In the context of parameter estimation for nextgeneration nonlinear radar system models impaired by nonGaussian clutter, reproducing kernel Hilbert space (RKHS)-based signal processing algorithms and information-theoretic learning (ITL) have emerged as promising. Notably, the RKHS and ITLbased approaches are found to outperform conventional maximum likelihood (ML) based methods. However, these RKHS/ITLbased approaches, together with neural network/Bayesian-based approaches, are known to depend on hyperparameters for parameter/criterion estimation. In the context of next-generation radar, this paper introduces a minimum error entropy with fiducial points (MEEF)-based parameter estimation for multi-input-multiple-output (MIMO) radar to estimate target position and velocity amid non-Gaussian additive noise processes, such as clutter. Furthermore, we utilize a kernel width sampling method to make the proposed MEEF estimator hyperparameter-free. The proposed hyperparameter-free MEEF-based RKHS estimator with kernel width sampling (MEEF-KWS) is found to outperform minimum mean squared error (MMSE) and other ITL-based adaptive estimation techniques with fixed best kernel width. Computer simulations are presented assuming practical MIMO radar scenarios, which indicate that the proposed hyperparameter-free MEEF-KWS delivers improved estimation accuracy and/or lower computations compared to the existing RKHS-based MMSE and other common ITL criteria with fixed kernel width.