Multiple nonlinear regression of the Markovian arrival process for estimating the daily global solar radiation

Abstract

Solar radiation is a global ecological phenomenon that affects life everywhere. In this study, a new statistical method, called the Quartiles-Moment's method, is proposed to estimate the scale and shape parameters of the exponentiated Gumbel maximum distribution (EGMD). The Kolomogorov–Smirnov test and the percentiles of the dataset are thus used to fit the dataset of the daily global solar radiation and the corresponding daily maximum temperature with EGMD. Thence, multiple nonlinear regression of the daily global solar radiation and the corresponding daily maximum temperature are produced and compared with the real dataset accordingly.     

Estimation of the parameters of a regression model with a multivariate t error variable

This paper deals with a regression model for several vari¬ables under the assumption that the errors have a multivariate t-distribution. The parameters of the model, the regression parameters, as well as the scale parameters and the degress of freedom of the error variable are estimated and the estimation procedure is illustrated by a numerical example, Also, the prop¬erties of the estimators and tests for the regression parameters are discussed.     

L1 for the simple linear regression model

By modifying the direct method to solve the overdetermined linear system we are able to present an algorithm for L₁ estimation which appears to be superior computationally to any other known algorithm for the simple linear regression problem.     

Estimation of gene/haplotype frequencies in genetic marker systems based on phenotype data

Two equivalent methods (gene counting and maximum likelihood) for estimating gene frequencies in a general genetic marker system based on observed phenotype data are derived. Under the maximum likelihood approach, an expression is given for the estimated covariance matrix from which estimated standard errors of the estimators can be found. In addition, consideration is given to the problem of estimating gene frequencies when there are available several independent population data sets.     

The Design of Scoring Schemes for Surveys Using the Block Total Response Method

ABSTRACT

In this article we investigate the design of scoring schemes for surveys using the block total response method. This method was first proposed by Raghavarao and Federer (1979 Raghavarao , D. , Federer , W. T. ( 1979 ). Block total response as an alternative to the randomized response method in surveys . J. Roy. Statist. Soc. 41 ( 1 ): 40 – 45 . [CSA] [CROSSREF]  [Google Scholar]) to provide accurate estimates of the base rates of sensitive characteristics using balanced incomplete block designs. The scoring scheme used in Raghavarao and Federer (1979 Raghavarao , D. , Federer , W. T. ( 1979 ). Block total response as an alternative to the randomized response method in surveys . J. Roy. Statist. Soc. 41 ( 1 ): 40 – 45 . [CSA] [CROSSREF]  [Google Scholar]) did not guarantee anonymity of answers and so the possibility of improving on this basic scoring scheme is considered in this article.     

A Similarity Measure Based on Species Proportions

ABSTRACT

There are several indices for measuring the similarity of two populations, including the ratio of the number of shared species to the number of distinct species (Jaccard's index) and the conditional probability of observing a shared species (Smith et al., 1996 Smith , W. , Solow , A. R. , Preston , P. E. ( 1996 ). An estimator of species overlap using a modified beta-binomial model. Biometrics 52 : 1472 – 1477 . [CSA] [CROSSREF] [Crossref], [Web of Science ®] , [Google Scholar]). However, these indices only take into account the number of species and species proportions of shared species. In this article, we propose a new similarity index which includes the species proportions of both the shared and non shared species in each population, and also propose a Nonparametric Maximum Likelihood Estimator (NPMLE) for this index. Bootstrap and delta methods are used to evaluate the standard errors of the NPMLE. Based on a loss function, we also compare a class of nonparametric estimators for the proposed index in various situations.     

Measuring and Decomposing Productivity Change

Measuring productivity change with Malmquist indices has become common practice, because they are easily computed using nonparametric programming techniques and can be readily decomposed into technical and efficiency change. However, this approach is nonstochastic and requires a constant returns to scale assumption to construct the reference technology. We propose estimating productivity change using a stochastic input distance frontier, imposing no restrictions on returns to scale. We derive the analogous decomposition of productivity change and develop a generalized method of moments strategy in which outputs or inputs may be endogenous. We compare two methods in an application to electric utilities.     

基尼系数的区间估计及其应用

 本文给出了收入为离散分布的三种计算基尼系数的新方法。利用收入份额法导出了基尼系数协方差算法的离散形式,并因此产生了计算基尼系数的回归系数法。文章重点讨论了基尼系数进行区间估计的两种方法,这些方法也适用于集中度指数,因而它们在测度社会经济领域的不平等中具有着十分广泛的用途。实际应用表明,新算法有效地简化了对基尼系数区间估计的标准差估算。