scholarly journals Some remarks on a pair of seemingly unrelated regression models

2019 ◽  
Vol 17 (1) ◽  
pp. 979-989 ◽  
Author(s):  
Jian Hou ◽  
Yong Zhao
Keyword(s):  
Linear Regression ◽  
Regression Models ◽  
Sufficient Conditions ◽  
Seemingly Unrelated Regression ◽  
Regression Equations ◽  
Linear Regression Models ◽  
Unknown Parameters ◽  
Unrelated Regression ◽  
Best Linear Unbiased ◽  
Best Linear Unbiased Estimators

Abstract Linear regression models are foundation of current statistical theory and have been a prominent object of study in statistical data analysis and inference. A special class of linear regression models is called the seemingly unrelated regression models (SURMs) which allow correlated observations between different regression equations. In this article, we present a general approach to SURMs under some general assumptions, including establishing closed-form expressions of the best linear unbiased predictors (BLUPs) and the best linear unbiased estimators (BLUEs) of all unknown parameters in the models, establishing necessary and sufficient conditions for a family of equalities of the predictors and estimators under the single models and the combined model to hold. Some fundamental and valuable properties of the BLUPs and BLUEs under the SURM are also presented.

scholarly journals QML Estimators in Linear Regression Models with Functional Coefficient Autoregressive Processes

2010 ◽  
Vol 2010 ◽  
pp. 1-30 ◽  
Author(s):  
Hongchang Hu
Keyword(s):  
Maximum Likelihood ◽  
Linear Regression ◽  
Regression Models ◽  
Asymptotic Properties ◽  
Asymptotic Distributions ◽  
Autoregressive Processes ◽  
Linear Regression Models ◽  
Unknown Parameters ◽  
Quasi Maximum Likelihood ◽  
Functional Coefficient

This paper studies a linear regression model, whose errors are functional coefficient autoregressive processes. Firstly, the quasi-maximum likelihood (QML) estimators of some unknown parameters are given. Secondly, under general conditions, the asymptotic properties (existence, consistency, and asymptotic distributions) of the QML estimators are investigated. These results extend those of Maller (2003), White (1959), Brockwell and Davis (1987), and so on. Lastly, the validity and feasibility of the method are illuminated by a simulation example and a real example.

scholarly journals Regression models for estimating chick hatchling weight from some egg geometry traits

2018 ◽  
Vol 34 (3) ◽  
pp. 323-334
Author(s):  
Nadya Mincheva ◽  
Mitko Lalev ◽  
Magdalena Oblakova ◽  
Pavlina Hristakieva
Keyword(s):  
Linear Regression ◽  
Surface Area ◽  
Regression Models ◽  
Linear Models ◽  
Geometric Mean ◽  
Coefficient Of Determination ◽  
Regression Equations ◽  
Linear Regression Models ◽  
Egg Weight ◽  
Mean Diameter

The prediction of chicks? weight before hatching is an important element of selection, aimed at improving the uniformity rate and productivity of birds. With this regards, our goal was to develop and evaluate optimum models for similar prediction in two White Plymouth Rock chickens lines - line L and line K on the basis of the incubation egg weight and egg geometry characteristics - egg maximum breadth (B), egg length (L), geometric mean diameter (Dg), egg volume (V), egg surface area (S). A total of 280 eggs (140 from each line) laid by 40-weekold hens were randomly selected. Mean arithmetic values, standard deviations and coefficients of variation of studied parameters were determined for each line. Correlation coefficients between the weight of hatchlings and predictors were the highest for egg weight, geometric mean diameter, volume and surface area of eggs (r=0.731-0.779 for line L; r=0.802-0.819 for line ?). Nine linear regression models were developed and their accuracy evaluated. The regression equations of hatchlings? weight vs egg length had the lowest coefficient of determination (0.175 for line K and 0.291 for line L), but when egg length and breadth entered the model together, its value increased significantly up to 0.541 and 0.665 for lines L and K, respectively. The weight of day-old chicks from line L could be predicted with higher accuracy with a model involving egg surface area apart egg weight (ChW=0.513EW+0.282S - 10.345; R2=0.620). In line ? a more accurate prognosis was attained by adding egg breadth as an additional predictor to the weight in the model (ChW=0.587EW+0.566? - 19.853; R2=0.692). The study demonstrated that multiple linear regression models were more precise that single linear models.

Prediction in Two­Equation Linear Regression Models

2005 ◽  
Vol 57 (3-4) ◽  
pp. 195-208
Author(s):  
Amitava Dey ◽  
V. K. Sharma ◽  
Himadri Ghosh
Keyword(s):  
Time Series ◽  
Linear Regression ◽  
Linear Regression Model ◽  
Regression Models ◽  
Time Series Data ◽  
Generalized Least Squares ◽  
Series Data ◽  
Linear Regression Models ◽  
Error Terms ◽  
Best Linear Unbiased

In regression models using time series data, the errors are generally correlated. The sample residuals contain useful information for predicting post­sample observations. This information, which is generally ignored, has been exploited here in deriving the best linear unbiased predictors in a 2­equation linear regression model. The gain in efficiency of the proposed predictors over the usual generalized least ­ squares predictors has been obtained and the particular case when error terms in the two equations follow AR(l) process has also been disscussed.

scholarly journals On best linear unbiased estimation and prediction under a constrained linear random-effects model

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Bo Jiang ◽  
Yongge Tian
Keyword(s):  
Random Effects ◽  
Optimization Problems ◽  
Sufficient Conditions ◽  
Covariance Matrices ◽  
Unbiased Estimation ◽  
Random Effects Model ◽  
Unknown Parameters ◽  
Best Linear Unbiased ◽  
Best Linear Unbiased Estimators ◽  
Linear Restrictions

<p style='text-indent:20px;'>This paper is concerned with solving some fundamental estimation, prediction, and inference problems on a linear random-effects model with its parameter vector satisfying certain exact linear restrictions. Our work includes deriving analytical formulas for calculating the best linear unbiased predictors (BLUPs) and the best linear unbiased estimators (BLUEs) of all unknown parameters in the model by way of solving certain constrained quadratic matrix optimization problems, characterizing various mathematical and statistical properties of the predictors and estimators, establishing various fundamental rank and inertia formulas associated with the covariance matrices of predictors and estimators, and presenting necessary and sufficient conditions for several equalities and inequalities of covariance matrices of the predictors and estimators to hold.</p>

FAKTOR DETERMINAN PENYALURAN KREDIT BANK PERSERO

2018 ◽  
Vol 23 (1) ◽  
pp. 60-71
Author(s):  
Wigiyanti Masodah
Keyword(s):  
Interest Rate ◽  
Linear Regression ◽  
Interest Rates ◽  
Regression Models ◽  
Linear Regression Models ◽  
Negative Impacts ◽  
Main Activity ◽  
The Impact ◽  
The Given ◽  
Multiple Linear Regression Models

Offering credit is the main activity of a Bank. There are some considerations when a bank offers credit, that includes Interest Rates, Inflation, and NPL. This study aims to find out the impact of Variable Interest Rates, Inflation variables and NPL variables on credit disbursed. The object in this study is state-owned banks. The method of analysis in this study uses multiple linear regression models. The results of the study have shown that Interest Rates and NPL gave some negative impacts on the given credit. Meanwhile, Inflation variable does not have a significant effect on credit given. Keywords: Interest Rate, Inflation, NPL, offered Credit.

Linear Regression Models for Interval-Valued Data using Log-transformation

2020 ◽  
Author(s):  
Nykolas Mayko Maia Barbosa ◽  
João Paulo Pordeus Gomes ◽  
César Lincoln Cavalcante Mattos ◽  
Diêgo Farias Oliveira
Keyword(s):  
Linear Regression ◽  
Regression Models ◽  
Linear Regression Models ◽  
Log Transformation ◽  
Interval Valued

THE PREDICTIVE CONTENT OF DISAGGREGATED NORMAL INCOME: An Empirical Study in the JSX

2003 ◽  
Vol 5 (3) ◽  
pp. 363 ◽  
Author(s):  
Slamet Sugiri
Keyword(s):  
Linear Regression ◽  
Regression Models ◽  
Stock Exchange ◽  
Manufacturing Firms ◽  
Single Step ◽  
Model Parameters ◽  
Linear Regression Models ◽  
Operating Income ◽  
Predictive Content ◽  
Multiple Step

The main objective of this study is to examine a hypothesis that the predictive content of normal income disaggregated into operating income and nonoperating income outperforms that of aggregated normal income in predicting future cash flow. To test the hypothesis, linear regression models are developed. The model parameters are estimated based on fifty-five manufacturing firms listed in the Jakarta Stock Exchange (JSX) up to the end of 1997.This study finds that empirical evidence supports the hypothesis. This evidence supports arguments that, in reporting income from continuing operations, multiple-step approach is preferred to single-step one.

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