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Parametric statistics
About: Parametric statistics is a research topic. Over the lifetime, 39200 publications have been published within this topic receiving 765761 citations.
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TL;DR: This article investigates the use of integrated square error, or L2 distance, as a theoretical and practical estimation tool for a variety of parametric statistical models and demonstrates by example the well-known result that minimum distance estimators, including L2E, are inherently robust.
Abstract: The likelihood function plays a central role in parametric and Bayesian estimation, as well as in nonparametric function estimation via local polynomial modeling. However, integrated square error has enjoyed a long tradition as the goodness-of-fit criterion of choice in nonparametric density estimation. In this article, I investigate the use of integrated square error, or L2 distance, as a theoretical and practical estimation tool for a variety of parametric statistical models. I show that the asymptotic inefficiency of the parameters estimated by minimizing the integrated square error or L2estimation (L2E) criterion versus the maximum likelihood estimator is roughly that of the median versus the mean. I demonstrate by example the well-known result that minimum distance estimators, including L2E, are inherently robust; however, L2E does not require specification of any tuning factors found in robust likelihood algorithms. L2E is particularly appropriate for analyzing massive datasets in which data cleanin...
226 citations
TL;DR: An automatic approach for the reconstruction of parametric 3D building models from indoor point clouds that goes beyond mere surface reconstruction of previous reconstruction methods and enables intuitive editing on level of building elements, e.g. moving whole walls.
225 citations
TL;DR: A new modified Kolmogorov-Smirnoff (KS) goodness-of-fit test is proposed; this modified test guarantees good fitting in the distribution tails, which is of fundamental importance for a correct design of CFAR processors.
Abstract: The performance of ground-based surveillance radars strongly depends on the distribution and spectral characteristics of ground clutter. To design signal processing algorithms that exploit the knowledge of clutter characteristics, a preliminary statistical analysis of ground-clutter data is necessary. We report the results of a statistical analysis of X-band ground-clutter data from the MIT Lincoln Laboratory Phase One program. Data non-Gaussianity of the in-phase and quadrature components was revealed, first by means of histogram and moments analysis, and then by means of a Gaussianity test based on cumulants of order higher than the second; to this purpose parametric autoregressive (AR) modeling of the clutter process was developed. The test is computationally attractive and has constant false alarm rate (CFAR). Incoherent analysis has also been carried out by checking the fitting to Rayleigh, Weibull, log-normal, and K-distribution models. Finally, a new modified Kolmogorov-Smirnoff (KS) goodness-of-fit test is proposed; this modified test guarantees good fitting in the distribution tails, which is of fundamental importance for a correct design of CFAR processors.
225 citations
TL;DR: The results suggest that analyses of 1D data based on 0D models of randomness are generally biased unless one explicitly identifies 0D variables before the experiment, and parametric and non-parametric 1D hypothesis testing provide an unambiguous framework for analysis when one׳s hypothesis explicitly or implicitly pertains to whole 1D trajectories.
225 citations
TL;DR: The proposed method may be a valid alternative when other existing techniques, either deterministic or stochastic, are not directly usable due to excessive conservatism or to numerical intractability caused by lack of convexity of the robust or chance-constrained optimization problem.
Abstract: This paper discusses a novel probabilistic approach for the design of robust model predictive control (MPC) laws for discrete-time linear systems affected by parametric uncertainty and additive disturbances. The proposed technique is based on the iterated solution, at each step, of a finite-horizon optimal control problem (FHOCP) that takes into account a suitable number of randomly extracted scenarios of uncertainty and disturbances, followed by a specific command selection rule implemented in a receding horizon fashion. The scenario FHOCP is always convex, also when the uncertain parameters and disturbance belong to nonconvex sets, and irrespective of how the model uncertainty influences the system's matrices. Moreover, the computational complexity of the proposed approach does not depend on the uncertainty/disturbance dimensions, and scales quadratically with the control horizon. The main result in this work is related to the analysis of the closed loop system under receding-horizon implementation of the scenario FHOCP, and essentially states that the devised control law guarantees constraint satisfaction at each step with some a priori assigned probability p, while the system's state reaches the target set either asymptotically, or in finite time with probability at least p. The proposed method may be a valid alternative when other existing techniques, either deterministic or stochastic, are not directly usable due to excessive conservatism or to numerical intractability caused by lack of convexity of the robust or chance-constrained optimization problem.
225 citations