Estimation Of Linear Regression Parameters Research Articles

Subgroup detection based on partially linear additive individualized model with missing data in response

Based on partially linear additive individualized model, a fusion-penalized inverse probability weighted least squares method is proposed to detect the subgroup for missing data in response. Firstly, the B-spline technique is used to approximate the unknown additive individualized functions and then an inverse probability weighted quadratic loss function is established with fusion penalty on the difference of subject-wise B-spline coefficients. Secondly, minimization of such quadratic loss function leads to the estimation of linear regression parameters and individualized B spline coefficients. With a proper tuning parameter, some differences in penalty term are shrunk into zero and thus the corresponding subjects will be clustered into the same subgroup. Thirdly, a clustering method is developed to automatically determine the subgroup membership for the subjects with missing data. Fourthly, large sample properties of resulting estimates are given under some regular conditions. Finally, numerical studies are presented to illustrate the performance of the proposed subgroup detection method.

A Perturbation Method to Optimize the Parameters of Autoregressive Conditional Heteroscedasticity Model

As a linear regression parameter estimation method, the least square method plays an indispensable role in the parameter estimation of ARCH model. Although the least squares solution can minimize the sum of the squared errors, it will cause uneven distribution of errors, that is, some fitting errors are too large, and some fitting errors are too small, which will lead to overfitting. In response to this situation, we adopt a novel perturbation method to solve this problem. The specific theoretical derivation of the perturbation method is given in this paper. It takes parameters estimated by the least squares method as its initial iteration value. The maximum fitting error will decrease continuously from a series of iterations to final convergence. Furthermore, based on the perturbation method, this paper finds a condition that makes the ARCH model satisfy the non-negative limit of parameters. The experimental process uses real stock fund’s fluctuation data for fitting analysis and prediction. The experimental results show that the perturbation method can achieve the expected effect in the parameter estimation of the ARCH model, it can also effectively ensure that the fitting errors fluctuate within the controllable range when predicting the price fluctuation of stock funds in the future.

Comparative Study on Variable Selection Approaches in Establishment of Remote Sensing Model for Forest Biomass Estimation

In the field of quantitative remote sensing of forest biomass, a prominent phenomenon is the increasing number of explanatory variables. Then how to effectively select explanatory variables has become an important issue. Linear regression model is one of the commonly used remote sensing models. In the process of establishing the linear regression model, a vital step is to select explanatory variables. Focusing on variable selection and model stability, this paper conducts a comparative study on the performance of eight linear regression parameter estimation methods (Stepwise Regression Method (SR), Criterions Based on The Bayes Method (BIC), Criterions Based on The Bayes Method (AIC), Criterions Based on Prediction Error (Cp), Least Absolute Shrinkage and Selection Operator (Lasso), Adaptive Lasso, Smoothly Clipped Absolute Deviation (SCAD), Non-negative garrote (NNG)) in the subtropical forest biomass remote sensing model development. For the purpose of comparison, OLS and RR, are commonly used as methods with no variable selection ability, and are also compared and discussed. The performance of five aspects are evaluated in this paper: (i) Determination coefficient, prediction error, model error, etc., (ii) significance test about the difference between determination coefficients, (iii) parameter stability, (iv) variable selection stability and (v) variable selection ability of the methods. All the results are obtained through a five ten-fold CV. Some evaluation indexes are calculated with or without degrees of freedom. The results show that BIC performs best in comprehensive evaluation, while NNG, Cp and AIC perform poorly as a whole. Other methods show a great difference in the performance on each index. SR has a strong capability in variable selection, although it is poor in commonly used indexes. The short-wave infrared band and the texture features derived from it are selected most frequently by various methods, indicating that these variables play an important role in forest biomass estimation. Some of the conclusions in this paper are likely to change as the study object changes. The ultimate goal of this paper is to introduce various model establishment methods with variable selection capability, so that we can have more choices when establishing similar models, and we can know how to select the most appropriate and effective method for specific problems.

Perbandingan Metode Koreksi Pencaran pada Data Hasil Alat Pemantau Kadar Glukosa Darah Non-Invasif

Scatter correction is one of the methods in data preprocessing that aim at eliminating the physical properties of the spectrum and reducing the variance between samples. The most commonly methods of scatter correction used are the Multiplicative Scatter Correction (MSC) and Standard Normal Variate (SNV) methods. The MSC method corrects the spectrum by utilizing the results of simple linear regression parameter estimation. The SNV method performs spectral correction with the median and standard deviation. Another alternative method of scatter correction is the Orthogonal Scatter Correction (OSC) applying the principle of orthogonality. The methods used in this research were MSC, SNV, and OSC methods in order to correct the result data of non-invasive blood glucose measuring instrument. The result of this research showed that the time domain spectrum data and intensity had different amount so that the summarized data was needed. Furthermore, this research found that the OSC method with the five series of statistics gained a good correction result compared to the other methods. The OSC method produced a smaller average value of the variance than the other methods.

Estimasi Parameter Regresi Linear Menggunakan Regresi Kuantil

Regression analysis is a statistical analysis method for estimating the relationship between dependent variables (Y) and one or more independent variables (X) . As the purpose of this study is to theoretically examine the quantile regression method in estimating linear regression parameters. In regression analysis usually the method used to estimate parameters is the least square method with assumptions that must be met that normal assumption, homoskedasticity, no autocorrelation and non multicollinearity. Basically the least square method is sensitive to the assumptions of deviations in the data, so that the estimations results will be lees good if the assumptions are not fulfilled. Therefore, to overcome the limitations of the least square method developed a quantile regression method for estimating linear regression parameters. Based on the result of research that has been done shows that the estimation of linear regression parameters using the quantile regression method is obtained by minimazing the absolute number of errors through the simplex algorithm.

ALGUMAS CONSIDERAÇÕES PRÁTICAS SOBRE A PRECISÃO DOS ESIMADORES DE MÍNIMOS QUADRADOS E MÁXIMA VEROSSIMILHANÇA PARA OS PARÂMETROS DE REGRESSÃO LINEAR NORMAL

In this paper, we discuss some practical considerations on the use of different methods for the estimation of linear regression parameters and their impact on the obtained inferences. In practice, it is common to use some existing statistical software to obtain the least squares estimators (MSE) for the regression parameters and consider a non-biased estimator for the variance based on the residual squared sum of the residuals. Alternatively, we discuss the use of the maximum likelihood estimator (MLE) for the variance of the error (an unbiased estimator, but with smaller squared error) which may lead to different conclusions in terms of inferences. Two numerical examples are presented to illustrate the proposed method.

Relationships Between Depression, Anxiety, and Pain in a Group of University Music Students

There is emerging interest in studying the incidence of music-related injuries and problems among students. The current study drew on a data set collected from 287 music majors and minors at a large US midwestern university school of music in order to determine if correlations existed between anxiety and/or depression and the reported presence of physical pain, and to understand the nature of any such relationships. Physical pain symptoms were scored on a scale of 0 (none) to 10 (excruciating) and summed across 21 body regions. Depression and anxiety symptoms were scored as none (0), mild (1), moderate (2), or severe (3), and each summed across either 13 symptoms for depression or 8 symptoms for anxiety. The potential linear relationship among these variables was evaluated using F-tests (as part of ANOVAs) and linear regression parameter estimation techniques. The explanatory value of these relationships was evaluated using R² values. Results indicate a clear positive linear relationship between both depression and pain, and anxiety and pain. However, the presence of depression and/or anxiety symptoms was insufficient to explain variability in pain scores of these participants.

On the Robust Parameter Estimation for Linear Model with Autocorrelated Errors

The Ordinary Least Squares (OLS) estimates become inefficient in the presence of autocorrelation problems. The Cochrane-Orcutt Prais-Winsten iterative method (COPW) is the most commonly used remedial measure to remedy this problem. However, this procedure is based on the OLS estimates, which is not robust and therefore easily affected by high leverage points (outliers in the x-direction). In this paper, we propose a robust Cochrane-Orcutt Prais-Winsten iterative method (RCOPW) based on MM estimator for the estimation of linear regression parameters in the situation where autocorrelated errors come together with the existence of outliers. The performance of this RCOPW is investigated extensively by real example and Monte Carlo simulation. The results of the study indicate that the RCOPW is more consistent and efficient as compared to COPW. It also provides a better one step ahead forecast than the OLS and COPW regression models.

Regularization of Linear Regression Problems

The study considers robust estimation of linear regression parameters by the regularization method, the pseudoinverse method, and the Bayesian method allowing for correlations and errors in the data. Regularizing algorithms are constructed and their relationship with pseudoinversion, the Bayesian approach, and BLUE is investigated.

Automated Well Test Analysis Using Robust (LAV) Nonlinear Parameter Estimation

ABSTRACT Most of the nonlinear regression algorithms used in automated well test interpretation perform a minimization of an objective function formed by the sum of the squares of the differences between the data and the model values. This constitutes a typical nonlinear least-squares problem. One of the drawbacks of the least squares approach is that it is significantly affected by outliers, which are data points that can be considered bad observations. This study proposes a robust algorithm that uses the LAV (Least Absolute Value) as the criterion for the minimization. One of the greatest advantages of the LAV approach is that it provides a smooth transition between full acceptance and total rejection of a given observation, providing a systematic way of rejecting outliers by automatically assigning them less weight in the objective function. The technique described in this work is based on the expansion of the model function in a Taylor series up to the first order terms. This poses a new problem which is solved iteratively after being transformed into a multiple linear regression parameter estimation. The procedure becomes therefore a sequence of multiple linear regression problems, which are solved using the least absolute value criterion. Because the equations of condition are solved, instead of the so-called normal equations (as in several implementations of nonlinear parameter estimation algorithms discussed in the literature), the method avoids unnecessary exacerbation of the ill-conditioning of the design matrix. Examples where no large errors in the data are present show that this method produces results similar to least-squares minimization. When outliers are introduced into the observations, however, the present technique yields much better estimates. Also, the least absolute value approach works better than the least-squares criterion when estimating parameters whose sensitivity is small, as in the case of obtaining the storativity ratio and the interporosity flow coefficient in a naturally fractured reservoir with double-porosity behavior.

An iterative algorithm for consistent and unbiased estimation of linear regression parameters when there are errors in both the x and y variables

Abstract This paper describes an algorithm for unbiased estimation of regression parameters dealing with data in which the variances of both the x and y variables are different and heterocedastic. The procedure gives consistent and unbiased estimations of parameters, as well as the elements of the variance-covariance matrix.

Bootstrapping the generalized least-squares estimator in colored Gaussian noise with unknown covariance parameters

It is demonstrated that in problems involving the estimation of linear regression parameters in colored Gaussian noise, the simple least-squares estimator can be significantly suboptimal. When the noise covariance function can be described as a known function of a finite number of unknown nonrandom parameters, it is possible to take advantage of this information to improve upon the least-squares estimator by an appropriate bootstrapping technique. Two examples are given, and comments that may lead to other examples are presented.

Comparison of Least Squares and Minimum Variance Estimates of Regression Parameters

The basic problem dealt with here is the estimation of linear regression parameters from a set of observations obscured by correlated noise. Two well-known solutions to this problem are minimum variance (or Markov, MV) and least squares (LS) estimation. Although MV is, by definition, an optimal method, LS possesses two distinct advantages which cause it to be used more frequently in practice: (1) computational simplicity and (2) the fact that it does not require knowledge of the correlation matrix of the noise, which in many cases is actually unknown. Therefore, a comparative study of these two methods to determine how much is lost by use of LS instead of MV is of value. In this connection, Grenander and Rosenblatt [1] have derived important asymptotic properties of LS and MV estimates when the noise is a stationary random process. The approach here is somewhat different from theirs, and no assumption regarding stationarity is made. The essence of this analysis is to re-formulate LS and MV in terms of the spectrum of the noise correlation matrix. This procedure offers some new insights into the nature of LS and MV and the differences between them. For example, it shows when they yield the same result and when LS performs worst compared with MV. It also exhibits the roles played by the maximum and minimum eigenvalues of the noise correlation matrix in setting bounds on the covariance matrices of both LS and MV estimates.