Annals of the Institute of Statistical Mathematics最新文献

In the mean-median-mode triad of univariate centrality measures, the mode has been overlooked for estimating the center of symmetry in continuous and unimodal settings. This paper expands on the connection between kernel mode estimators and M-estimators for location, bridging the gap between the nonparametrics and robust statistics communities. The variance of modal estimators is studied in terms of a bandwidth parameter, establishing conditions for an optimal solution that outperforms the household sample mean. A purely nonparametric approach is adopted, modeling heavy-tailedness through regular variation. The results lead to an estimator proposal that includes a novel one-parameter family of kernels with compact support, offering extra robustness and efficiency. The effectiveness and versatility of the new method are demonstrated in a real-world case study and a thorough simulation study, comparing favorably to traditional and more competitive alternatives. Several myths about the mode are clarified along the way, reopening the quest for flexible and efficient nonparametric estimators.

We consider the nonparametric estimation of the value of a quadratic functional evaluated at the density of a strictly positive random variable X based on an iid. sample from an observation Y of X corrupted by an independent multiplicative error U. Quadratic functionals of the density covered are the ({mathbb{L}^{2} })-norm of the density and its derivatives or the survival function. We construct a fully data-driven estimator when the error density is known. The plug-in estimator is based on a density estimation combining the estimation of the Mellin transform of the Y density and a spectral cut-off regularized inversion of the Mellin transform of the error density. The main issue is the data-driven choice of the cut-off parameter using a Goldenshluger–Lepski-method. We discuss conditions under which the fully data-driven estimator attains oracle-rates up to logarithmic deteriorations. We compute convergence rates under classical smoothness assumptions and illustrate them by a simulation study.

This paper focuses on vector-valued composite functionals, which may be nonlinear in probability. Our goal is establishing central limit theorems for these functionals when employed by mixed estimators. Our study is relevant to the evaluation and comparison of risk in decision-making contexts and extends to functionals that arise in machine learning. A generalized family of composite risk functionals is presented, which encompasses coherent risk measures, including systemic risk. The paper makes two main contributions. First, we analyze vector-valued functionals and provide a framework for evaluating high-dimensional risks. This enables comparison of multiple risk measures and supports estimation and asymptotic analysis of systemic risk and its optimal value in decision-making. Second, we derive new central limit theorems for optimized composite functionals using mixed estimators, including empirical and smoothed types. We give verifiable conditions for central limit formulae and demonstrate their applicability to several risk measures.

A single-index regression model is considered, from which a robust and efficient inference about the model parameters is proposed. From a local linear approximation of the unknown regression function, such a function is estimated using the generalized signed-rank approach. Next considering the estimated function together with the estimating equation obtained from the generalized sign-rank objective function, a penalized empirical likelihood objective function of the index parameter is defined, from which its asymptotic distribution is established under mild regularity conditions. The performance of the proposed method is demonstrated via extensive Monte Carlo simulation experiments. The obtained simulation results are compared with those obtained from a normal approximation alternative and those obtained based on the least squares and least absolute deviations approaches. Finally, a real data example is given to illustrate the proposed methodology.

We consider model selection via (ell _0)-penalty for high-dimensional sparse quantile regression models. This procedure is almost equivalent to model selection via information criterion due to similarity in penalty. We deal with linear models, additive models, and varying coefficient models in a unified way and establish the model selection consistency results rigorously when the size of the relevant index set goes to infinity. The treatment of this situation is challenging and the theoretical novelty of our results is important because such information criteria are commonly used. We consider two different setups and propose tuning parameters in the (ell _0)-penalty. Besides, we propose a feasible algorithm for computation of our estimator and the numerical study results are presented.

This paper proposes a novel method to estimate the success probability of the binomial distribution. The proposed method employs the Cramer-von Mises type optimization which has been commonly used in estimating parameters of continuous distributions. Upon obtaining the estimator through the proposed method, its desirable properties, such as asymptotic distribution and robustness, are rigorously investigated. Simulation studies serve to demonstrate that the proposed method compares favorably with other well-celebrated methods, including the maximum likelihood method.