Estimation of a time-dependent density

•Estimation of a time-dependent density is considered.•The error of the estimate is measured by the L1-error.•Results concerning consistency and rate of convergence are presented.

The problem of estimating a time-dependent density at each time point t∈[0,1] is considered, where independent samples of the density at equidistant time points in [0,1] are given. Here all the samples have the same sample size. It is assumed that the distribution corresponding to the density of time t depends smoothly on t. The error of the estimate is measured by the L1-error. Results concerning consistency and rate of convergence of a local average of kernel density estimates of the density at the discrete time points are presented. The finite sample size performance of the estimate is illustrated by applying it to simulated data.