Remodeling and Estimation for Sparse Partially Linear Regression Models

Table 1

MSEs on the parameter 𝛽 and MSPEs of the two-stage adjusted linear model (12) compared with the submodel, the SCAD-penalized model, the multistep adjusted model and the full model.

No.	Item	𝛽𝑆	𝛽SCAD	𝛽𝑀	𝛽TS	𝛽𝐹
		0.3079	0.0457	0.0660	0.0571	1.6105×10^3
		0.1763	0.0206	0.0346	0.0176	1.0940×10^3
Case (I)	MSEs	0.1396	0.0481	0.0631	0.0461	4.2049×10^3
𝑐=0.5		0.1870	0.0196	0.0349	0.0186	5.0183×10^3
		0.1131	0.0517	0.0609	0.0430	6.2615×10^3
	MSPEs	3.4780	1.1896	1.6512	1.0679	3.0499×10^2
		0.1568	0.6191	0.0934	0.0826	1.2494×10^3
		0.6239	0.1060	0.0090	0.0083	1.0456×10^2
Case (I)	MSEs	0.8829	0.8173	0.0895	0.1039	2.6368×10^2
𝑐=0.8		0.5882	0.0919	0.0107	0.0100	7.6452×10^1
		1.0799	0.9829	0.0961	0.0929	1.1610×10^3
	MSPEs	4.7930	2.6700	0.8354	0.7771	1.3223×10^2
		0.4272	0.0660	0.0849	0.0557	4.3002×10^2
		0.6371	0.0318	0.0499	0.0295	3.7893×10^3
Case (II)	MSEs	0.4560	0.0715	0.0927	0.0588	1.2784×10^3
𝑐=0.5		0.5926	0.0306	0.0491	0.0287	6.7354×10^3
		0.9052	0.0734	0.0874	0.0583	2.5047×10^2
	MSPEs	6.8634	1.5096	2.0780	1.2077	5.0464×10^3
		0.6764	0.4263	0.1212	0.0960	1.3904×10^3
		0.9721	0.1060	0.0107	0.0102	4.0743×10^2
Case (II)	MSEs	0.6242	0.4756	0.1146	0.1003	1.0498×10^3
𝑐=0.8		1.0282	0.0954	0.0112	0.0098	5.6031×10^2
		1.3420	0.5474	0.1341	0.1124	9.9632×10^2
	MSPEs	7.9928	2.1165	0.9514	0.8469	2.3110×10^2