Table 3.

Average entropy loss, denoted by EL, (SD in parentheses) and average quadratic loss, denoted by QL, (SD in parentheses), based on 100 simulations, for estimating multiple precision matrices in Example 3. Here “Smooth”, “Lasso”, “TLP”, “Our-con” and “Ours” denote estimation of individual matrices with kernel smoothing method proposed in [25], the L₁ sparseness penalty, that with non-convex TLP penalty, the convex counterpart of our method with the Li-penalty for sparseness and clustering, and our non-convex estimates by solving (2) with penalty (6). The best performer is bold-faced.

Set-up	Method	n = 120		n = 300
(p,L)		EL	QL	EL	QL
(30, 4)	Smooth	0.468(.042)	0.941(.097)	0.231(.056)	0.476(.034)
	Lasso	1.158(.062)	2.534(.175)	0.736(.036)	1.434(.086)
	TLP	1.546(.100)	3.625(.262)	0.575(.045)	1.301(.121)
	Our-con	0.897(.066)	1.823(.166)	0.699(.038)	1.317(.085)
	Ours	0.501(.063)	1.143(.160)	0.247(.017)	0.524(.042)
(200, 4)	Smooth	6.882(.220)	13.26(.535)	2.578(.066)	4.843(.130)
	Lasso	10.37(.173)	21.92(.498)	5.449(.094)	10.84(.211)
	TLP	12.34(.202)	25.87(.560)	5.523(.153)	12.08(.365)
	Our-con	6.091(.199)	12.34(.484)	4.625(.098)	8.625(.209)
	Ours	5.079(.265)	11.84(.658)	1.682(.038)	3.551(.096)
(20, 30)	Smooth	0.490(.021)	0.878(.042)	0.278(.008)	0.492(.015)
	Lasso	0.786(.020)	1.670(.052)	0.564(.012)	1.066(.027)
	TLP	0.987(.036)	2.454(.107)	0.355(.014)	0.819(.035)
	Our-con	0.653(.023)	1.281(.055)	0.528(.012)	0.959(.027)
	Ours	0.317(.013)	0.730(.036)	0.183(.005)	0.391(.014)
(10, 90)	Smooth	0.230(.008)	0.409(.017)	0.115(.003)	0.203(.005)
	Lasso	0.318(.008)	0.694(.022)	0.205(.004)	0.398(.008)
	TLP	0.402(.012)	1.010(.043)	0.148(.004)	0.346(.011)
	Our-con	0.240(.008)	0.487(.019)	0.180(.004)	0.335(.007)
	Ours	0.158(.005)	0.369(.014)	0.082(.002)	0.176(.005)