scholarly journals APPLICATION OF STATISTICAL TECHNIQUES IN THE PRACTICE OF BUILDING A DEFILIENCE SCALE

2021 ◽  
Vol 5 (40) ◽  
pp. 35-44
Author(s):  
Ye. Pavliuk ◽  
O. Pavliuk
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Default Probability ◽  
Extrapolation Method ◽  
Classification Model ◽  
Weibull Function ◽  
Slow Increase ◽  
Moderate Growth ◽  
S Curve ◽  
Number Of Classes

Abstract. The main substantial features of the PD curve (default probability) formed in practical modeling are substantiated in the articles. It is proved that the main characteristics of the PD curve are that it is based on data on the actually restored default rate in each of the risk classes over a period of time and has a shape that approximate for coincides with the exposure function. It is shown that the best aspect that affects the calibration is the number of rating classes and ways to build them. It is determined that the slope of the curve demonstrates the classification model of efficiency. It is determined that the slope of the curve demonstrates the classification efficiency of the model. Models with high discriminant properties are characterized by a curve shape that has a slow increase in the rating classes of the upper part of the scale and a significant acceleration of growth in the last risk classes. Two main approaches to determining the number of risk classes are analyzed: the percentile-based approach and the equal score range approach. It is shown that when forming classes, it is necessary to take into account the total amount of sample observations, the proportion of «good» and «bad», and choose the number of classes so that it is not too large and not too small. Calibration practice shave been shown to be influenced by data, purpose, and study limitations. The application of the least squares method and the extrapolation method is considered on practical examples. The least squares method and in particular the derived extrapolation method allow to build a calibration curve on the basis of data on the relative frequency of defaults. It is determined that the mathematical apparatus of the family of nonlinear curves allows to model the process of exponential growth with different levels of intensity. The exponential curve and related functions may be useful in modeling more conservative PD estimates or for models with highly discriminatory properties, while the Weibull function, S-curve, and power function may be better adapted to moderate growth processes. The application of practical methods of constructing the PD scale is important for many domestic banking professionals who deal with internal models of credit risk. Keywords: Calibration, Default, Probability, Curves, Probability of default curve calibration, Least squares method, Extrapolation method. JEL Classіfіcatіon С44 Formulas: 21; fig.: 1; tabl.: 7; bibl.: 10.

scholarly journals Gait Phase Classification and Assist Torque Prediction for a Lower Limb Exoskeleton System Using Kernel Recursive Least-Squares Method

Sensors ◽  
2019 ◽  
Vol 19 (24) ◽  
pp. 5449 ◽  
Author(s):  
Yue Ma ◽  
Xinyu Wu ◽  
Can Wang ◽  
Zhengkun Yi ◽  
Guoyuan Liang
Keyword(s):  
Least Squares ◽  
Joint Angle ◽  
Least Squares Method ◽  
Classification Model ◽  
Recursive Least Squares ◽  
Support Vector ◽  
Exoskeleton Robot ◽  
Phase Classification ◽  
Gait Features ◽  
Gait Phase

The gait phase classification method is a key technique to control an exoskeleton robot. Different people have different gait features while wearing an exoskeleton robot due to the gap between the exoskeleton and the wearer and their operation habits, such as the correspondence between the joint angle and the moment at which the foot contacts the ground, the amplitude of the joint angle and others. In order to enhance the performance of the gait phase classification in an exoskeleton robot using only the angle of hip and knee joints, a kernel recursive least-squares (KRLS) algorithm is introduced to build a gait phase classification model. We also build an assist torque predictor based on the KRLS algorithm in this work considering the adaptation of unique gait features. In this paper, we evaluate the classification performance of the KRLS model by comparing with two other commonly used gait recognition methods—the multi-layer perceptron neural network (MLPNN) method and the support vector machine (SVM) algorithm. In this experiment, the training and testing datasets for the models built by KRLS, MLPNN and SVM were collected from 10 healthy volunteers. The gait data are collected from the exoskeleton robot that we designed rather than collected from the human body. These data depict the human-robot coupling gait that includes unique gait features. The KRLS classification results are in average 3% higher than MLPNN and SVM. The testing average accuracy of KRLS is about 86%. The prediction results of KRLS are twice as good as MLPNN in assist torque prediction experiments. The KRLS performs in a good, stable, and robust way and shows model generalization abilities.

The least-squares triangle: a new method for evaluation of solid phase compositions from solubility measurements

1981 ◽  
Vol 59 (21) ◽  
pp. 3076-3083 ◽  
Author(s):  
John W. Lorimer
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Solid Phase ◽  
Extrapolation Method ◽  
New Method ◽  
Initial Composition ◽  
Hypothesis Tests ◽  
Error Analyses ◽  
Solid Phases

A least-squares method is described for calculating compositions of equilibrium solid phases from data on solubilities and either wet residues or initial compositions for systems of three or more thermodynamic components. The method minimizes the squares of areas of triangles formed by the solubility, wet residue (or initial composition), and solid composition points. Full descriptions of error analyses and hypothesis tests are given, along with an illustrative example and detailed comparisons with the traditional extrapolation method.

A new data extrapolation method based on the modified Helmholtz equation least-squares method

2012 ◽  
Vol 227 (6) ◽  
pp. 1252-1265
Author(s):  
R Wang ◽  
J Chen ◽  
GM Dong
Keyword(s):  
Helmholtz Equation ◽  
Least Squares ◽  
Acoustic Field ◽  
Least Squares Method ◽  
Acoustic Radiation ◽  
Near Field ◽  
Extrapolation Method ◽  
Modified Helmholtz Equation ◽  
Helmholtz Equation Least Squares ◽  
Data Extrapolation

Fast Fourier transform-based near-field acoustic holography requires that the measurement aperture should completely enclose the source, which is impractical for large-scale sound sources. Helmholtz equation least-squares method can reconstruct the acoustic field with fewer measurements than fast Fourier transform-based near-field acoustic holography. However, it is not suitable for reconstructing acoustic radiation from multiple sources or a complicated source which consists of several separated parts. To circumvent this difficulty and enhance the reconstruction accuracy, a new data extrapolation method based on the modified Helmholtz equation least-squares method is proposed. The base of this data extrapolation method is a modified Helmholtz equation least-squares method which expresses the acoustic field of a complicated source as the superposition of the acoustic radiation from all of its separated parts. Using the acoustic pressures reconstructed with the modified Helmholtz equation least-squares method, the measurement surface is extended through an iterative procedure. Meanwhile, Tikhonov regularization method together with generalized cross-validation parameter choice method is utilized to treat the ill-posed problem in reconstructions. In the end, taking the extrapolated pressures as input data, the acoustic field can be reconstructed more precisely. Numerical simulation and experimental results demonstrate that this method can significantly enhance the reconstruction accuracy and efficiency.

‘Least squares’ method—theorem or law?

1980 ◽  
Vol 59 (9) ◽  
pp. 8
Author(s):  
D.E. Turnbull
Keyword(s):  
Least Squares ◽  
Least Squares Method

An Augmented Iteratively Re-weighted and Refined Least Squares Method for lp Minimization Problem in Inverse Modeling of Potential Field Magnetic Data

2020 ◽  
Vol 1 (3) ◽  
Author(s):  
Maysam Abedi
Keyword(s):  
Magnetic Field ◽  
Magnetic Susceptibility ◽  
Least Squares ◽  
Minimization Problem ◽  
Potential Field ◽  
Field Data ◽  
Least Squares Method ◽  
Porphyry Copper ◽  
Magnetic Data ◽  
Magnetic Field Data

The presented work examines application of an Augmented Iteratively Re-weighted and Refined Least Squares method (AIRRLS) to construct a 3D magnetic susceptibility property from potential field magnetic anomalies. This algorithm replaces an lp minimization problem by a sequence of weighted linear systems in which the retrieved magnetic susceptibility model is successively converged to an optimum solution, while the regularization parameter is the stopping iteration numbers. To avoid the natural tendency of causative magnetic sources to concentrate at shallow depth, a prior depth weighting function is incorporated in the original formulation of the objective function. The speed of lp minimization problem is increased by inserting a pre-conditioner conjugate gradient method (PCCG) to solve the central system of equation in cases of large scale magnetic field data. It is assumed that there is no remanent magnetization since this study focuses on inversion of a geological structure with low magnetic susceptibility property. The method is applied on a multi-source noise-corrupted synthetic magnetic field data to demonstrate its suitability for 3D inversion, and then is applied to a real data pertaining to a geologically plausible porphyry copper unit.  The real case study located in  Semnan province of  Iran  consists  of  an arc-shaped  porphyry  andesite  covered  by  sedimentary  units  which  may  have  potential  of  mineral  occurrences, especially  porphyry copper. It is demonstrated that such structure extends down at depth, and consequently exploratory drilling is highly recommended for acquiring more pieces of information about its potential for ore-bearing mineralization.

Theoretical accuracy of the last squares method in the isotope dilution analysis

1984 ◽  
Vol 49 (4) ◽  
pp. 805-820
Author(s):  
Ján Klas
Keyword(s):  
Least Squares ◽  
Isotope Dilution ◽  
Least Squares Method ◽  
Isotope Dilution Analysis ◽  
Straight Line ◽  
The One ◽  
Two Parameter ◽  
Theoretical Accuracy

The accuracy of the least squares method in the isotope dilution analysis is studied using two models, viz a model of a two-parameter straight line and a model of a one-parameter straight line.The equations for the direct and the inverse isotope dilution methods are transformed into linear coordinates, and the intercept and slope of the two-parameter straight line and the slope of the one-parameter straight line are evaluated and treated.

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