A Bayesian approach to non-parametric monotone function estimation

Summary.  The paper proposes two Bayesian approaches to non-parametric monotone function estimation. The first approach uses a hierarchical Bayes framework and a characterization of smooth monotone functions given by Ramsay that allows unconstrained estimation. The second approach uses a Bayesian regression spline model of Smith and Kohn with a mixture distribution of constrained normal distributions as the prior for the regression coefficients to ensure the monotonicity of the resulting function estimate. The small sample properties of the two function estimators across a range of functions are provided via simulation and compared with existing methods. Asymptotic results are also given that show that Bayesian methods provide consistent function estimators for a large class of smooth functions. An example is provided involving economic demand functions that illustrates the application of the constrained regression spline estimator in the context of a multiple-regression model where two functions are constrained to be monotone.     

Optimality Of Some Two-Stage Sampling Methods

Two-stage sampling plans in which the estimator is computed from the second sample only, and has a guaranteed precision irrespective of the parameter value, are considered. We prove the following optimality property for existing strategies in binomial and Poisson populations: there exists no other

strategy, of the same form, that guarantees the same precision, without increasing the expected sample size for some parameter valucs. The method of proof is illustrnted by proving a similar result for normal populations     

A note on nonlinear regression for the autoregressive moving average with non-hd errors

Estimation by nonlinear regression of the parameters for the stationary and invertible autoregressive moving average (ARMA) model with mixing or martingale difference errors is considered. Simple proofs of consistency and asymptotic normality for the nonlinear least squares estimator are given by exploiting results from nonlinear estimation theory and mixing and mixingale theory.     

The Statistics of Simulating Chaos

When simulating a dynamical system, the computation is actually of a spatially discretized system, because finite machine arithmetic replaces continuum state space. For chaotic dynamical systems, the discretized simulations often have collapsing effects, to a fixed point or to short cycles. Statistical properties of these phenomena can be modelled with random mappings with an absorbing centre. The model gives results which are very much in line with computational experiments. The effects are discussed with special reference to the family of mappings f (x)=1-|1-2x|,x [0,1],1,<,,<,. Computer experiments show close agreement with predictions of the model.     

Non‐parametric Threshold Estimation for Models with Stochastic Diffusion Coefficient and Jumps

Abstract. We consider a stochastic process driven by diffusions and jumps. Given a discrete record of observations, we devise a technique for identifying the times when jumps larger than a suitably defined threshold occurred. This allows us to determine a consistent non‐parametric estimator of the integrated volatility when the infinite activity jump component is Lévy. Jump size estimation and central limit results are proved in the case of finite activity jumps. Some simulations illustrate the applicability of the methodology in finite samples and its superiority on the multipower variations especially when it is not possible to use high frequency data.     

自旋电子在钙钛矿锰氧化物中输运性质研究

本文对国内外研究钙钛矿锰氧化物磁电性质及CMR效应的现状进行了分析,指出有必要研究自旋电子在钙铁矿锰氧化物中的输运性质与材料的磁性以及外加磁场的关系,并对研究方法进行了探讨。     

On Bayesian estimators in multistage binomial designs

A new class of Bayesian estimators for a proportion in multistage binomial designs is considered. Priors belong to the beta-J distribution family, which is derived from the Fisher information associated with the design. The transposition of the beta parameters of the Haldane and the uniform priors in fixed binomial experiments into the beta-J distribution yields bias-corrected versions of these priors in multistage designs. We show that the estimator of the posterior mean based on the corrected Haldane prior and the estimator of the posterior mode based on the corrected uniform prior have good frequentist properties. An easy-to-use approximation of the estimator of the posterior mode is provided. The new Bayesian estimators are compared to Whitehead's and the uniformly minimum variance estimators through several multistage designs. Last, the bias of the estimator of the posterior mode is derived for a particular case.     

Serial dependence and regression of Poisson INARMA models

Time series of counts occur in many fields of practice, with the Poisson distribution as a popular choice for the marginal process distribution. A great variety of serial dependence structures of stationary count processes can be modelled by the INARMA family. In this article, we propose a new approach to the INMA(q) family in general, including previously known results as special cases. In the particular case of Poisson marginals, we will derive new results concerning regression properties and the serial dependence structure of INAR(1) and INMA(q) models. Finally, we present explicit expressions for the distribution of jumps in such processes.     

蜘蛛丝的结构与力学性能

本文主要介绍了蜘蛛丝的形成和力学性能特征，分析了其结构与力学性能间的关系。