Table 1.

Differences between naive and the proposed estimates, and their bootstrap standard errors. β̂ is the estimated coefficient using the proposed method, while β̂_(a) is that from the naive estimation. The standard error of (β̂ − β̂_(a)) is calculated based on 50 bootstrap sample

		Quantile level (τ)
Weight at		0.66	0.68	0.71	0.73	0.76	0.78	0.80	0.83	0.85
1 yr	β̂ − β̂(a)	0.48	0.61	0.66	0.76	0.74	0.79	0.84	1.04	0.98
	Bootstrap SE	0.40	0.41	0.37	0.36	0.39	0.42	0.40	0.40	0.50
	p-value	0.114	0.069	0.038	0.019	0.029	0.030	0.018	0.005	0.024
7 yrs	β̂ − β̂(a)	−0.19	−0.17	−0.12	−0.09	−0.08	−0.12	−0.09	−0.16	−0.12
	Bootstrap SE	0.10	0.10	0.10	0.10	0.11	0.10	0.09	0.09	0.15
	p-value	0.969	0.960	0.883	0.827	0.767	0.881	0.828	0.958	0.973