TABLE 3.

Performance of principal component analysis (PCA) of hybrid functional and vector data (HFV-PCA) in terms of $\mathrm{RSE}\left({\widehat{\lambda }}_m\right)$, $\mathrm{RSE}\left({\widehat{\xi }}_m\right)$ and $\mathrm{ASE}\left({\widehat{\rho }}_m\right)$, m = 1, 2, 3, averaged across 500 simulated datasets of sizes n = 150 and n = 300 (with SDs in parentheses) for each setting (I/II). Given two functions per observation unit, three combinations of the types of multivariate functional data are considered: SIR-SIR, SIR-DR, and DR-DR

		Setting I			Setting II
n	R(A)SE	SIR-SIR	SIR-DR	DR-DR	SIR-SIR	SIR-DR	DR-DR
150	$\mathrm{RSE}\left({\widehat{\lambda }}_1\right)$	0.054 (0.044)	0.026 (0.027)	0.014 (0.019)	0.054 (0.045)	0.025 (0.027)	0.014 (0.019)
	$\mathrm{RSE}\left({\widehat{\lambda }}_2\right)$	0.104 (0.060)	0.042 (0.038)	0.014 (0.018)	0.104 (0.061)	0.042 (0.037)	0.014 (0.018)
	$\mathrm{RSE}\left({\widehat{\lambda }}_3\right)$	0.183 (0.067)	0.075 (0.049)	0.021 (0.026)	0.174 (0.068)	0.072 (0.049)	0.020 (0.024)
	$\mathrm{RSE}\left({\widehat{\xi }}_1\right)$	0.047 (0.026)	0.035 (0.023)	0.020 (0.022)	0.049 (0.027)	0.035 (0.023)	0.020 (0.022)
	$\mathrm{RSE}\left({\widehat{\xi }}_2\right)$	0.108 (0.043)	0.076 (0.037)	0.037 (0.032)	0.115 (0.048)	0.076 (0.038)	0.037 (0.033)
	$\mathrm{RSE}\left({\widehat{\xi }}_3\right)$	0.277 (0.077)	0.161 (0.056)	0.045 (0.036)	0.273 (0.083)	0.161 (0.055)	0.045 (0.036)
	$\mathrm{ASE}\left({\widehat{\rho }}_1\right)$	0.044 (0.013)	0.026 (0.012)	0.017 (0.012)	0.046 (0.013)	0.026 (0.012)	0.017 (0.012)
	$\mathrm{ASE}\left({\widehat{\rho }}_2\right)$	0.043 (0.019)	0.029 (0.019)	0.024 (0.021)	0.045 (0.020)	0.029 (0.019)	0.024 (0.021)
	$\mathrm{ASE}\left({\widehat{\rho }}_3\right)$	0.030 (0.011)	0.020 (0.012)	0.017 (0.012)	0.031 (0.012)	0.020 (0.012)	0.017 (0.012)
300	$\mathrm{RSE}\left({\widehat{\lambda }}_1\right)$	0.046 (0.031)	0.018 (0.018)	0.007 (0.009)	0.047 (0.031)	0.018 (0.018)	0.007 (0.009)
	$\mathrm{RSE}\left({\widehat{\lambda }}_2\right)$	0.093 (0.043)	0.035 (0.026)	0.008 (0.011)	0.095 (0.043)	0.034 (0.026)	0.008 (0.011)
	$\mathrm{RSE}\left({\widehat{\lambda }}_3\right)$	0.180 (0.047)	0.070 (0.034)	0.015 (0.017)	0.173 (0.048)	0.068 (0.033)	0.014 (0.016)
	$\mathrm{RSE}\left({\widehat{\xi }}_1\right)$	0.031 (0.013)	0.023 (0.013)	0.011 (0.012)	0.031 (0.014)	0.023 (0.013)	0.011 (0.012)
	$\mathrm{RSE}\left({\widehat{\xi }}_2\right)$	0.074 (0.025)	0.052 (0.022)	0.019 (0.016)	0.078 (0.026)	0.052 (0.022)	0.019 (0.016)
	$\mathrm{RSE}\left({\widehat{\xi }}_3\right)$	0.215 (0.054)	0.121 (0.037)	0.022 (0.016)	0.212 (0.057)	0.121 (0.037)	0.022 (0.016)
	$\mathrm{ASE}\left({\widehat{\rho }}_1\right)$	0.037 (0.007)	0.020 (0.007)	0.010 (0.007)	0.039 (0.007)	0.020 (0.007)	0.011 (0.007)
	$\mathrm{ASE}\left({\widehat{\rho }}_2\right)$	0.034 (0.011)	0.020 (0.011)	0.014 (0.011)	0.035 (0.011)	0.020 (0.011)	0.014 (0.011)
	$\mathrm{ASE}\left({\widehat{\rho }}_3\right)$	0.023 (0.005)	0.013 (0.006)	0.010 (0.006)	0.023 (0.006)	0.013 (0.006)	0.009 (0.006)

Abbreviations: ASE, average squared error; DR, dense and regular; DIR, dense and irregular; RSE, relative squared error; SIR, sparse and irregular.