Subgroup Analysis of a Single-Index Threshold Penalty Quantile Regression Model Based on Variable Selection | Wuhan University Journal of Natural Sciences

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Table 4

Estimation results of parameters in the case where $ε_{i} \sim M V T_{3} (0, Σ)$ and $Σ$ follows an $A R$ -1 structure

Parameter		$p = d = 10$						$p = d = 20$
		$n = 400$			$n = 800$			$n = 400$			$n = 800$
		Bias	RMSE	SD	Bias	RMSE	SD	Bias	RMSE	SD	Bias	RMSE	SD
$τ = 0.25$	$β_{1}$	0.002 4	0.100 4	0.100 4	0.002 4	0.072 3	0.072 3	0.003 1	0.096 4	0.096 4	0.006 4	0.070 4	0.070 2
	$β_{2}$	-0.010 3	0.053 6	0.052 7	-0.004 5	0.039 1	0.038 9	-0.011 9	0.054 8	0.053 6	-0.008 4	0.039 3	0.038 5
	$β_{3}$	0.004 3	0.039 6	0.039 4	0.000 4	0.027 9	0.027 9	0.002 9	0.037 5	0.037 5	0.000 6	0.026 4	0.026 4
	$δ_{1}$	0.019 9	0.106 8	0.105 0	0.004 7	0.076 6	0.076 5	0.015 2	0.113 2	0.112 3	0.003 1	0.077 5	0.077 5
	$δ_{2}$	0.011 9	0.076 2	0.075 3	0.007 5	0.056 3	0.055 9	0.015 6	0.079 6	0.078 1	0.009 8	0.054 9	0.054 0
	$ψ_{0}$	0.015 6	0.0697	0.068 0	0.011 3	0.051 8	0.050 6	0.008 6	0.066 2	0.065 7	0.008 4	0.051 2	0.050 6
	$ψ_{1}$	0.000 4	0.056 7	0.056 7	0.005 1	0.039 0	0.038 7	0.006 6	0.053 8	0.053 5	0.007 8	0.041 5	0.040 8
$τ = 0.50$	$β_{1}$	-0.001 3	0.078 1	0.078 2	-0.001 0	0.050 9	0.051 0	-0.005 9	0.077 6	0.077 4	-0.002 0	0.051 3	0.051 5
	$β_{2}$	-0.006 2	0.041 7	0.041 3	-0.006 0	0.031 9	0.031 4	-0.007 2	0.041 8	0.041 2	-0.002 0	0.030 2	0.030 3
	$β_{3}$	0.001 8	0.031 8	0.041 3	0.000 2	0.022 7	0.022 7	0.000 2	0.030 7	0.030 7	0.002 3	0.021 4	0.021 3
	$δ_{1}$	0.012 6	0.090 7	0.090 0	0.004 4	0.060 4	0.060 3	0.021 2	0.092 1	0.089 8	0.001 5	0.064 3	0.064 5
	$δ_{2}$	0.013 0	0.063 1	0.061 9	0.009 7	0.046 5	0.045 5	0.011 1	0.058 2	0.057 1	0.008 8	0.047 5	0.046 8
	$ψ_{0}$	-0.001 1	0.060 1	0.060 2	0.000 1	0.044 1	0.044 2	-0.005 2	0.061 8	0.061 6	-0.003 4	0.043 8	0.043 8
	$ψ_{1}$	0.002 6	0.053 2	0.053 3	0.000 5	0.036 9	0.036 9	0.006 2	0.050 7	0.050 4	0.006 2	0.037 6	0.037 2
$τ = 0.75$	$β_{1}$	-0.017 5	0.095 4	0.093 9	-0.006 1	0.067 0	0.066 8	-0.017 3	0.089 7	0.088 2	-0.010 0	0.066 1	0.065 4
	$β_{2}$	-0.005 4	0.051 0	0.050 8	0.000 5	0.034 2	0.034 2	0.000 0	0.051 8	0.051 9	0.000 4	0.035 5	0.035 6
	$β_{3}$	-0.003 2	0.036 9	0.036 8	0.000 3	0.027 0	0.046 0	-0.003 2	0.038 2	0.038 2	-0.000 9	0.025 6	0.025 6
	$δ_{1}$	0.009 6	0.110 5	0.110 2	0.001 4	0.076 9	0.077 0	0.012 0	0.115 6	0.115 3	0.000 0	0.072 4	0.072 5
	$δ_{2}$	0.019 8	0.079 0	0.076 6	0.010 9	0.053 4	0.052 4	0.015 1	0.081 7	0.080 4	0.010 3	0.052 3	0.051 3
	$ψ_{0}$	-0.022 1	0.072 5	0.069 1	-0.019 2	0.049 9	0.046 0	-0.020 9	0.075 1	0.072 2	-0.017 3	0.050 0	0.047 0
	$ψ_{1}$	0.006 1	0.058 0	0.057 7	0.001 3	0.038 5	0.038 5	0.004 9	0.058 7	0.058 6	0.002 4	0.037 8	0.037 8

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