FANOVA {ftsa}

Functional analysis of variance fitted by means.

Description

Decomposition by functional analysis of variance fitted by means.

Usage

FANOVA(data_pop1, data_pop2, year=1959:2020, age= 0:100, 
	       n_prefectures=51, n_populations=2)

Arguments

data_pop1

It's a p by n matrix

data_pop2

It's a p by n matrix

year

Vector with the years considered in each population.

n_prefectures

Number of prefectures

age

Vector with the ages considered in each year.

n_populations

Number of populations.

Value

FGE_mean

FGE_mean, a vector of dimension p

FRE_mean

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

FCE_mean

FCE_mean, a matrix of dimension length(column_partition_index) by p.

Author(s)

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".

Ramsay, J. and B. Silverman (2006). Functional Data Analysis. Springer Series in Statistics. Chapter 13. New York: Springer

See Also

Two_way_median_polish

Examples

# The US mortality data  1959-2020 for two populations and three states 
# (New York, California, Illinois)
# Compute the functional Anova decomposition fitted by means.
FANOVA_means <- FANOVA(data_pop1 = t(all_hmd_male_data), 
					      data_pop2 = t(all_hmd_female_data),
					      year = 1959:2020, age =  0:100, 
					      n_prefectures = 3, n_populations = 2)

##1. The funcional grand effect
FGE = FANOVA_means$FGE_mean
##2. The funcional row effect
FRE = FANOVA_means$FRE_mean
##3. The funcional column effect
FCE = FANOVA_means$FCE_mean