MFDM: Multilevel functional data method

Description

Fit a multilevel functional principal component model. The function uses two-step functional principal component decompositions.

Usage

MFDM(mort_female, mort_male, mort_ave, percent_1 = 0.95, percent_2 = 0.95, fh, 
	     level = 80, alpha = 0.2, MCMCiter = 100, fmethod = c("auto_arima", "ets"), 
		   BC = c(FALSE, TRUE), lambda)

Value

first_percent: Percentage of total variation explained by the first common functional principal component.
female_percent: Percentage of total variation explained by the first female functional principal component in the residual.
male_percent: Percentage of total variation explained by the first male functional principal component in the residual.
mort_female_fore: Forecast female mortality in the original scale.
mort_male_fore: Forecast male mortality in the original scale.

Arguments

mort_female: Female mortality (p by n matrix), where p denotes the dimension and n denotes the sample size.
mort_male: Male mortality (p by n matrix).
mort_ave: Total mortality (p by n matrix).
percent_1: Cumulative percentage used for determining the number of common functional principal components.
percent_2: Cumulative percentage used for determining the number of sex-specific functional principal components.
fh: Forecast horizon.
level: Nominal coverage probability of a prediction interval.
alpha: 1 - Nominal coverage probability.
MCMCiter: Number of MCMC iterations.
fmethod: Univariate time-series forecasting method.
BC: If Box-Cox transformation is performed.
lambda: If BC = TRUE, specify a Box-Cox transformation parameter.

Author

Han Lin Shang

Details

The basic idea of multilevel functional data method is to decompose functions from different sub-populations into an aggregated average, a sex-specific deviation from the aggregated average, a common trend, a sex-specific trend and measurement error. The common and sex-specific trends are modelled by projecting them onto the eigenvectors of covariance operators of the aggregated and sex-specific centred stochastic process, respectively.

References

C. M. Crainiceanu and J. Goldsmith (2010) "Bayesian functional data analysis using WinBUGS", Journal of Statistical Software, 32(11).

C-Z. Di and C. M. Crainiceanu and B. S. Caffo and N. M. Punjabi (2009) "Multilevel functional principal component analysis", The Annals of Applied Statistics, 3(1), 458-488.

V. Zipunnikov and B. Caffo and D. M. Yousem and C. Davatzikos and B. S. Schwartz and C. Crainiceanu (2015) "Multilevel functional principal component analysis for high-dimensional data", Journal of Computational and Graphical Statistics, 20, 852-873.

H. L. Shang, P. W. F. Smith, J. Bijak, A. Wisniowski (2016) "A multilevel functional data method for forecasting population, with an application to the United Kingdom", International Journal of Forecasting, 32(3), 629-649.