametric mixture of binomial regression with a degenerate component. Statistica Sinica, 27-46.

See Also

semimrBin, semimrBinOne

Examples

nobs = 50
tobs = seq(from = 0, to = 1, length.out = nobs)
pi1Tru = 0.4
ptTru = 0.3 * (1.5 + cos(2 * pi * tobs))
nfine = nobs
tfine = seq(from = 0, to = 1, length.out = nfine)
b = rbinom(nobs, size = 1, pi1Tru)
yobs = apply(X = matrix(ptTru), 1, rbinom, n = 1, size = 7)
yobs = ifelse(b == 1, 0, yobs)
ftfull = semimrBinFull(t = tobs, x = yobs, N = 7, tg = tfine)