Testing Heteroscedasticity in Nonparametric Regression Based on Trend Analysis

Table 1

Rejection frequencies of 500 replications of the testing procedure.

Model	𝑎	𝑁(0,1)		𝑈(−√3,√3)		𝜒^2(4)
		Proposed method	Zhang and Mei [7]	Proposed method	Zhang and Mei [7]	Proposed method	Zhang and Mei [7]
		𝑛=100
Model 1	0	0.022	0.038	0.032	0.022	0.058	0.024
	0.50	0.346	0.014	0.402	0.002	0.348	0.026
	1.00	0.540	0.020	0.570	0.006	0.506	0.012
Model 2	0	0.020	0.038	0.038	0.024	0.048	0.030
	0.50	0.294	0.020	0.490	0.048	0.352	0.064
	1.00	0.996	0.032	1.000	0.056	0.996	0.080
Model 3	0	0.024	0.038	0.038	0.026	0.044	0.032
	0.50	0.162	0.510	0.258	0.796	0.202	0.248
	1.00	0.544	0.954	0.736	1.000	0.574	0.714
		𝑛=200
Model 1	0	0.034	0.034	0.034	0.018	0.062	0.032
	0.50	0.596	0.012	0.678	0.002	0.620	0.014
	1.00	0.870	0.014	0.884	0.004	0.952	0.016
Model 2	0	0.032	0.040	0.038	0.018	0.058	0.030
	0.50	0.436	0.022	0.690	0.052	0.514	0.068
	1.00	1.000	0.034	1.000	0.058	1.000	0.072
Model 3	0	0.038	0.042	0.038	0.018	0.058	0.030
	0.50	0.236	0.692	0.358	0.946	0.318	0.362
	1.00	0.714	0.996	0.912	1.000	0.750	0.862