Table 3.

Regression coefficient estimation under a quantile regression model with ten coefficients

				t = 0.2				t = 0.5				t = 0.8
Orig			B	25	1	−13	−8	8	−9	−15	−8	−18	−13	−8	−11
			SD	620	442	450	448	493	344	347	330	460	307	310	312
			SE	701	466	465	463	536	360	358	357	477	318	321	319
			CI	96.8	96.6	96.2	95.3	96.2	95.0	95.6	96.4	95.2	94.3	94.6	95.6
$\text{AI-}\widehat{𝕏}$	MAE	0.87	B	−27	14	−9	−4	7	−9	−15	−8	4	−22	−21	−6
	RMISE	0.95	SD	593	414	434	431	493	343	347	329	431	287	297	287
	BRK	0.01	CI	97.8	97.1	96.4	95.9	96.2	95.2	95.5	96.3	96.1	96.1	95.9	96.6

Orig: the original estimator; $\text{AI-}\widehat{𝕏}$: the proposed adaptive interpolation estimator with $\widehat{𝕏}$ and τ ≏ 0.5.

MAE: maximum absolute error over [0.1, 0.9]; RMISE: root mean integrated squared error over [0.1, 0.9]; BRK: number of knots or breakpoints. All are average measures, reported as relative to the original estimator. B: Empirical bias (×1000); SD: Empirical standard deviation (×1000); SE: Average standard error (×1000); CI: Empirical coverage (%) of 95% Wald confidence interval.

Under each t value are the first four estimated coefficients; the fourth is representative of the last seven.