quantlet/gaplmsbk

gaplmsbk

Name of QuantLet:  gaplmsbk

Published in:      Default Prediction by Generalized Additive Partially Linear Model

Description:       'Spline-backfitted kernel estimation for component function in Generalized Addtive Partially Linear Model'

Keywords:          spline, kernel, partial, linear, estimation

Author:            Rong Liu

Submitted:         September 07 2016 by Rong Liu

Input:             x: n*p matrix y: n*1 vector

Output:            Spline-backfitted kernel estimation for component function

R Code

# Spline-backfitted kernel estimation for component function in Generalized Addtive Partially Linear Model x: n*p matrix y: n*1 vector alpha:
# the component function to be estimated xfixed: the x values for the estimation of component function initial: initial value for the
# component function to be estimated c1,c2: adjust the number of knots for spline ch: adjust the bandwidth of kernel family: provide a
# convenient way to specify the details of the models used, same as as glm in R.

gaplmsbk <- function(x, t, y, alpha, xfixed, initial, c1, c2, ch, family, thetaalphaoracle) {
    
    library("splines")
    
    
    d = ncol(x)
    n = nrow(x)
    dt = ncol(t)
    B = array(1, c(n, 1))
    N = floor(c1 * (n^(1/4)) * log(n)) + c2  #number of knots
    N = min(N, floor((n/4 - 1)/d - 1))
    
    i = 1
    while (i <= d) {
        Bi = bs(x[, i], knots = min(x[, i]) + (max(x[, i]) - min(x[, i])) * c(1:(N - 1))/N, degree = 1)
        B = cbind(B, Bi)
        i = i + 1
    }
    
    Nd = ncol(B)
    result = glm(y ~ cbind(B[, 2:Nd], t), family)
    lamda = data.matrix(result$coefficients)
    beta = lamda[(Nd + 1):(Nd + dt)]
    lamda = lamda[1:Nd]
    mhat = data.matrix(lamda[1] * B[, 1])
    chat = lamda[1]
    
    i = 1
    while (i <= d) {
        mhati = B[, ((i - 1) * N + 2):(i * N + 1)] %*% lamda[((i - 1) * N + 2):(i * N + 1)]
        chat = chat + data.matrix(colMeans(mhati))
        mhat = cbind(mhat, mhati - colMeans(mhati))
        i = i + 1
    }
    
    mhat[, 1] = chat
    xfixed = t(xfixed)
    dfixed = ncol(xfixed)
    initial = t(initial)
    mhatsbk = initial
    
    xalpha = data.matrix(x[, alpha])
    hoptalpha = sqrt(var(xalpha)) * (n^(-0.2))
    halpha = ch * hoptalpha
    ualpha = xalpha %*% array(1, c(1, dfixed)) - array(1, c(n, 1)) %*% xfixed
    kalpha = 15/16 * ((1 - (ualpha/halpha[1])^2 + abs(1 - (ualpha/halpha[1])^2))/2)^2/halpha[1]
    
    theta = rowSums(mhat) + t %*% beta
    mhatalpha = mhat[, alpha + 1]
    thetaalpha = theta - mhatalpha
    difference = 1
    delta = 1e-07
    
    i = 1
    while (i <= 20 & difference > delta) {
        thetanew = thetaalpha %*% array(1, c(1, dfixed)) + array(1, c(n, 1)) %*% mhatsbk
        lderiv1 = colSums((y %*% array(1, c(1, dfixed)) - 1/(1 + exp(-thetanew))) * kalpha)
        lderiv2 = colSums(-((exp(-thetanew)/((1 + exp(-thetanew))^2))) * kalpha)
        mhatsbki = lderiv1/lderiv2
        mhatsbk = mhatsbk - mhatsbki
        difference = max(abs(t(mhatsbki)))
        i = i + 1
    }
    
    mhatsbkoracle = initial
    differenceoracle = 1
    deltaoracle = 1e-07
    
    i = 1
    while (i <= 20 & differenceoracle > deltaoracle) {
        thetaneworacle = thetaalphaoracle %*% array(1, c(1, dfixed)) + array(1, c(n, 1)) %*% mhatsbkoracle
        lderiv1oracle = colSums((y %*% array(1, c(1, dfixed)) - 1/(1 + exp(-thetaneworacle))) * kalpha)
        lderiv2oracle = colSums(-((exp(-thetaneworacle)/((1 + exp(-thetaneworacle))^2))) * kalpha)
        mhatsbkioracle = lderiv1oracle/lderiv2oracle
        mhatsbkoracle = mhatsbkoracle - mhatsbkioracle
        differenceoracle = max(abs(t(mhatsbkioracle)))
        i = i + 1
    }
    mhatsbkalpha = cbind(t(mhatsbk), t(mhatsbkoracle))
    return(mhatsbkalpha)
    
}

automatically created on 2018-10-15

gaplmsbk's Issues

Change for your code

1. I checked the keywords list again, please correct your keywords as follows (because they must have existed alreaday in the keyword list of quantnet and at least 5 keywords): spline, kernel, partial, linear, estimation
2. published in: write the name of your paper. Otherwise delete this item.
3. Just delete the items which you do not fill. Do not use NA to fill them.
4. What are .gitattributes and .gitignore files? Do they belong to your code? If not, delete them.