Robust Statistical Procedures in Problems of Linear Regression with Special Reference to Quantitative Bio-Assays, I

1971 ◽  
Vol 39 (1) ◽  
pp. 21 ◽  
Author(s):  
Pranab Kumar Sen
Keyword(s):  
Linear Regression ◽  
Special Reference ◽  
Statistical Procedures

A robust random coefficient regression representation of the chain-ladder method

2021 ◽  
pp. 1-32
Author(s):  
Ioannis Badounas ◽  
Apostolos Bozikas ◽  
Georgios Pitselis
Keyword(s):  
Linear Regression ◽  
Linear Regression Model ◽  
Random Coefficients ◽  
Regression Coefficients ◽  
Varying Coefficients ◽  
Statistical Procedures ◽  
Chain Ladder Method ◽  
Loss Reserving ◽  
Random Coefficient Regression ◽  
Chain Ladder

Abstract It is well known that the presence of outliers can mis-estimate (underestimate or overestimate) the overall reserve in the chain-ladder method, when we consider a linear regression model, based on the assumption that the coefficients are fixed and identical from one observation to another. By relaxing the usual regression assumptions and applying a regression with randomly varying coefficients, we have a similar phenomenon, i.e., mis-estimation of the overall reserves. The lack of robustness of loss reserving regression with random coefficients on incremental payment estimators leads to the development of this paper, aiming to apply robust statistical procedures to the loss reserving estimation when regression coefficients are random. Numerical results of the proposed method are illustrated and compared with the results that were obtained by linear regression with fixed coefficients.

scholarly journals Identifying atypical change at the individual level from childhood to adolescence

2018 ◽  
Author(s):  
Eduardo Estrada
Keyword(s):  
Linear Regression ◽  
Longitudinal Data ◽  
Statistical Model ◽  
Verbal Ability ◽  
Individual Change ◽  
Important Goal ◽  
Individual Level ◽  
Statistical Procedures ◽  
Potential Applications ◽  
The Individual

Identifying change at the individual level is an important goal for researchers, educators, and clinicians. We present a set of statistical procedures for identifying individuals who depart from a normative change. Using Latent Change Scores models (LCS), we illustrate how the Individual Likelihood computed from a statistical model for change (IL) and from an alternative unrestricted model (ILsat) can be used to identify atypical trajectories in situations with several measurement occasions. Using LCS and linear regression, we also show how the observed and latent change residuals can be used to identify atypical individual change between 2 measurement occasions. We apply these methods to a measure of general verbal ability (from WISC–R), from a large sample of individuals assessed every 2 years from Grade 1 to 9. We demonstrate the efficiency of these techniques, illustrate their use to identify individual change in longitudinal data, and discuss potential applications in developmental research.

Prelude

2019 ◽  
pp. 1-4
Author(s):  
M. D. Edge
Keyword(s):  
Probability Theory ◽  
Linear Regression ◽  
Programming Language ◽  
Statistical Estimation ◽  
Statistical Technique ◽  
Mathematical Approach ◽  
Simple Linear Regression ◽  
Statistical Procedures ◽  
Statistical Programming ◽  
Analyze Data

There are two traditional ways to learn statistics. One way is to pass over the mathematical underpinnings and focus on developing relatively shallow knowledge about a wide variety of statistical procedures. Another is to spend years learning the mathematics necessary for traditional mathematical approaches to statistics. For many people who need to analyze data, neither of these paths is sufficient. The shallow-but-wide approach fails to provide students with the foundation that allows for confidence and creativity in analyzing modern datasets, and many researchers—though possibly motivated to learn math—do not have the background to start immediately on a traditional mathematical approach. This book exists to help researchers jump between tracks, providing motivated students whose knowledge of mathematics may be incomplete or rusty with a serious introduction to statistics that allows further study from more mathematical sources. This is done by focusing on a single statistical technique that is fundamental to statistical practice—simple linear regression—and supplementing the exposition with ample simulations conducted in the statistical programming language R. The first half of the book focuses on preliminaries, including the use of R and probability theory, whereas the second half covers statistical estimation and inference from semiparametric, parametric, and Bayesian perspectives.

TESTING ALGORITHMS AND PROGRAMS OF MULTIVARIATE STATISTICAL PROCEDURES—NECESSARY ASSUMPTION OF BUILDING EXPERT SYSTEMS

1989 ◽  
Vol 03 (01) ◽  
pp. 121-133 ◽  
Author(s):  
ENE-MARGIT TIIT
Keyword(s):  
Regression Analysis ◽  
Linear Regression ◽  
Expert Systems ◽  
Linear Regression Analysis ◽  
New Method ◽  
Simple Linear Regression ◽  
Multivariate Statistical ◽  
Statistical Procedures ◽  
Testing Algorithms ◽  
Very High

Sometimes programs, for multivariate statistical procedures are included into expert systems. The requirements of accuracy, exactness and reliability for such programs are very high. In this paper a new method for testing algorithms and programs of multivariate statistical procedures—the so-called “exact samples method” is introduced. The programs of simple linear regression analysis from four most popular standard packages are tested and compared with the help of the new method.

scholarly journals Unreliability of rate constants derived from a linear transformation of kinetic data, with special reference to cholesterol equilibration between phospholipid vesicles

1992 ◽  
Vol 283 (2) ◽  
pp. 537-539 ◽  
Author(s):  
N Gains
Keyword(s):  
Linear Regression ◽  
Special Reference ◽  
Correlation Coefficient ◽  
Rate Constant ◽  
Rate Constants ◽  
Kinetic Data ◽  
Time Dependent ◽  
Phospholipid Vesicles ◽  
Zero Time ◽  
Made In

In the time-dependent transfer of a lipid from a donor to an acceptor vesicle population a(t) is the amount transferred to the acceptor vesicles at time t, a infinity is the equilibrium transfer value and a0 is the value at zero time. In order to plot kinetic data (a(t) as ln[(a infinity - a(t))/(a infinity - a(t))] against time and to fit these with a linear regression, it is necessary to know the equilibrium value, a infinity, or to choose one. Here it is shown that even if a very larger error is made in the choice of a infinity, the resulting plot can still be acceptably linear and the correlation coefficient of the regression acceptably high. When a infinity is overestimated the rate constant derived from the slope of such a plot is underestimated. In extreme cases a 10-fold error can occur.

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