Some statistical problems in the presence of an outlier when sampling from truncation parameter densities

Summary In this paper we derive some recurrence relations for moments of order statistics of a random sample from a truncation parameter density when one of the observations is an outlier. We also derive uniform minimum variance unbiased estimator of a parametric function.     

超超临界参数机组的发展和热力分析

文章介绍了超超临界参数技术的发展历史和现状,对超超临界参数机组的热力参数和效率进行了分析。     

Minimax estimation under convex loss when the parameter interval is bounded

In the present paper families of truncated distributions with a Lebesgue density forx=(x ₁,...,x _n ) ε ℝ ⁿ are considered, wheref ₀:ℝ → (0, ∞) is a known continuous function andC _n (ϑ) denotes a normalization constant. The unknown truncation parameterϑ which is assumed to belong to a bounded parameter intervalΘ=[0,d] is to be estimated under a convex loss function. It is studied whether a two point prior and a corresponding Bayes estimator form a saddle point when the parameter interval is sufficiently small.     

Nonparametric estimation of distribution functions

Summary Using Silverman and Young’s (1987) idea of rescaling a rescaled smoothed empirical distribution function is defined and investigated when the smoothing parameter depends on the data. The rescaled smoothed estimator is shown to be often better than the commonly used ordinary smoothed estimator.     

Asymptotics and smoothing parameter selection for penalized spline regression with various loss functions

Penalized splines are used in various types of regression analyses, including non‐parametric quantile, robust and the usual mean regression. In this paper, we focus on the penalized spline estimator with general convex loss functions. By specifying the loss function, we can obtain the mean estimator, quantile estimator and robust estimator. We will first study the asymptotic properties of penalized splines. Specifically, we will show the asymptotic bias and variance as well as the asymptotic normality of the estimator. Next, we will discuss smoothing parameter selection for the minimization of the mean integrated squares error. The new smoothing parameter can be expressed uniquely using the asymptotic bias and variance of the penalized spline estimator. To validate the new smoothing parameter selection method, we will provide a simulation. The simulation results show that the consistency of the estimator with the proposed smoothing parameter selection method can be confirmed and that the proposed estimator has better behavior than the estimator with generalized approximate cross‐validation. A real data example is also addressed.     

自适应粒子群优化算法在混沌系统参数估计中的应用

惯性权重w的变化会影响粒子群优化算法的搜索能力,本文针对基本粒子群算法不能适应复杂的非线性优化搜索过程的问题,在其基础上提出了一种动态改变惯性权的自适应粒子群算法。该自适应算法引入了h来衡量算法的进化速度,引入s来衡量算法的粒子聚集度,并将其作为函数w的变量,使w与算法的运行状态相关,从而使算法具有动态自适应性。最后,本文引入了两个经典的测试函数对该PSO算法进行测试,结果表明该算法明显优于基本PSO算法。     

Optimal rules and robust Bayes estimation of a Gamma scale parameter

For estimating an unknown scale parameter of Gamma distribution, we introduce the use of an asymmetric scale invariant loss function reflecting precision of estimation. This loss belongs to the class of precautionary loss functions. The problem of estimation of scale parameter of a Gamma distribution arises in several theoretical and applied problems. Explicit form of risk-unbiased, minimum risk scale-invariant, Bayes, generalized Bayes and minimax estimators are derived. We characterized the admissibility and inadmissibility of a class of linear estimators of the form $cX\,{+}\,d$ , when $X\sim \varGamma (\alpha ,\eta )$ . In the context of Bayesian statistical inference any statistical problem should be treated under a given loss function by specifying a prior distribution over the parameter space. Hence, arbitrariness of a unique prior distribution is a critical and permanent question. To overcome with this issue, we consider robust Bayesian analysis and deal with Gamma minimax, conditional Gamma minimax, the stable and characterize posterior regret Gamma minimax estimation of the unknown scale parameter under the asymmetric scale invariant loss function in detail.     

Tuning parameter selection in penalized generalized linear models for discrete data

In recent years, we have seen an increased interest in the penalized likelihood methodology, which can be efficiently used for shrinkage and selection purposes. This strategy can also result in unbiased, sparse, and continuous estimators. However, the performance of the penalized likelihood approach depends on the proper choice of the regularization parameter. Therefore, it is important to select it appropriately. To this end, the generalized cross‐validation method is commonly used. In this article, we firstly propose new estimates of the norm of the error in the generalized linear models framework, through the use of Kantorovich inequalities. Then these estimates are used in order to derive a tuning parameter selector in penalized generalized linear models. The proposed method does not depend on resampling as the standard methods and therefore results in a considerable gain in computational time while producing improved results. A thorough simulation study is conducted to support theoretical findings; and a comparison of the penalized methods with the L₁, the hard thresholding, and the smoothly clipped absolute deviation penalty functions is performed, for the cases of penalized Logistic regression and penalized Poisson regression. A real data example is being analyzed, and a discussion follows. © 2014 The Authors. Statistica Neerlandica © 2014 VVS.     

协同学在多级库存系统分析中的应用初探

讨论了协同学的基本概念;特别讨论了绝热消去方法(伺服原理)在协同学方法论中的作用、地位和意义;并运用协同学处理问题的一般步骤分析了多级库存系统,得到了序参量方程和势函数。     

Large time-varying parameter VARs

In this paper, we develop methods for estimation and forecasting in large time-varying parameter vector autoregressive models (TVP-VARs). To overcome computational constraints, we draw on ideas from the dynamic model averaging literature which achieve reductions in the computational burden through the use forgetting factors. We then extend the TVP-VAR so that its dimension can change over time. For instance, we can have a large TVP-VAR as the forecasting model at some points in time, but a smaller TVP-VAR at others. A final extension lies in the development of a new method for estimating, in a time-varying manner, the parameter(s) of the shrinkage priors commonly-used with large VARs. These extensions are operationalized through the use of forgetting factor methods and are, thus, computationally simple. An empirical application involving forecasting inflation, real output and interest rates demonstrates the feasibility and usefulness of our approach.     

A heuristic method for parameter selection in LS-SVM: Application to time series prediction

Least Squares Support Vector Machines (LS-SVM) are the state of the art in kernel methods for regression. These models have been successfully applied for time series modelling and prediction. A critical issue for the performance of these models is the choice of the kernel parameters and the hyperparameters which define the function to be minimized. In this paper a heuristic method for setting both the σ parameter of the Gaussian kernel and the regularization hyperparameter based on information extracted from the time series to be modelled is presented and evaluated.     

Sequential point estimation of the powers of a normal scale parameter

We consider the sequential point estimation problem of the powers of a normal scale parameter σ^r with r≠ 0 when the loss function is squared error plus linear cost. It is shown that the regret due to using our fully sequential procedure in ignorance of σ is asymptotically minimized for estimating σ⁻². We also propose a bias-corrected procedure to reduce the risk and show that the larger the distance between r and −2 is, the more effective our bias-corrected procedure is. Received August 2000     

A Bayesian test of a parameter shift and an application

The paper formulates a Bayesian test of a parameter shift in two regressions whose error terms have multivariate student-t distributions with zero location vectors. The test is derived first with diffuse and then with natural conjugate prior probability density functions. The Bayesian test is then applied to examine whether or not a parameter shift in expenditure on vitamins and other nutritional supplements can be observed since 1969 in Japan. The empirical test implies that there is a sudden parameter shift in 1971 due to a consumer protection movement.     

Estimation strategies for the regression coefficient parameter matrix in multivariate multiple regression

We consider improved estimation strategies for the parameter matrix in multivariate multiple regression under a general and natural linear constraint. In the context of two competing models where one model includes all predictors and the other restricts variable coefficients to a candidate linear subspace based on prior information, there is a need of combining two estimation techniques in an optimal way. In this scenario, we suggest some shrinkage estimators for the targeted parameter matrix. Also, we examine the relative performances of the suggested estimators in the direction of the subspace and candidate subspace restricted type estimators. We develop a large sample theory for the estimators including derivation of asymptotic bias and asymptotic distributional risk of the suggested estimators. Furthermore, we conduct Monte Carlo simulation studies to appraise the relative performance of the suggested estimators with the classical estimators. The methods are also applied on a real data set for illustrative purposes.     

Admissibility of generalized Bayes estimators in an one parameter nonregular family

Consider an estimation problem under squared error loss in an one parameter nonregular family of distributions with the lower endpoint of the support depending on an unknown parameter. Using Karlin's ([3]) method, sufficient conditions are given for generalized Bayes estimators to be admissible for estimating an arbitrary nonnegative, differentiable, monotone parametric function. The results are then applied to the case when both endpoints of the support of the distribution depend on the parameter . Finally, some examples are subsequently given.Research supported by a grant from Hanyang University, 1989.     

Minimax estimators for a bounded location parameter

Summary Recently, Bischoff and Fieger (1992) considered the classical problem of estimating a bounded normal mean when the loss is thep-th power of the error. They proved that forp>-2 a two point prior is least favourable in case the parameter interval is small enough. In the present paper it is shown that this result remains valid forp>1. Moreover, the normal family is generalized to location parameter families. Finally, it is proved that no two point prior is least favourable for absolute error loss, i.e., forp=1.     

The sampling distribution of forecasts from a first-order autoregression

Previous work on characterising the distribution of forecast errors in time series models by statistics such as the asymptotic mean square error has assumed that observations used in estimating parameters are statistically independent of those used to construct the forecasts themselves. This assumption is quite unrealistic in practical situations and the present paper is intended to tackle the question of how the statistical dependence between the parameter estimates and the final period observations used to generate forecasts affects the sampling distribution of the forecast errors. We concentrate on the first-order autoregression and, for this model, show that the conditional distribution of forecast errors given the final period observation is skewed towards the origin and that this skewness is accentuated in the majority of cases by the statistical dependence between the parameter estimates and the final period observation.     

浅谈电流、电压互感器的选择对保护测量回路的影响

随着电力基础设施建设的日趋完善,以及电力技术研究和应用的不断加强,我国现已基本构建了具有安全性、稳定性特征的电力供应和传输系统,为社会经济的发展及人们的日常生活提供了稳定的电力能源供应。在电力系统的构建与管理中,电流、电压互感器对于实现继电保护功能具有重大的意义,其二次参数和测量表计的特性与继电保护相符合。电磁式模式是传统继电保护装置的基础形态,其主要特点是模拟量输入、精度低、耗电量大,因此配置的电流和电压互感器模拟式容量大。随着电子信息技术的高速发展和在电力系统中的扩大化应用,继电保护装置也相应普及于电力系统中,同时采用计算机控制。这些微机控制的数字式设备功能强大、反应速度快、测量精度高、电压和电流的回路能耗小。电流、电压互感器在其供电负荷特性发生变化的过程中,其二次参数并没有发生相应的改变,这就导致了参数的不协调。文章对电流、电压互感器参数的选择对测量回路的影响进行了简要分析,以供同行参考。     

基于模型分析的液压伺服系统性能参数预测

为了提高液压伺服系统的控制精度,文章对液压伺服系统中的一些非线性参数进行了预测与估计。参数估计之前,首先对目标液压工作系统进行了建模与参数化描述,抽取了其控制和工作模型,计算并推导了模型中主要的液压参数直接的数学关系,如液压受力分析、受力传递函数、噪声信号过滤函数等。在此基础上,采用最小二乘估计算法对液压伺服系统中的非线性参数进行预测,给出了详细的参数分析过程和预测参数推导过程,建立了主要参数的估计计算公式。最后,对所估计的非线性参数进行了仿真和测试。结果表明,文章所选择的参数预测结果与实际的运行结果基本吻合,预测算法参数估计误差小。     

Admissible and minimax estimators of 363-1363-1363-1in the gamma distribution with truncated parameter space

In this paper we consider asmissible and minimax estimation of the parameter in the gamma distribution with truncated parameter space. We give a necessary and sufficient condition for minimaxity (Theorem 1) and obtain the classes of new minimax and asmissible estimators. The results of the paper can be applied to estimation of parameters in the normal, lognormal, Pareto, generalized gamma, generalized Laplace and other distributions.