ftsa (version 6.4)

One_way_median_polish: One-way functional median polish from Sun and Genton (2012)

Description

Decomposition by one-way functional median polish.

Usage

One_way_median_polish(Y, n_prefectures=51, year=1959:2020, age=0:100)

Value

grand_effect

Grand_effect, a vector of dimension p.

row_effect

Row_effect, a matrix of dimension length(row_partition_index) by p.

Arguments

Y

The multivariate functional data, which are a matrix with dimension n by 2p, where n is the sample size and p is the dimensionality.

year

Vector with the years considered in each population.

n_prefectures

Number of prefectures.

age

Vector with the ages considered in each year.

Author

Cristian Felipe Jimenez Varon, Ying Sun, Han Lin Shang

References

C. F. Jimenez Varon, Y. Sun and H. L. Shang (2023) ``Forecasting high-dimensional functional time series: Application to sub-national age-specific mortality", arXiv. \ Sun, Ying, and Marc G. Genton (2012) ``Functional Median Polish", Journal of Agricultural, Biological, and Environmental Statistics 17(3), 354-376.

See Also

One_way_Residuals, Two_way_median_polish, Two_way_Residuals

Examples

# The US mortality data  1959-2020, for one populations (female) 
# and 3 states (New York, California, Illinois)
# first define the parameters and the row  partitions.
# Define some parameters.
year = 1959:2020
age = 0:100
n_prefectures = 3

#Load the US data. Make sure it is a matrix. 
Y <-  all_hmd_female_data
# Compute the functional median polish decomposition. 
FMP <- One_way_median_polish(Y,n_prefectures=3,year=1959:2020,age=0:100)
# The results
##1. The funcional grand effect
FGE <- FMP$grand_effect
##2. The funcional row effect
FRE <- FMP$row_effect