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Home-range estimators are commonly tested with simulated animal locational data in the laboratory before the estimators are used in practice. Although kernel density estimation (KDE) has performed well as a home-range estimator for simulated data, several recent studies have reported its poor performance when used with data collected in the field. This difference may be because KDE and other home-range estimators are generally tested with simulated point locations that follow known statistical distributions, such as bivariate normal mixtures, which may not represent well the space-use patterns of all wildlife species. We used simulated animal locational data of 5 point pattern shapes that represent a range of wildlife utilization distributions to test 4 methods of home-range estimation: 1) KDE with reference bandwidths, 2) KDE with least-squares cross-validation, 3) KDE with plug-in bandwidths, and 4) minimum convex polygon (MCP). For the point patterns we simulated, MCP tended to produce more accurate area estimates than KDE methods. However, MCP estimates were markedly unstable, with bias varying widely with both sample size and point pattern shape. The KDE methods performed best for concave distributions, which are similar to bivariate normal mixtures, but still overestimated home ranges by about 40–50% even in the best cases. For convex, linear, perforated, and disjoint point patterns, KDE methods overestimated home-range sizes by 50–300%, depending on sample size and method of bandwidth selection. These results indicate that KDE does not produce home-range estimates that are as accurate as the literature suggests, and we recommend exploring other techniques of home-range estimation.

We investigate the choice of the bandwidth for the regression discontinuity estimator. We focus on estimation by local linear regression, which was shown to have attractive properties (Porter, J. 2003, \"Estimation in the Regression Discontinuity Model\" (unpublished, Department of Economics, University of Wisconsin, Madison)). We derive the asymptotically optimal bandwidth under squared error loss. This optimal bandwidth depends on unknown functionals of the distribution of the data and we propose simple and consistent estimators for these functionals to obtain a fully data-driven bandwidth algorithm. We show that this bandwidth estimator is optimal according to the criterion of Li (1987, \"Asymptotic Optimality for C p , C L , Cross-validation and Generalized Cross-validation: Discrete Index Set\", Annals of Statistics, 15, 958–975), although it is not unique in the sense that alternative consistent estimators for the unknown functionals would lead to bandwidth estimators with the same optimality properties. We illustrate the proposed bandwidth, and the sensitivity to the choices made in our algorithm, by applying the methods to a data set previously analysed by Lee (2008, \"Randomized Experiments from Non-random Selection in U.S. House Elections\", Journal of Econometrics, 142, 675–697) as well as by conducting a small simulation study.

We propose a new bandwidth selection method for kernel estimators of spatial point process intensity functions. The method is based on an optimality criterion motivated by the Campbell formula applied to the reciprocal intensity function. The new method is fully nonparametric, does not require knowledge of higher-order moments, and is not restricted to a specific class of point process. Our approach is computationally straightforward and does not require numerical approximation of integrals.

We propose an adaptive bandwidth selector via cross validation for local M-estimators in locally stationary processes. We prove asymptotic optimality of the procedure under mild conditions on the underlying parameter curves. The results are applicable to a wide range of locally stationary processes such linear and nonlinear processes. A simulation study shows that the method works fairly well also in misspecified situations.

The authors study the problem of testing whether two populations have the same law by comparing kernel estimators of the two density functions. The proposed test statistic is based on a local empirical likelihood approach. They obtain the asymptotic distribution of the test statistic and propose a bootstrap approximation to calibrate the test. A simulation study is carried out in which the proposed method is compared with two competitors, and a procedure to select the bandwidth parameter is studied. The proposed test can be extended to more than two samples and to multivariate distributions. /// Les auteurs s'intéressent au problème de tester l'égalité des lois de deux populations, en comparant des estimateurs à noyaux de leurs densités. La statistique de test proposée est basée sur une approche de vraisemblance empirique locale. La distribution asymptotique de la statistique du test est obtenue et une approximation par bootstrap est proposée aux fins de calibration. Une étude de simulation est effectuée, dans laquelle la méthode proposée est comparée avec deux compétiteurs et une procédure de sélection du paramètre de lissage est étudiée. Le test proposé peut être généralisé à plus de deux échantillons et au cas de distributions multivariées.

We introduce a new fully non-parametric two-step adaptive bandwidth selection method for kernel estimators of spatial point process intensity functions based on the Campbell–Mecke formula and Abramson’s square root law. We present a simulation study to assess its performance relative to other adaptive and global bandwidth selectors, investigate the influence of the pilot estimator and apply the technique to two data sets: A pattern of trees and an earthquake catalogue.

This paper proposes a wind power probabilistic model (WPPM) using the reflection method and multi-kernel function kernel density estimation (KDE). With the increasing penetration of renewable energy sources (RESs) into power systems, several probabilistic approaches have been introduced to assess the impact of RESs on the power system. A probabilistic approach requires a wind power scenario (WPS), and the WPS is generated from the WPPM. Previously, WPPM was generated using a parametric density estimation, and it had limitations in reflecting the characteristics of wind power data (WPD) due to a boundary bias problem. The paper proposes a WPPM generated using the KDE, which is a non-parametric method. Additionally, the paper proposes a reflection method correcting for the boundary bias problem caused by the double-bounded characteristic of the WPD and the multi-kernel function KDE minimizing the effect of tied values. Six bandwidth selectors are used to calculate the bandwidth for the KDE, and one is selected by analyzing the correlation between the normalized WPD and the calculated bandwidth. The results were validated by generating WPPMs with WPDs in six regions of the Republic of Korea, and it was confirmed that the accuracy and goodness-of-fit are improved when the proposed method is used.

This paper develops a statistically principled approach to kernel density estimation on a network of lines, such as a road network. Existing heuristic techniques are reviewed, and their weaknesses are identified. The correct analogue of the Gaussian kernel is the 'heat kernel', the occupation density of Brownian motion on the network. The corresponding kernel estimator satisfies the classical time-dependent heat equation on the network. This 'diffusion estimator' has good statistical properties that follow from the heat equation. It is mathematically similar to an existing heuristic technique, in that both can be expressed as sums over paths in the network. However, the diffusion estimate is an infinite sum, which cannot be evaluated using existing algorithms. Instead, the diffusion estimate can be computed rapidly by numerically solving the time-dependent heat equation on the network. This also enables bandwidth selection using cross-validation. The diffusion estimate with automatically selected bandwidth is demonstrated on road accident data.

This paper proposes a robust methodology for displaying two-dimensional environmental contour lines based on measured ocean wave data at two offshore sites. For implementing the robust environmental contour lines methodology, we propose the use of bivariate kernel density estimation with smoothed cross-validation bandwidth selection. The environmental contours obtained by using the proposed robust methodology have been compared with those obtained by using the Gumbel copula transformation method and another recently published method, and the effectiveness and superiority of our proposed robust methodology have been clearly substantiated. The research results in this paper demonstrate that our proposed robust methodology can be utilized as an effective tool for predicting the long-term extreme dynamic responses of ocean engineering structures.

This paper studies local polynomial estimation of expectile regression. Expectiles and quantiles both provide a full characterization of a (conditional) distribution function, but have each their own merits and inconveniences. Local polynomial fitting as a smoothing technique has a major advantage of being simple, allowing for explicit expressions and henceforth advantages when doing inference theory. The aim of this paper is twofold: to study in detail the use of local polynomial fitting in the context of expectile regression and to contribute to the important issue of bandwidth selection, from theoretical and practical points of view. We discuss local polynomial expectile regression estimators and establish an asymptotic normality result for them. The finite-sample performance of the estimators, combined with various bandwidth selectors, is investigated in a simulation study. Some illustrations with real data examples are given.