Irregular sampling of stochastic processes gives the theoretical possibility to estimate spectral densities up to very high frequencies. However, the methods developed tend to be heavily biased at higher frequencies or fail to produce a spectrum that is positive for all frequencies. A new estimator is introduced that applies autoregressive spectral estimation to unevenly spaced data. This estimator approximates the data by equidistant resampling with a special nearest neighbor algorithm, that only accepts data if the nearest irregular data point is within half the slot width of the resampling time grid. The algorithm searches for uninterrupted sequences of resampled data and analyzes those sequences using the Burg algorithm for segmented data. With sufficient data, results can be accurate at frequencies higher than the mean data rate.