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The asymptotic distributions of kernel estimators of the mode

1982; Springer Nature; Volume: 59; Issue: 3 Linguagem: Inglês

10.1007/bf00532221

0044-3719

William F. Eddy,

Bayesian Methods and Mixture Models

In a decreasing sequence of intervals centered on the true mode the normalized kernel estimate of the density converges weakly to a nonstationary Gaussian random process. The expected value of this process is a parabola through the origin. The covariance function of this process depends on the smoothness of the kernel. When the kernel is mean-square differentiable the location of the maximum of this process has a normal distribution. When the kernel is discontinuous the location of the maximum has a distribution related to a solution of the heat equation.