Table 2:

Mean square errors (MSE) of the estimates of the inner product $\text{I}(\mathit{\text{β}},\mathit{\text{γ}})$ and the normalized inner product $\text{R}(\mathit{\beta },\mathit{\gamma })$ for various signal strength parameters. Lasso: plugin estimator with the scaled Lasso estimator; De-biased: plug-in estimator with the de-biased estimator; Thresholded: plug-in estimator with the thresholded estimator; FDE: the proposed estimator $\widehat{\text{I}}(\mathit{\text{β}},\mathit{\text{γ}})$; FDE-S: the proposed estimator $\widehat{\text{R}}(\mathit{\beta },\mathit{\gamma })$ with sample splitting; FDE-NS: the proposed estimator $\widehat{\text{R}}(\mathit{\beta },\mathit{\gamma })$ without sample splitting.

		Strength parameters, $({\tau }_1,{\tau }_2)$
		(1.8, .4)	(2.2, .3)	(2.6, .2)	(3, .1)	(.1, 1.6)	(.2, 1.4)	(.3, 1.2)	(.4, 1)
$\text{I}(\mathit{\text{β}},\mathit{\text{γ}})$	Truth	8.088	7.414	5.841	3.370	1.797	3.145	4.044	4.493
MSE
	Lasso	9.295	11.564	12.560	7.279	2.377	4.889	5.409	4.800
	De-biased	1.733	2.191	2.324	1.386	.449	.838	.985	.886
	Thresholded	2.029	3.377	6.463	5.789	1.877	3.024	2.432	1.546
	FDE	1.847	2.471	2.662	2.118	.734	.995	1.028	.986
$\text{R}(\mathit{\text{β}},\mathit{\text{γ}})$	Truth	.5314	.5314	.5314	.5314	.5314	.5314	.5314	.5314
MSE
	Lasso	.0023	.0075	.0332	.1260	.1574	.0624	.0227	.0087
	De-biased	.0208	.0415	.0864	.1590	.1736	.1068	.0627	.0373
	Thresholded	.0045	.0139	.0585	.1753	.0964	.0981	.0389	.0153
	FDE-S	.0337	.0303	.0621	.0678	.2130	.1199	.0694	.0616
	FDE-NS	.0036	.0064	.0163	.0580	.0892	.0237	.0116	.0061