Ficult to obtain c analytically. One obvious alternative would be the

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Therefore, c can be estimated empirically from a large number of realizations of the ^ GSK343 site Conditional distribution of suptI |W /s| given the data. For t , define the process ^ ^ B T (t)U ^ 1 d( i Ni ) + ^ 2 d( i Ni ) ^ Wn (t) = n 0i n1 i>n^ T (t)U ^ B = n ^ C(t) + n^ C(t) + ntti n1^1 d( i Ni ) +i>n 1^2 d( i Ni )i>ni n^ i i 1 (X i )I (X i) +^ i i 2 (X i )I (X ii n^ i i 1 (X i )I (X it) +i>n^ i i 2 (X i )I (X iwhere i , i = 1, . . . , n, are independent variables that are also independent from the data. Furthermore, these variables have mean zero and variance converging to one as n . In the normal resampling approach mentioned above, the i 's are the standard normal variables. However, the standard normal variables often result fpsyg.2015.00360 in lower coverage probabilities in various simulation studies. Thus, with moderate sized samples, we need to make some adjustment. ^ Conditional on (X i , i , Z i ), i = 1, . .Ficult to obtain c analytically. One obvious alternative would be the bootstrapping method. However, it is very time-consuming and results in lower than nominal coverage probabilities in some simulation studies. Lin and others (1993) used a normal resampling approximation to simulate the asymptoticS. YANG AND R. L. P RENTICEdistribution of sums of martingale residuals for checking the Cox regression model. The normal resampling approach reduces computing time significantly and has become a standard method. It has been used in many works, including Lin and others (1994), Cheng and others (1997), Gilbert and others (2002), Tian and others (2005), and Peng and Huang (2007). We will modify this approach for our problem here. For t , define the process ^ ^ B T (t)U ^ 1 d( i Ni ) + ^ 2 d( i Ni ) ^ Wn (t) = n 0i n1 i>n^ T (t)U ^ B = n ^ C(t) + n^ C(t) + ntti n1^1 d( i Ni ) +i>n 1^2 d( i Ni )i>ni n^ i i 1 (X i )I (X i) +^ i i 2 (X i )I (X ii n^ i i 1 (X i )I (X it) +i>n^ i i 2 (X i )I (X iwhere i , i = 1, . . . , n, are independent variables that are also independent from the data.Ficult to obtain c analytically. One obvious alternative would be the bootstrapping method. However, it is very time-consuming and results in lower than nominal coverage probabilities in some simulation studies. Lin and others (1993) used a normal resampling approximation to simulate the asymptoticS. YANG AND R. L. P RENTICEdistribution of sums of martingale residuals for checking the Cox regression model. The normal resampling approach reduces computing time significantly and has become a standard method. It has been used in many works, including Lin and others (1994), Cheng and others (1997), Gilbert and others (2002), Tian and others (2005), and Peng and Huang (2007). We will modify this approach for our problem here. For t , define the process ^ ^ B T (t)U ^ 1 d( i Ni ) + ^ 2 d( i Ni ) ^ Wn (t) = n 0i n1 i>n^ T (t)U ^ B = n ^ C(t) + n^ C(t) + ntti n1^1 d( i Ni ) +i>n 1^2 d( i Ni )i>ni n^ i i 1 (X i )I (X i) +^ i i 2 (X i )I (X ii n^ i i 1 (X i )I (X it) +i>n^ i i 2 (X i )I (X iwhere i , i = 1, . . .