Preface
Contents
1 Kernel Density Function Estimator
1.1 Boundary Bias Problem
1.2 Bias and Variance Reductions
1.3 Simulation Studies
References
2 Kernel Distribution Function Estimator
2.1 Properties of KDFE
2.2 Bias Reduction of KDFE
2.3 Simulation Results
References
3 Kernel Quantile Estimation
3.1 Quantile Estimators
3.2 Properties of Quantile Estimators
3.3 Asymptotic Properties of Quantile Estimators
3.4 Numerical Comparisons
3.4.1 Estimation of Quantiles of the Standard Normal Distribution
3.4.2 Estimation of Quantiles of the Standard Exponential Distribution
3.4.3 Estimation of Quantiles of the Gamma Distribution
References
4 Mean Residual Life Estimator
4.1 Estimators of the Survival Function and the Cumulative Survival Function
4.2 Estimators of the Mean Residual Life Function
4.3 Numerical Studies
References
5 Kernel-Based Nonparametric Tests
5.1 Naive Kernel Goodness-of-Fit Tests
5.2 Boundary-Free Kernel-Type Goodness-of-Fit Tests
5.2.1 Boundary-Free KDFE
5.2.2 Boundary-Free Kernel-Smoothed KS and CvM Tests
5.2.3 Numerical Results
5.3 Smoothed Nonparametric Tests and Approximation of p-Value
5.3.1 Asymptotic Properties of Smoothed Tests
5.3.2 Selection of Bandwidth and Kernel Function
5.3.3 Higher Order Approximation
References