Noise and error analysis and optimization in particle-based kinetic plasma simulations

•Numerical noise is studied in a finite particle number system, by kernel density estimation.•Ornstein-Uhlenbeck bridge describes the electric field correlations.•Optimal kernel width minimizes the error by bias-variance optimization.•Particle shapes of arbitrary width are possible, and partition of unity gives charge conservation on the grid.•Results apply to particle-in-cell (PIC), delta-f, and hybrid methods.