The non-identifiability of the competing risks model requires researchers to work with restrictions on the model to obtain informative results. We present a new identifiability solution based on an exclusion restriction. Many areas of applied research use methods that rely on exclusion restrcitions. It appears natural to also use them for the identifiability of competing risks models. By imposing the exclusion restriction couple with an Archimedean copula, we are able to avoid any parametric restriction on the marginal distributions. We introduce a semiparametric estimation approach for the nonparametric marginals and the parametric copula. Our simulation results demonstrate the usefulness of the suggested model, as the degree of risk dependence can be estimated without parametric restrictions on the marginal distributions.
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Two-stage weighted least squares estimator of multivariate discrete-valued observation-driven models
In this work a general semi-parametric multivariate model where the first two conditional moments are assumed to be multivariate time series is introduced. The focus of the estimation is the conditional mean parameter vector for discrete-valued distributions. Quasi-Maximum Likelihood Estimators (QMLEs) based on the linear exponential family are typically employed for such estimation problems when the true multivariate conditional probability distribution is unknown or too complex. Although QMLEs provide consistent estimates they may be inefficient. In this paper novel two-stage Multivariate Weighted Least Square Estimators (MWLSEs) are introduced which enjoy the same consistency property as the QMLEs but can provide improved efficiency with suitable choice of the covariance matrix of the observations. The proposed method allows for a more accurate estimation of model parameters in particular for count and categorical data when maximum likelihood estimation is unfeasible. Moreover, consistency and asymptotic normality of MWLSEs are derived. The estimation performance of QMLEs and MWLSEs is compared through simulation experiments and a real data application, showing superior accuracy of the proposed methodology.
We observe a large variety of robots in terms of their bodies, sensors, and actuators. Given the commonalities in the skill sets, teaching each skill to each different robot independently is inefficient and not scalable when the large variety in the robotic landscape is considered. If we can learn the correspondences between the sensorimotor spaces of different robots, we can expect a skill that is learned in one robot can be more directly and easily transferred to the other robots. In this paper, we propose a method to learn correspondences between robots that have significant differences in their morphologies: a fixed-based manipulator robot with joint control and a differential drive mobile robot. For this, both robots are first given demonstrations that achieve the same tasks. A common latent representation is formed while learning the corresponding policies. After this initial learning stage, the observation of a new task execution by one robot becomes sufficient to generate a latent space representation pertaining to the other robot to achieve the same task. We verified our system in a set of experiments where the correspondence between two simulated robots is learned (1) when the robots need to follow the same paths to achieve the same task, (2) when the robots need to follow different trajectories to achieve the same task, and (3) when complexities of the required sensorimotor trajectories are different for the robots considered. We also provide a proof-of-the-concept realization of correspondence learning between a real manipulator robot and a simulated mobile robot.
A new mechanical model on noncircular shallow tunnelling considering initial stress field is proposed in this paper by constraining far-field ground surface to eliminate displacement singularity at infinity, and the originally unbalanced tunnel excavation problem in existing solutions is turned to an equilibrium one of mixed boundaries. By applying analytic continuation, the mixed boundaries are transformed to a homogenerous Riemann-Hilbert problem, which is subsequently solved via an efficient and accurate iterative method with boundary conditions of static equilibrium, displacement single-valuedness, and traction along tunnel periphery. The Lanczos filtering technique is used in the final stress and displacement solution to reduce the Gibbs phenomena caused by the constrained far-field ground surface for more accurte results. Several numerical cases are conducted to intensively verify the proposed solution by examining boundary conditions and comparing with existing solutions, and all the results are in good agreements. Then more numerical cases are conducted to investigate the stress and deformation distribution along ground surface and tunnel periphery, and several engineering advices are given. Further discussions on the defects of the proposed solution are also conducted for objectivity.
We study how to construct a stochastic process on a finite interval with given `roughness' and finite joint moments of marginal distributions. We first extend Ciesielski's isomorphism along a general sequence of partitions, and provide a characterization of H\"older regularity of a function in terms of its Schauder coefficients. Using this characterization we provide a better (pathwise) estimator of H\"older exponent. As an additional application, we construct fake (fractional) Brownian motions with some path properties and finite moments of marginal distributions same as (fractional) Brownian motions. These belong to non-Gaussian families of stochastic processes which are statistically difficult to distinguish from real (fractional) Brownian motions.
Rational function approximations provide a simple but flexible alternative to polynomial approximation, allowing one to capture complex non-linearities without oscillatory artifacts. However, there have been few attempts to use rational functions on noisy data due to the likelihood of creating spurious singularities. To avoid the creation of singularities, we use Bernstein polynomials and appropriate conditions on their coefficients to force the denominator to be strictly positive. While this reduces the range of rational polynomials that can be expressed, it keeps all the benefits of rational functions while maintaining the robustness of polynomial approximation in noisy data scenarios. Our numerical experiments on noisy data show that existing rational approximation methods continually produce spurious poles inside the approximation domain. This contrasts our method, which cannot create poles in the approximation domain and provides better fits than a polynomial approximation and even penalized splines on functions with multiple variables. Moreover, guaranteeing pole-free in an interval is critical for estimating non-constant coefficients when numerically solving differential equations using spectral methods. This provides a compact representation of the original differential equation, allowing numeric solvers to achieve high accuracy quickly, as seen in our experiments.
Whether class labels in a given data set correspond to meaningful clusters is crucial for the evaluation of clustering algorithms using real-world data sets. This property can be quantified by separability measures. A review of the existing literature shows that neither classification-based complexity measures nor cluster validity indices (CVIs) adequately incorporate the central aspects of separability for density-based clustering: between-class separation and within-class connectedness. A newly developed measure (density cluster separability index, DCSI) aims to quantify these two characteristics and can also be used as a CVI. Extensive experiments on synthetic data indicate that DCSI correlates strongly with the performance of DBSCAN measured via the adjusted rand index (ARI) but lacks robustness when it comes to multi-class data sets with overlapping classes that are ill-suited for density-based hard clustering. Detailed evaluation on frequently used real-world data sets shows that DCSI can correctly identify touching or overlapping classes that do not form meaningful clusters.
We develop randomized matrix-free algorithms for estimating partial traces. Our algorithm improves on the typicality-based approach used in [T. Chen and Y-C. Cheng, Numerical computation of the equilibrium-reduced density matrix for strongly coupled open quantum systems, J. Chem. Phys. 157, 064106 (2022)] by deflating important subspaces (e.g. corresponding to the low-energy eigenstates) explicitly. This results in a significant variance reduction for matrices with quickly decaying singular values. We then apply our algorithm to study the thermodynamics of several Heisenberg spin systems, particularly the entanglement spectrum and ergotropy.
The distribution-free chain ladder of Mack justified the use of the chain ladder predictor and enabled Mack to derive an estimator of conditional mean squared error of prediction for the chain ladder predictor. Classical insurance loss models, i.e. of compound Poisson type, are not consistent with Mack's distribution-free chain ladder. However, for a sequence of compound Poisson loss models indexed by exposure (e.g. number of contracts), we show that the chain ladder predictor and Mack's estimator of conditional mean squared error of prediction can be derived by considering large exposure asymptotics. Hence, quantifying chain ladder prediction uncertainty can be done with Mack's estimator without relying on the validity of the model assumptions of the distribution-free chain ladder.
Covariance matrices of random vectors contain information that is crucial for modelling. Certain structures and patterns of the covariances (or correlations) may be used to justify parametric models, e.g., autoregressive models. Until now, there have been only few approaches for testing such covariance structures systematically and in a unified way. In the present paper, we propose such a unified testing procedure, and we will exemplify the approach with a large variety of covariance structure models. This includes common structures such as diagonal matrices, Toeplitz matrices, and compound symmetry but also the more involved autoregressive matrices. We propose hypothesis tests for these structures, and we use bootstrap techniques for better small-sample approximation. The structures of the proposed tests invite for adaptations to other covariance patterns by choosing the hypothesis matrix appropriately. We prove their correctness for large sample sizes. The proposed methods require only weak assumptions. With the help of a simulation study, we assess the small sample properties of the tests. We also analyze a real data set to illustrate the application of the procedure.
We establish precise structural and risk equivalences between subsampling and ridge regularization for ensemble ridge estimators. Specifically, we prove that linear and quadratic functionals of subsample ridge estimators, when fitted with different ridge regularization levels $\lambda$ and subsample aspect ratios $\psi$, are asymptotically equivalent along specific paths in the $(\lambda,\psi)$-plane (where $\psi$ is the ratio of the feature dimension to the subsample size). Our results only require bounded moment assumptions on feature and response distributions and allow for arbitrary joint distributions. Furthermore, we provide a data-dependent method to determine the equivalent paths of $(\lambda,\psi)$. An indirect implication of our equivalences is that optimally tuned ridge regression exhibits a monotonic prediction risk in the data aspect ratio. This resolves a recent open problem raised by Nakkiran et al. for general data distributions under proportional asymptotics, assuming a mild regularity condition that maintains regression hardness through linearized signal-to-noise ratios.
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