可持续发展的精确林业思想研究

在分析我国林业生产现状的基础上,介绍和评价了熵定律和生态学马克思主义及其揭示的全球性问题;基于可持续发展理念,研究了精确林业系统的系统性、集成性和组织性思想,最后分析了精确林业系统的支撑技术及其实施策略。     

A note on L1 consistent estimation

Let (??, ??) be a space with a σ-field, M = {P_s; s o} a family of probability measures on A, Θ arbitrary, X₁,…,X_n independently and identically distributed P random variables. Metrize Θ with the L₁ distance between measures, and assume identifiability. Minimum-distance estimators are constructed that relate rates of convergence with Vapnik-Cervonenkis exponents when M is “regular”. An alternative construction of estimates is offered via Kolmogorov's chain argument.     

A note on bias reduction in variable-kernel density estimates

It is well known that the inverse-square-root rule of Abramson (1982) for the bandwidth h of a variable-kernel density estimator achieves a reduction in bias from the fixed-bandwidth estimator, even when a nonnegative kernel is used. Without some form of “clipping” device similar to that of Abramson, the asymptotic bias can be much greater than O(h⁴) for target densities like the normal (Terrell and Scott 1992) or even compactly supported densities. However, Abramson used a nonsmooth clipping procedure intended for pointwise estimation. Instead, we propose a smoothly clipped estimator and establish a globally valid, uniformly convergent bias expansion for densities with uniformly continuous fourth derivatives. The main result extends Hall's (1990) formula (see also Terrell and Scott 1992) to several dimensions, and actually to a very general class of estimators. By allowing a clipping parameter to vary with the bandwidth, the usual O(h⁴) bias expression holds uniformly on any set where the target density is bounded away from zero.     

Nonparametric estimation of the entropy using a ranked set sample

This article is concerned with nonparametric estimation of the entropy in ranked set sampling. Theoretical properties of the proposed estimator are studied. The proposed estimator is compared with the rival estimator in simple random sampling. The applications of the proposed estimator to the mutual information estimation as well as estimation of the Kullback–Leibler divergence are provided. Several Monté-Carlo simulation studies are conducted to examine the performance of the estimator. The results are applied to the longleaf pine (Pinus palustris) trees and the body fat percentage datasets to illustrate applicability of theoretical results.     

Kernel‐based Generalized Cross‐validation in Non‐parametric Mixed‐effect Models

Abstract. Although generalized cross‐validation (GCV) has been frequently applied to select bandwidth when kernel methods are used to estimate non‐parametric mixed‐effect models in which non‐parametric mean functions are used to model covariate effects, and additive random effects are applied to account for overdispersion and correlation, the optimality of the GCV has not yet been explored. In this article, we construct a kernel estimator of the non‐parametric mean function. An equivalence between the kernel estimator and a weighted least square type estimator is provided, and the optimality of the GCV‐based bandwidth is investigated. The theoretical derivations also show that kernel‐based and spline‐based GCV give very similar asymptotic results. This provides us with a solid base to use kernel estimation for mixed‐effect models. Simulation studies are undertaken to investigate the empirical performance of the GCV. A real data example is analysed for illustration.     

Entropy-based model-free feature screening for ultrahigh-dimensional multiclass classification

Most feature screening methods for ultrahigh-dimensional classification explicitly or implicitly assume the covariates are continuous. However, in the practice, it is quite common that both categorical and continuous covariates appear in the data, and applicable feature screening method is very limited. To handle this non-trivial situation, we propose an entropy-based feature screening method, which is model free and provides a unified screening procedure for both categorical and continuous covariates. We establish the sure screening and ranking consistency properties of the proposed procedure. We investigate the finite sample performance of the proposed procedure by simulation studies and illustrate the method by a real data analysis.     

Entropic representation and estimation of diversity indices

This paper serves a twofold purpose. First, a unified perspective on diversity indices is introduced based on an entropic basis. It is shown that the class of all linear combinations of the entropic basis, referred to as the class of linear diversity indices, covers a wide range of diversity indices used in the literature. Second, a class of estimators for linear diversity indices is proposed and it is shown that these estimators have rapidly decaying biases and asymptotic normality.     

A new lifetime model with decreasing,increasing, bathtub-shaped,and upside-down bathtub-shaped hazard rate function

A new three-parameter distribution with decreasing, increasing, bathtub-shaped and upside-down bathtub-shaped hazard rate function is proposed. The new distribution encompasses some previously known distributions as special cases. Basic mathematical properties of the new distribution (including the moment-generating function, moments, order statistics properties, Rényi entropy and stress–strength parameter) are derived. Its parameters are estimated by the method of maximum likelihood. An application is illustrated using a real data set.     

Maximum-Entropy Prior Uncertainty and Correlation of Statistical Economic Data

Empirical estimates of source statistical economic data such as trade flows, greenhouse gas emissions, or employment figures are always subject to uncertainty (stemming from measurement errors or confidentiality) but information concerning that uncertainty is often missing. This article uses concepts from Bayesian inference and the maximum entropy principle to estimate the prior probability distribution, uncertainty, and correlations of source data when such information is not explicitly provided. In the absence of additional information, an isolated datum is described by a truncated Gaussian distribution, and if an uncertainty estimate is missing, its prior equals the best guess. When the sum of a set of disaggregate data is constrained to match an aggregate datum, it is possible to determine the prior correlations among disaggregate data. If aggregate uncertainty is missing, all prior correlations are positive. If aggregate uncertainty is available, prior correlations can be either all positive, all negative, or a mix of both. An empirical example is presented, which reports relative uncertainties and correlation priors for the County Business Patterns database. In this example, relative uncertainties range from 1% to 80% and 20% of data pairs exhibit correlations below ?0.9 or above 0.9. Supplementary materials for this article are available online.     

A statistical uncertainty principle for estimating the time of a discrete shift in the mean of a continuous time random process

The purpose of this article is to present a statistical uncertainty principle that can be used when localizing a single change in the mean of a band-limited stationary random process. The statistical model investigated is a continuous time process that experiences a shift in its mean. This continuous time process is presumed to be sampled using an ideal low-pass filter. The least squares estimate of the location of the change in mean is asymptotically Gaussian. The standard deviation of the least squares estimate of the location of the change-point provides a physical limit to the accuracy of the estimate of the time of the mean shift which cannot be bettered.