README.md

In ZhuolinSong/wpe: Written Preliminary Exam or Literature Review: Methods for Functional Snippets

WPE

Written Preliminary Exam or Literature Review: Methods for Functional Snippets. (modified from the mcfda package)

Install

devtools::install_github("zhuolinsong/wpe")

Demonstration

library(wpe)

set.seed(1)

set grid and simulate functional snippet dataset

grid <- regular.grid()

sim <- sim1(50, 0.1, delta=.2, m_avg = 4, sigx='matern', mu=1)

spaghetti plot

library(ggplot2)

pp <- ggplot(data=sim$data,aes(x=argvals,y=y,group=subj)) + geom_line(color='gray') + geom_point(shape=18) + xlim(0, 1) + xlab("t") + ylab("Y(t)") + geom_line(data = data.frame(argvals=grid, y=sim$truemugrid, subj = 1), size = 1.5)

print(pp)

estimate by 'FACE' method

fit1 = face::face.sparse(sim$data,argvals.new = grid)

estimate by 'PACE' method

fit2 = covfunc(sim$t, sim$y, method='PACE', newt=grid, bw=sqrt(2)/2*(1-0.2), delta=1)

estimate by 'FOURIER' method

fit3 = covfunc(sim$t, sim$y, method='FOURIER', newt=grid, ext=0.1, p=10, domain=c(0,1))

estimate by 'SP' method

fit4 = covfunc(sim$t, sim$y, method='SP', newt=grid, domain=c(0,1))

estimate by 'SAMC' method

X = t(to.wide(sim$data,sim$grid)); p=length(sim$grid) A=getA1_new_cv(X, p, dl=0.91000.5, incre=0.11000.5, bw = NA, kernel = 'epan',sigma2hat= NA)$A fit5 = tcrossprod(A)

estract mean and cov estimation over grid

sim1 = list(data=sim$data, truemugrid=sim$truemugrid, truecovgrid=sim$truecovgrid, muface = fit1$mu.new, Cface = fit1$Chat.new, mupace = fit2$mu$fitted, Cpace = fit2$fitted, mufour = fit3$mu$fitted, Cfour = fit3$fitted, musnpt = fit4$mu$fitted, Csnpt = fit4$fitted, Csamc = fit5)

calculate relative error in mise

aggf = function(u){ mumseface = mean((u$muface - u$truemugrid)^2)/mean(u$truemugrid^2) covmseface = mean((u$Cface - u$truecovgrid)^2)/mean(u$truemugrid^2)

mumsepace = mean((u$mupace - u$truemugrid)^2)/mean(u$truemugrid^2) covmsepace = mean((u$Cpace - u$truecovgrid)^2)/mean(u$truemugrid^2)

mumsefour = mean((u$mufour - u$truemugrid)^2)/mean(u$truemugrid^2) covmsefour = mean((u$Cfour - u$truecovgrid)^2)/mean(u$truemugrid^2)

mumsesnpt = mean((u$musnpt - u$truemugrid)^2)/mean(u$truemugrid^2) covmsesnpt = mean((u$Csnpt - u$truecovgrid)^2)/mean(u$truemugrid^2)

covmsesamc = mean((u$Csamc - u$truecovgrid)^2)/mean(u$truemugrid^2) return(c(mumseface,covmseface, mumsepace,covmsepace, mumsefour,covmsefour, mumsesnpt,covmsesnpt, covmsesamc)) }

agg1 = aggf(sim1) A = matrix(agg1, 1) colnames(A) = c("mumseface","covmseface", "mumsepace","covmsepace", "mumsefour","covmsefour", "mumsesnpt","covmsesnpt", "covmsesamc") print(A)

References

Lin, Z. and Wang, J.-L. (2020+). Mean and covariance estimation for functional snippets. Journal of the American Statistical Association. Volume 117, 2022 - Issue 537

Lin, Z., Wang, J.-L. and Zhong, Q. (2021). Basis expansions for functional snippets. Biometrika, Volume 108, Issue 3, September 2021, Pages 709–726

Zhang, A., and Chen, K. (2022). Nonparametric covariance estimation for mixed longitudinal studies, with applications in midlife women's health. Statistica Sinica 32 (2022), 1-21.

Yao, F., Müller, H.-G. and Wang, J.-L. (2005). Functional Data Analysis for Sparse Longitudinal Data. Journal of the American Statistical Association. 100(470): 577-590.

ZhuolinSong/wpe documentation built on Oct. 31, 2022, 7:38 p.m.