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Earthquake source inversion, which estimates the heterogeneous slip distribution on fault from geophysical data, is a fundamental technique for estimating earthquake rupture process and obtaining information about the physics of fault rupture. Source inversion requires the spatial discretization of fault, which can be performed uniformly and non-uniformly. Uniform fault discretization is a conventional approach that requires smoothing and/or non-negative constraints of slips as prior information to obtain a stable and reliable solution; however, the combination of uniform discretization and these prior constraints may distort a source-inversion solution. As a non-uniform discretization approach, source inversion using a trans-dimensional inversion approach has recently attracted attention. To study the effect of fault discretization on geodetic source inversion, through the analysis of geodetic data on the 2015 Gorkha, Nepal, earthquake and synthetic tests, we investigated what kind of solution the conventional source inversion with uniform discretization and the trans-dimensional source inversion provide and what kind of uncertainty their solutions have. We found that the combination of uniform discretization and non-negative constraint led to excessively smooth solutions with poor data fit. Even without using the non-negative constraint, the conventional inversion with uniform discretization provided distorted and sometimes overfitted solutions, which could not be identified based on uncertainty information. In contrast, the trans-dimensional source inversion provided reasonable solutions composed only of meaningful slips, which were required to explain the data. We also found that uncertainty information depends on the source-inversion method; consequently, the evaluation of method-induced uncertainty is difficult. This suggests that we look at earthquake ruptures through the lens of source inversion with inherent method-dependent bias. [ABSTRACT FROM AUTHOR]

We consider the estimation of mean and covariance functions for longitudinal and sparse functional data by using the full quasi-likelihood coupling a modification of the local kernel smoothing method. The proposed estimators are shown to be consistent, asymptotically normal, and semiparametrically efficient in terms of their linear functionals. Their superiority to the competitors is further illustrated numerically through simulation studies. The method is applied to analyze AIDS study and atmospheric study. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

In this paper, a novel freeway traffic speed estimation method based on probe data is presented. In contrast to other traffic speed estimators, it only requires velocity data from probes and does not depend on any additional data inputs such as density or flow information. In the first step the method determines the three traffic phases free flow, synchronized flow, and Wide Moving Jam (WMJ) described by Kerner et al. in space and time. Subsequently, reported data is processed with respect to the prevailing traffic phase in order to estimate traffic velocities. This two-step approach allows incorporating empirical features of phase fronts into the estimation procedure. For instance, downstream fronts of WMJs always propagate upstream with approximately constant velocity, and downstream fronts of synchronized flow phases usually stick to bottlenecks. The second step assures the validity of measured velocities is limited to the extent of its assigned phase. Effectively, velocity information in space-time can be estimated more distinctively and the result is therefore more accurate even if the input data density is low. The accuracy of the proposed Phase-Based Smoothing Method (PSM) is evaluated using real floating car data collected during two traffic congestions on the German freeway A99 and compared to the performance of the Generalized Adaptive Smoothing Method (GASM) as well as a naive algorithm. The quantitative and qualitative results show that the PSM reconstructs the congestion pattern more accurately than the other two. A subsequent analysis of the computational efficiency and sensitivity demonstrates its practical suitability. [ABSTRACT FROM AUTHOR]

Tree-based methods similar to CART have recently been utilized for problems in which the main goal is to estimate some set of interest. It is often the case that the boundary of the true set is smooth in some sense, however tree-based estimates will not be smooth, as they will be a union of ‘boxes’. We propose a general methodology for smoothing such sets that allows for varying levels of smoothness on the boundary automatically. The method is similar to the idea underlying support vector machines, which is applying a computationally simple technique to data after a non-linear mapping to produce smooth estimates in the original space. In particular, we consider the problem of level-set estimation for regression functions and the dyadic tree-based method of Willett and Nowak [Minimax optimal level-set estimation, IEEE Trans. Image Process. 16 (2007), pp. 2965–2979]. [ABSTRACT FROM AUTHOR]

Abstract: Common simplifications of the bandwidth matrix cannot be applied to existing kernels for density estimation with compositional data. In this paper, kernel density estimation methods are modified on the basis of recent developments in compositional data analysis and bandwidth matrix selection theory. The isometric log-ratio normal kernel is used to define a new estimator in which the smoothing parameter is chosen from the most general class of bandwidth matrices on the basis of a recently proposed plug-in algorithm. Both simulated and real examples are presented in which the behaviour of our approach is illustrated, which shows the advantage of the new estimator over existing proposed methods. [Copyright &y& Elsevier]

Abstract: This Note proposes a procedure based on the cross-validation method to select the smoothing parameter of the conditional U-statistics. We state here that the obtained data-driven bandwidths are asymptotically optimal with respect to various criteria. Notice that by suitable choices of the U-statistic kernel, say φ, our results allow to deduce in a straightforward way the optimal smoothing parameter of various usual nonparametric estimates. [Copyright &y& Elsevier]

In this article, we propose a penalized likelihood method to estimate time-varying parameters in standard linear state space models. The time-varying parameter is modeled as a smoothing spline and then expressed as a state space model. The maximum likelihood method is used to estimate the smoothing parameter. The proposed method is assessed by a simulation study and applied to virological response data from an HIV-infected patient receiving antiretroviral treatment. [ABSTRACT FROM AUTHOR]

Two general classes of nonparametric kernel estimators of the hazard function are introduced, which include both a 1-parameter estimator and a more complex 3-parameter estimator. In addition, employing the idea of cross-validation, the authors present a data-based algorithm for smoothing parameter selection. The article compares the data-based 1- and 3-parameter estimators in a simulation experiment to the maximum likelihood estimator assuming the correct failure distribution and censoring mechanism. The 3-parameter estimator is found to perform well over a wide range of settings. On the average, the estimator recovers the shape of the underlying failure hazard and is competitive with the parametric estimator over a subset of the positive half line. Two examples illustrate possible uses of the nonparametric estimators. [ABSTRACT FROM AUTHOR]