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Nonparametric estimation and testing on discontinuity of positive supported densities: A kernel truncation approach

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Figure

Figure 2: Density Estimates of School Enrollments
Table 1: Biases, Standard Deviations and RMSEs of Estimators of J (c) Estimator J (c)˜ with δ Distribution c n J ˆ M (c) 0.49 0.64 0.81 Gamma 1.7057 500 Bias -0.0381 0.0019 0.0011 0.0006 (30%) StdDev 0.0461 0.0786 0.0812 0.0837 RMSE 0.0598 0.0786 0.0812 0.
Table 2: Finite-Sample Size Properties of Test Statistics for Discontinuity (%) T 1 (c) with δ T 2 (c) with δ Distribution c n Nominal 0.49 0.64 0.81 0.49 0.64 0.81 Gamma 1.7057 500 5% 3.2 3.1 3.1 4.4 4.0 3.7 (30%) 10% 7.5 7.5 7.8 8.8 8.8 8.6 1000 5% 3.9 3
Table 3: Finite-Sample Power Properties of Test Statistics for Discontinuity
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