A revised simplex algorithm for the absolute deviation curve fitting problem

The statistical properties of quasi-ranges in small samples from a gamma density are the objects of study in this paper.The methods of computing the "Coefficient MatrixnA(j,k), which plays a major role for computing moments and quantiles from such a density using high speed digital computers, are presented. Limited tables of central and non-central moments as well as tables of quantile values, are given. More extensive tables can be easily constructed by using the methods described here when the need arises. Also, a table of values for kurtosis and skewness is presented.     

An alternative algorithm of the empirical likelihood estimation for the parameter of a linear regression model

ABSTRACT

Empirical likelihood (EL) is a nonparametric method based on observations. EL method is defined as a constrained optimization problem. The solution of this constrained optimization problem is carried on using duality approach. In this study, we propose an alternative algorithm to solve this constrained optimization problem. The new algorithm is based on a newton-type algorithm for Lagrange multipliers for the constrained optimization problem. We provide a simulation study and a real data example to compare the performance of the proposed algorithm with the classical algorithm. Simulation and the real data results show that the performance of the proposed algorithm is comparable with the performance of the existing algorithm in terms of efficiencies and cpu-times.     

The best subset of parameters in min-max linear regression

These Fortran-77 subroutines provide building blocks for Generalized Cross-Validation (GCV) (Craven and Wahba, 1979) calculations in data analysis and data smoothing including ridge regression (Golub, Heath, and Wahba, 1979), thin plate smoothing splines (Wahba and Wendelberger, 1980), deconvolution (Wahba, 1982d), smoothing of generalized linear models (O'sullivan, Yandell and Raynor 1986, Green 1984 and Green and Yandell 1985), and ill-posed problems (Nychka et al., 1984, O'sullivan and Wahba, 1985). We present some of the types of problems for which GCV is a useful method of choosing a smoothing or regularization parameter and we describe the structure of the subroutines.Ridge Regression: A familiar example of a smoothing parameter is the ridge parameter X in the ridge regression problem which we write.     

Improved best linear unbiased estimators for the simple linear regression model using double ranked set sampling schemes

ABSTRACT

In this paper, we consider the best linear unbiased estimators (BLUEs) based on double ranked set sampling (DRSS) and ordered DRSS (ODRSS) schemes for the simple linear regression model with replicated observations. We assume three symmetric distributions for the random error term, i.e., normal, Laplace and some scale contaminated normal distributions. The proposed BLUEs under DRSS (BLUEs-DRSS) and ODRSS (BLUEs-ODRSS) are compared with the BLUEs based on ordered simple random sampling (OSRS), ranked set sampling (RSS), and ordered RSS (ORSS) schemes. These estimators are compared in terms of relative efficiency (RE), RE of determinant (RED), and RE of trace (RET). It is found that the BLUEs-ODRSS are uniformly better than the BLUEs based on OSRS, RSS, ORSS, and DRSS schemes. We also compare the estimators based on imperfect RSS (IRSS) schemes. It is worth mentioning here that the BLUEs under ordered imperfect DRSS (OIDRSS) are better than their counterparts based on IRSS, ordered IRSS (OIRSS), and imperfect DRSS (IDRSS) methods. Moreover, for sensitivity analysis of the BLUEs, we calculate REs and REDs of the BLUEs under the assumption of normality when in fact the parent distribution follows a non normal symmetric distribution. It turns out that even under violation of normality assumptions, BLUEs of the intercept and the slope parameters are found to be unbiased with equal REs under each sampling scheme. It is also observed that the BLUEs under ODRSS are more efficient than the existing BLUEs.     

Slope modified confidence bands for a simple linear regression model

Considerable attention has been directed in the statistical literature towards the construction of confidence bands for a simple linear regression model. These confidence bands allow the experimenter to make inferences about the model over a particular region of interest. However, in practice an experimenter will usually first check the significance of the regression line before proceeding with any further inferences such as those provided by the confidence bands. From a theoretical point of view, this raises the question of what the conditional confidence level of the confidence bands might be, and from a practical point of view it is unsatisfactory if the confidence bands contain lines that are inconsistent with the directional decision on the slope. In this paper it is shown how confidence bands can be modified to alleviate these two problems.     

Stability of linear programming solutions using regression coefficients

In at least one important application of stochastic linear programming (Lavaca-Tres Palacios Estuary:A Study of the Influence of Freshwater Inflows, 1980)constraint parameters are simultaneously estimated using multiple regression with historic data for the values of the decision variables and the right hand side of the constraint function. In this circumstance, the question immediately arises "How stable is the linear programming (LP) solution with regard to regression issues such as sample size, magnitude of the error variance, centroids of the decision variables, apd collinearity?" This paper reports a simulation designed to assess the stability of the LP solution and to compare the effectiveness of ridge as an alternative to ordinary least squares (OLS) regression. For the given scenario, the LP solution is consistently "biased." The amount of bias is exacerbated by small samples, large error variances, and collinearity among observations of the decision variables. The best regression criterion is a function not only of collinearity, but also of the magnitude of the error variance and the sum of the means of the decision variables relative to the right hand side of the stochastic constraint

In the application that motivated this research, the LP solutions were recommended fresh water inflows from Lake Texana into the estuaries of the Gulf of Mexico. The stochastic constraint estimates commercial fish harvest as a function of seasonal fresh water inflow. The historic data set used to estimate parameters of the constraint comprised rainfall data and fish harvest data prior to the construction of the Lake Texana dam, of necessity a small sample with collinear seasonal rainfall. It is not the authors' intent to solve this application, but rather to investigate through a simpler simulated systemwhether or not regression estimates in similar circumstances might introduce a systematic and predictable bias. The answer to this latter question is a qualified Yes!.     

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.     

The bivariate linear model: a geometris approach

The geometric approach to the general linear model is in accessible to the majorityof statistics students be cause the computations require matrix algebra.This article presents the geometric approach for the special case of the bivariate linear model,for which the only tool require dis the in ner product.The geometric approach is introduced by showing the dual2-dimensional and5-dimensional representations of several bivariate samples x of size5.The assumptions of the bivariate model are stated geometrically,and the distributions of the regression coefficient sare derived.Theanalysis of variance(ANOVA)right triangle is pictured and the sides of the triang leare associated with their corresponding entries in the ANOVA table.     

An inspection procedure for radio frequency repeaters using a multiple linear regression method

Abstract

A radio frequency (RF) repeater is a wireless electronic device that transmits signals from a base transceiver station to a mobile station. When inspecting RF repeaters, various items are required to be tested to ensure their quality. In this paper, we propose a systematic procedure for the inspection by using a multiple linear regression method. The basic idea is to predict the inspection result without real inspection. In particular, a multicollinearity problem is considered in the regression analysis. Two case studies are conducted for validating the proposed method with an RF repeater production company in Korea.     

An algorithm for the minimum sum of weighted absolute errors regression

We propose an algorithm to estimate the unknown constants in a multiple linear regression model under the minimum sum of weighted absolute errors (MSWAE). The proposed algorithm, a generalization of an earlier algorithm, is compared to a bounded variable algorithm. Some somputational experience is reported.     

A simple method for fitting a linear model involving variance components

This paper describes combined maximum likelihood estimation of treatment effects and variance components in a linear mixed model. Estimates are obtained by a simple modification of iterative weighted least squares. The method is illustrated using plating efficiencies of Solanum and Lycopersicon species.     

An efficient algorithm for Harrison-Stevens forecasting using the multi-process multivariate dynamic linear model

This paper develops a computationally efficient algorithm for Harrison-Stevens forecasting in a multivariate time series which has correlated errors. The algorithm uses the observation vector one component at a time on the multiprocess multivariate dynamic linear model. This gives a computationally efficient, robust, quick adapting forecasting method for non stationary multivariate time series.     

Best linear unbiased estimators of parameters of a simple linear regression model based on ordered ranked set samples

As an alternative to an estimation based on a simple random sample (BLUE-SRS) for the simple linear regression model, Moussa-Hamouda and Leone [E. Moussa-Hamouda and F.C. Leone, The o-blue estimators for complete and censored samples in linear regression, Technometrics, 16 (3) (1974), pp. 441–446.] discussed the best linear unbiased estimators based on order statistics (BLUE-OS), and showed that BLUE-OS is more efficient than BLUE-SRS for normal data. Using the ranked set sampling, Barreto and Barnett [M.C.M. Barreto and V. Barnett, Best linear unbiased estimators for the simple linear regression model using ranked set sampling. Environ. Ecoll. Stat. 6 (1999), pp. 119–133.] derived the best linear unbiased estimators (BLUE-RSS) for simple linear regression model and showed that BLUE-RSS is more efficient for the estimation of the regression parameters (intercept and slope) than BLUE-SRS for normal data, but not so for the estimation of the residual standard deviation in the case of small sample size. As an alternative to RSS, this paper considers the best linear unbiased estimators based on order statistics from a ranked set sample (BLUE-ORSS) and shows that BLUE-ORSS is uniformly more efficient than BLUE-RSS and BLUE-OS for normal data.     

A mixed-integer programming approach to the clustering problem

A mixed-integer programing formulation for clustering is proposed, one that encompasses a wider range of objectives--and side conditions--than standard clustering approaches. The flexibility of the formulation is demonstrated in diagrams of sample problems and solutions. Preliminary computational tests in a practical setting confirm the usefulness of the formulation.     

A special purpose linear programming algorithm for obtaining least absolute value estimators in a linear model with dummy variables

Dummy (0, 1) variables are frequently used in statistical modeling to represent the effect of certain extraneous factors. This paper presents a special purpose linear programming algorithm for obtaining least-absolute-value estimators in a linear model with dummy variables. The algorithm employs a compact basis inverse procedure and incorporates the advanced basis exchange techniques available in specialized algorithms for the general linear least-absolute-value problem. Computational results with a computer code version of the algorithm are given.     

A unified approach to estimating association measures via a joint generalized linear model for paired binary data

Paired binary data arise frequently in biomedical studies with unique features of their own. For instance, in clinical studies involving pairs such as ears, eyes etc., often both the intrapair association parameter and the event probability are of interest. In addition, we may be interested in the dependence of the association parameter on certain covariates as well. Although various methods have been proposed to model paired binary data, this paper proposes a unified approach for estimating various intrapair measures under a generalized linear model with simultaneous maximum likelihood estimates of the marginal probabilities and the intrapair association. The methods are illustrated with a twin morbidity study.     

Detection of jump location curve in spatial linear regression model with two-dimensional threshold

In the context of spatial linear regression, we discuss detection of jump location curve treated as threshold curve which cannot be expressed by independent variables but indirectly determines two specific model forms. The threshold curve in this paper is described by a straight line with two location variables, longitude and latitude, and can be estimated by maximizing the coefficient difference between two one-sided linear regression models. Theoretical results show that the estimator is consistent. Our method performs well by numerical studies.     

A non-iterative posterior sampling algorithm for Laplace linear regression model

In this article, a non-iterative sampling algorithm is developed to obtain an independently and identically distributed samples approximately from the posterior distribution of parameters in Laplace linear regression model. By combining the inverse Bayes formulae, sampling/importance resampling, and expectation maximum algorithm, the algorithm eliminates the diagnosis of convergence in the iterative Gibbs sampling and the samples generated from it can be used for inferences immediately. Simulations are conducted to illustrate the robustness and effectiveness of the algorithm. Finally, real data are studied to show the usefulness of the proposed methodology.     

An iterative self-weighting procedure for fitting straight lines to heteroscedastic data

An iterative, self-weighting procedure is presented for the fitting of straight lines to data with heteroscedastic error-variances in the response variable. The error-variances are assumed to be unknown, even relative to each other. The procedure is compared with the “resistant line” method advocated by Emerson and Hoaglin [Emerson and Hoaglin, 1983], using extensive Monte-Carlo calculations. The proposed method is simple and easily automated, and gives parameter-estimates with smaller variance (higher efficiency) than those resulting from the resistant line technique. A BASIC program to perform the self-weighting fit is given in an appendix     

Interval-valued data regression using partial linear model

Semi-parametric modelling of interval-valued data is of great practical importance, as exampled by applications in economic and financial data analysis. We propose a flexible semi-parametric modelling of interval-valued data by integrating the partial linear regression model based on the Center & Range method, and investigate its estimation procedure. Furthermore, we introduce a test statistic that allows one to decide between a parametric linear model and a semi-parametric model, and approximate its null asymptotic distribution based on wild Bootstrap method to obtain the critical values. Extensive simulation studies are carried out to evaluate the performance of the proposed methodology and the new test. Moreover, several empirical data sets are analysed to document its practical applications.