Higher order approximations by a two-stage procedure for a negative exponential distribution

This paper deals with the problem of fixed-width confidence interval estimation of the location μ of a negative exponential distribution with unknown scale σ. Suppose we have information on the scale parameter σ such that σ>σ_L where σ_L(>0) is known to the experimenter from past experiences. We propose a two-stage procedure and provide higher order asymptotic expansions of the expected sample size and the coverage probability.     

Confidence intervals based on L-moments for quantiles of the GP and GEV distributions with application to market-opening asset prices data

In a ground-breaking paper published in 1990 by the Journal of the Royal Statistical Society, J.R.M. Hosking defined the L-moment of a random variable as an expectation of certain linear combinations of order statistics. L-moments are an alternative to conventional moments and recently they have been used often in inferential statistics. L-moments have several advantages over the conventional moments, including robustness to the the presence of outliers, which may lead to more accurate estimates in some cases as the characteristics of distributions. In this contribution, asymptotic theory and L-moments are used to derive confidence intervals of the population parameters and quantiles of the three-parametric generalized Pareto and extreme-value distributions. Computer simulations are performed to determine the performance of confidence intervals for the population quantiles based on L-moments and to compare them to those obtained by traditional estimation techniques. The results obtained show that they perform well in comparison to the moments and maximum likelihood methods when the interest is in higher quantiles, or even best. L-moments are especially recommended when the tail of the distribution is rather heavier and the sample size is small. The derived intervals are applied to real economic data, and specifically to market-opening asset prices.     

Normalization of the origin-shifted exponential distribution for control chart construction

This study demonstrates that a location parameter of an exponential distribution significantly influences normalization of the exponential. The Kullback–Leibler information number is shown to be an appropriate index for measuring data normality using a location parameter. Control charts based on probability limits and transformation are compared for known and estimated location parameters. The probabilities of type II error (β-risks) and average run length (ARL) without a location parameter indicate an ability to detect an out-of-control signal of an individual chart using a power transformation similar to using probability limits. The β-risks and ARL of control charts with an estimated location parameter deviate significantly from their theoretical values when a small sample size of n≤50 is used. Therefore, without taking into account of the existence of a location parameter, the control charts result in inaccurate detection of an out-of-control signal regardless of whether a power or natural logarithmic transformation is used. The effects of a location parameter should be eliminated before transformation. Two examples are presented to illustrate these findings.     

Semiparametric analysis for case-control studies: a partial smoothing spline approach

Case-control data are often used in medical-related applications, and most studies have applied parametric logistic regression to analyze such data. In this study, we investigated a semiparametric model for the analysis of case-control data by relaxing the linearity assumption of risk factors by using a partial smoothing spline model. A faster computation method for the model by extending the lower-dimensional approximation approach of Gu and Kim 4 Gu, C. and Kim, Y.-J. 2002. Penalized likelihood regression: General formulation and efficient approximation. Canad. J. Statist., 30: 619–628. [Crossref], [Web of Science ®] [Google Scholar] developed in penalized likelihood regression is considered to apply to case-control studies. Simulations were conducted to evaluate the performance of the method with selected smoothing parameters and to compare the method with existing methods. The method was applied to Korean gastric cancer case-control data to estimate the nonparametric probability function of age and regression parameters for other categorical risk factors simultaneously. The method could be used in preliminary studies to identify whether there is a flexible function form of risk factors in the semiparametric logistic regression analysis involving a large data set.     

A note on the equivariant estimation of an exponential scale using progressively censored data

We consider the problem of estimating the scale parameter θ$\theta$ of the shifted exponential distribution with unknown location based on a type II progressively censored sample. Under a large class of bowl-shaped loss functions, a smooth estimator, that dominates the minimum risk equivariant estimator of θ$\theta$, is proposed. A numerical study is performed and shows that the improved estimator yields significant risk reduction over the MRE.     

时变参数模型的最优滚动窗宽选择标准及应用

宏观经济领域中存在严重的结构突变性,模型估计量的优劣对估计样本规模是敏感的。本文针对时变参数模型,建立了滚动窗宽选择标准,通过最小化估计量的近似二次损失函数及最大化各子样本估计量间的曼哈顿距离选择窗宽大小,权衡了模型估计量的准确性和时变性两个相悖目标。蒙特卡罗模拟实验表明,本文所提出的方法在各种结构突变情形下均适用,能够应用于线性关系和非线性关系的时变参数模型中,且均具有稳健性。将该方法应用于我国金融网络的结构突变识别过程,显著改善了传统窗宽选择方法的结果。     

A two-phase approach to estimating time-varying parameters in the capital asset pricing model

Following the development of the economy and the diversification of investment, mutual funds are a popular investment tool nowadays. Choosing excellent targets from hundreds of mutual funds has become more and more crucial to investors. The capital asset pricing model (CAPM) has been widely used in the capital cost estimation and performance evaluation of mutual funds. In this study, we propose a new two-phase approach to estimating the time-varying parameters of CAPM. We implemented a simulation study to evaluate the efficiency of the proposed method and compared it with the commonly used state space and rolling regression methods. The results showed that the new method is more efficient in most scenarios. Meanwhile, the proposed approach is very practical and it is unnecessary to judge and adjust the estimating process for different situations. Finally, we applied the proposed method to equity mutual funds in the Taiwan stock market and reported the performances of two funds for demonstration.     

Automatic and asymptotically optimal data sharpening for nonparametric regression

In this article we consider data-sharpening methods for nonparametric regression. In particular modifications are made to existing methods in the following two directions. First, we introduce a new tuning parameter to control the extent to which the data are to be sharpened, so that the amount of sharpening is adaptive and can be tuned to best suit the data at hand. We call this new parameter the sharpening parameter. Second, we develop automatic methods for jointly choosing the value of this sharpening parameter as well as the values of other required smoothing parameters. These automatic parameter selection methods are shown to be asymptotically optimal in a well defined sense. Numerical experiments were also conducted to evaluate their finite-sample performances. To the best of our knowledge, there is no bandwidth selection method developed in the literature for sharpened nonparametric regression.     

Functional principal component analysis via regularized Gaussian basis expansions and its application to unbalanced data

This paper introduces regularized functional principal component analysis for multidimensional functional data sets, utilizing Gaussian basis functions. An essential point in a functional approach via basis expansions is the evaluation of the matrix for the integral of the product of any two bases (cross-product matrix). Advantages of the use of the Gaussian type of basis functions in the functional approach are that its cross-product matrix can be easily calculated, and it creates a much more flexible instrument for transforming each individual's observation into a functional form. The proposed method is applied to the analysis of three-dimensional (3D) protein structural data that can be referred to as unbalanced data. It is shown that our method extracts useful information from unbalanced data through the application. Numerical experiments are conducted to investigate the effectiveness of our method via Gaussian basis functions, compared to the method based on B-splines. On performing regularized functional principal component analysis with B-splines, we also derive the exact form of its cross-product matrix. The numerical results show that our methodology is superior to the method based on B-splines for unbalanced data.     

大规模定制产品柔性分析

提出了一种表达大规模定制产品及其设计参数定制难易程度的指标———柔性指数。基于公理化设计理论,建立了定制方程,导出了柔性指数的计算方法。提出了一种通过计算直接影响设计参数数量和间接影响设计参数数量来比较柔性指数的简便方法。