scholarly journals CONDITIONAL LEAST SQUARES ESTIMATION OF THE PARAMETERS OF HIGHER ORDER RANDOM ENVIRONMENT INAR MODElS

2019 ◽  
pp. 525
Author(s):  
Petra N. Laketa ◽  
Aleksandar S. Nastic
Keyword(s):  
Least Squares ◽  
Random Environment ◽  
Nonnegative Integer ◽  
Simulated Data ◽  
Higher Order ◽  
Counting Processes ◽  
Autoregressive Processes ◽  
New Approach ◽  
Conditional Least Squares ◽  
Parameter Values

Two different random environment INAR models of higher order, precisely RrNGINARmax(p) and RrNGINAR1(p), are presented as a new approach to modeling non-stationary nonnegative integer-valued autoregressive processes. The interpretation of these models is given in order to better understand the circumstances of their application to random environment counting processes. The estimation statistics, defined using the Conditional Least Squares (CLS) method, is introduced and the properties are tested on the replicated simulated data obtained by RrNGINAR models with different parameter values. The obtained CLS estimates are presented and discussed.

Uncertainty of a Least Squares Curve Fit through Points with Known Uncertainties

1995 ◽  
Vol 23 (4) ◽  
pp. 315-326
Author(s):  
Ronald D. Flack
Keyword(s):  
Experimental Data ◽  
Least Squares ◽  
Fourth Order ◽  
Simulated Data ◽  
Higher Order ◽  
Individual Data ◽  
Linear Quadratic ◽  
Curve Fit ◽  
Data Points ◽  
The Individual

Uncertainties in least squares curve fits to data with uncertainties are examined. First, experimental data with nominal curve shapes, representing property profiles between boundaries, are simulated by adding known uncertainties to individual points. Next, curve fits to the simulated data are achieved and compared to the nominal curves. By using a large number of different sets of data, statistical differences between the two curves are quantified and, thus, the uncertainty of the curve fit is derived. Studies for linear, quadratic, and higher-order nominal curves with curve fits up to fourth order are presented herein. Typically, curve fits have uncertainties that are 50% or less than those of the individual data points. These uncertainties increase with increasing order of the least squares curve fit. The uncertainties decrease with increasing number of data points on the curves.

scholarly journals Penalized partial least squares for pleiotropy

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Camilo Broc ◽  
Therese Truong ◽  
Benoit Liquet
Keyword(s):  
Least Squares ◽  
Partial Least Squares ◽  
Association Studies ◽  
A Priori ◽  
Simulated Data ◽  
Real Data ◽  
Genome Wide Association Studies ◽  
Genetic Associations ◽  
Multiple Traits ◽  
Application Fields

Abstract Background The increasing number of genome-wide association studies (GWAS) has revealed several loci that are associated to multiple distinct phenotypes, suggesting the existence of pleiotropic effects. Highlighting these cross-phenotype genetic associations could help to identify and understand common biological mechanisms underlying some diseases. Common approaches test the association between genetic variants and multiple traits at the SNP level. In this paper, we propose a novel gene- and a pathway-level approach in the case where several independent GWAS on independent traits are available. The method is based on a generalization of the sparse group Partial Least Squares (sgPLS) to take into account groups of variables, and a Lasso penalization that links all independent data sets. This method, called joint-sgPLS, is able to convincingly detect signal at the variable level and at the group level. Results Our method has the advantage to propose a global readable model while coping with the architecture of data. It can outperform traditional methods and provides a wider insight in terms of a priori information. We compared the performance of the proposed method to other benchmark methods on simulated data and gave an example of application on real data with the aim to highlight common susceptibility variants to breast and thyroid cancers. Conclusion The joint-sgPLS shows interesting properties for detecting a signal. As an extension of the PLS, the method is suited for data with a large number of variables. The choice of Lasso penalization copes with architectures of groups of variables and observations sets. Furthermore, although the method has been applied to a genetic study, its formulation is adapted to any data with high number of variables and an exposed a priori architecture in other application fields.

scholarly journals A New Approach to the Quality Control of Slope and Aspect Classes Derived from Digital Elevation Models

2021 ◽  
Vol 13 (11) ◽  
pp. 2069
Author(s):  
M. V. Alba-Fernández ◽  
F. J. Ariza-López ◽  
M. D. Jiménez-Gamero
Keyword(s):  
Quality Control ◽  
Hypothesis Test ◽  
Simulated Data ◽  
Slope Aspect ◽  
New Approach ◽  
Reference Set ◽  
Digital Elevation ◽  
Using Data ◽  
Elevation Model ◽  
Degree Of Similarity

The usefulness of the parameters (e.g., slope, aspect) derived from a Digital Elevation Model (DEM) is limited by its accuracy. In this paper, a thematic-like quality control (class-based) of aspect and slope classes is proposed. A product can be compared against a reference dataset, which provides the quality requirements to be achieved, by comparing the product proportions of each class with those of the reference set. If a distance between the product proportions and the reference proportions is smaller than a small enough positive tolerance, which is fixed by the user, it will be considered that the degree of similarity between the product and the reference set is acceptable, and hence that its quality meets the requirements. A formal statistical procedure, based on a hypothesis test, is developed and its performance is analyzed using simulated data. It uses the Hellinger distance between the proportions. The application to the slope and aspect is illustrated using data derived from a 2×2 m DEM (reference) and 5×5 m DEM in Allo (province of Navarra, Spain).

Assessment of a Hierarchical Model Using Partial Least Squares (PLS): The Case of Enterprise Resource Planning (ERP) System Continued Usage

2021 ◽  
Vol 39 (10) ◽  
Author(s):  
T. Ramayah ◽  
Lo May-Chiun ◽  
Sarminah Samad ◽  
Noor Hazlina Ahmad ◽  
Hasliza Abdul Halim
Keyword(s):  
Empirical Study ◽  
Least Squares ◽  
Partial Least Squares ◽  
Hierarchical Model ◽  
Enterprise Resource Planning ◽  
Questionnaire Survey ◽  
Resource Planning ◽  
Higher Order ◽  
Continuance Intention ◽  
Erp System

This paper is an empirical study that highlights the usage of Enterprise Resource Planning (ERP) system among individual users.  Questionnaire survey was carried out with measures gleaned from the literature. In this study we have proposed and tested a hierarchical reflective model of quality unlike other studies. The results support the higher order hierarchical reflective model tested using the Partial least Squares (PLS) software of SmartPLS. We further found support for all the hypotheses developed. Quality was a significant predictor of continuance intention and satisfaction. Satisfaction also drives continuance intention and mediates the effect of quality on the continuance intention relationship. Implications of the findings are further explored.

Autoregressive processes with infinite variance

1977 ◽  
Vol 14 (02) ◽  
pp. 411-415 ◽  
Author(s):  
E. J. Hannan ◽  
Marek Kanter
Keyword(s):  
Least Squares ◽  
Autoregressive Model ◽  
Infinite Variance ◽  
Autoregressive Processes ◽  
Stable Law ◽  
Least Squares Estimators ◽  
Data Points

The least squares estimators β i(N), j = 1, …, p, from N data points, of the autoregressive constants for a stationary autoregressive model are considered when the disturbances have a distribution attracted to a stable law of index α < 2. It is shown that N1/δ(β i(N) – β) converges almost surely to zero for any δ > α. Some comments are made on alternative definitions of the βi (N).

scholarly journals Deformation analysis with Total Least Squares

2006 ◽  
Vol 6 (4) ◽  
pp. 663-669 ◽  
Author(s):  
M. Acar ◽  
M. T. Özlüdemir ◽  
O. Akyilmaz ◽  
R. N. Çelik ◽  
T. Ayan
Keyword(s):  
Least Squares ◽  
Total Least Squares ◽  
Transformation Model ◽  
Deformation Analysis ◽  
New Approach ◽  
Main Research ◽  
Research Fields ◽  
Analysis Process ◽  
Alternative Methodology ◽  
Coordinate Changes

Abstract. Deformation analysis is one of the main research fields in geodesy. Deformation analysis process comprises measurement and analysis phases. Measurements can be collected using several techniques. The output of the evaluation of the measurements is mainly point positions. In the deformation analysis phase, the coordinate changes in the point positions are investigated. Several models or approaches can be employed for the analysis. One approach is based on a Helmert or similarity coordinate transformation where the displacements and the respective covariance matrix are transformed into a unique datum. Traditionally a Least Squares (LS) technique is used for the transformation procedure. Another approach that could be introduced as an alternative methodology is the Total Least Squares (TLS) that is considerably a new approach in geodetic applications. In this study, in order to determine point displacements, 3-D coordinate transformations based on the Helmert transformation model were carried out individually by the Least Squares (LS) and the Total Least Squares (TLS), respectively. The data used in this study was collected by GPS technique in a landslide area located nearby Istanbul. The results obtained from these two approaches have been compared.

scholarly journals Higher Order Haar Wavelet Method for Solving Differential Equations

2020 ◽  
Author(s):  
Jüri Majak ◽  
Mart Ratas ◽  
Kristo Karjust ◽  
Boris Shvartsman
Keyword(s):  
Differential Equations ◽  
Computational Cost ◽  
Haar Wavelet ◽  
Higher Order ◽  
Wavelet Method ◽  
Haar Wavelet Method ◽  
Convergence Results ◽  
Key Characteristics ◽  
Parameter Values ◽  
Excellent Accuracy

The study is focused on the development, adaption and evaluation of the higher order Haar wavelet method (HOHWM) for solving differential equations. Accuracy and computational complexity are two measurable key characteristics of any numerical method. The HOHWM introduced recently by authors as an improvement of the widely used Haar wavelet method (HWM) has shown excellent accuracy and convergence results in the case of all model problems studied. The practical value of the proposed HOHWM approach is that it allows reduction of the computational cost by several magnitudes as compared to HWM, depending on the mesh and the method parameter values used.

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