scholarly journals Selection of the Bandwidth Matrix in Spatial Varying Coefficient Models to Detect Anisotropic Regression Relationships

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2343
Author(s):  
Xijian Hu ◽  
Yaori Lu ◽  
Huiguo Zhang ◽  
Haijun Jiang ◽  
Qingdong Shi
Keyword(s):  
Spatial Data ◽  
Geographic Location ◽  
Two Dimensions ◽  
Varying Coefficient Models ◽  
Two Dimensional ◽  
Varying Coefficient Model ◽  
Varying Coefficient ◽  
Fitting Method ◽  
Adaptive Bandwidth ◽  
Selection Of

The commonly used Geographically Weighted Regression (GWR) fitting method for a spatial varying coefficient model is to select a bandwidth h for the geographic location (u, v), and assign the same weight to the two dimensions. However, spatial data usually present anisotropy. The introduction of a two-dimensional bandwidth matrix not only gives weight from two dimensions separately, but also increases the direction of kernel smoothness. The adaptive bandwidth matrix is more flexible. Therefore, in this paper, a two dimensional bandwidth matrix is introduced into the spatial varying coefficient model for parameter estimation. Through simulation experiments, the results obtained under the adaptive bandwidth matrix are compared with those obtained under the global bandwidth matrix, indicating the effectiveness of introducing the adaptive bandwidth matrix.

scholarly journals Liu Estimator in Semiparametric Partially Linear Varying Coefficient Models

2019 ◽  
Vol 8 (6) ◽  
pp. 69
Author(s):  
Jing Li ◽  
Xueyan Li
Keyword(s):  
Varying Coefficient Models ◽  
Varying Coefficient Model ◽  
Liu Estimator ◽  
Biased Estimation ◽  
Varying Coefficient ◽  
Partially Linear ◽  
Constant Coefficients ◽  
Linear Restrictions

This paper considers biased estimation for partially linear varying coefficient model to overcome the problem of multicollinearity. By the Liu estimation approach, we construct a profile Liu estimator for the constant coefficients. Furthermore, a restricted profile-Liu estimator is proposed for the situation that some additional linear restrictions are available. The properties of the proposed estimators are investigated.

scholarly journals Variable selection of varying coefficient models in quantile regression

2012 ◽  
Vol 6 (0) ◽  
pp. 1220-1238 ◽  
Author(s):  
Hohsuk Noh ◽  
Kwanghun Chung ◽  
Ingrid Van Keilegom
Keyword(s):  
Variable Selection ◽  
Quantile Regression ◽  
Varying Coefficient Models ◽  
Varying Coefficient ◽  
Selection Of

scholarly journals Robust SiZer Approach for Varying Coefficient Models

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Hui-Guo Zhang ◽  
Chang-Lin Mei ◽  
He-Ling Wang
Keyword(s):  
Confidence Interval ◽  
Environmental Data ◽  
Varying Coefficient Models ◽  
Bootstrap Confidence Interval ◽  
Varying Coefficient Model ◽  
Absolute Deviation ◽  
Data Set ◽  
Zero Crossing ◽  
Varying Coefficient ◽  
Fitting Procedure

Varying coefficient models have widely been applied to many practical fields for exploring dynamic patterns of the regression relationships. In this study, we propose a robust scenario of SiZer (significant zero crossing of derivatives) inference approach based on the local least absolute deviation fitting procedure and the bootstrap confidence interval to uncover the statistically significant features of the coefficient functions in a varying coefficient model under different smoothing scales. The simulation study shows that the proposed SiZer approach is quite robust to outliers and performs well in finding the significant features of the coefficient functions. Furthermore, a real environmental data set is analyzed to demonstrate the application of the proposed approach.

Local influence for elliptical partially varying-coefficient model

2017 ◽  
Vol 18 (2) ◽  
pp. 149-174
Author(s):  
Germán Ibacache-Pulgar ◽  
Sebastián Reyes
Keyword(s):  
Penalized Likelihood ◽  
Smoothing Splines ◽  
Local Influence ◽  
Likelihood Method ◽  
Varying Coefficient Models ◽  
Varying Coefficient Model ◽  
Real Dataset ◽  
Varying Coefficient ◽  
Maximum Penalized Likelihood ◽  
Heavy Tailed

In this article, we extend varying-coefficient models with normal errors to elliptical errors in order to permit distributions with heavier and lighter tails than the normal ones. This class of models includes all symmetric continuous distributions, such as Student-t, Pearson VII, power exponential and logistic, among others. Estimation is performed by maximum penalized likelihood method and by using smoothing splines. In order to study the sensitivity of the penalized estimates under some usual perturbation schemes in the model or data, the local influence curvatures are derived and some diagnostic graphics are proposed. A real dataset previously analysed by using varying-coefficient models with normal errors is reanalysed under varying-coefficient models with heavy-tailed errors.

Bridging the Gap between Quantitative and Qualitative Historical Research: an application of multiple regression analysis and homogeneity analysis with alternating least squares

1996 ◽  
Vol 8 (3) ◽  
pp. 133-144 ◽  
Author(s):  
María del Mar del Pozo Andrés ◽  
Jacques F A Braster
Keyword(s):  
Least Squares ◽  
Multiple Regression ◽  
Historical Research ◽  
Alternating Least Squares ◽  
Categorical Variables ◽  
Two Dimensional ◽  
Homogeneity Analysis ◽  
Regression Approach ◽  
Dimensional Picture ◽  
Selection Of

In this article we propose two research techniques that can bridge the gap between quantitative and qualitative historical research. These are: (1) a multiple regression approach that gives information about general patterns between numerical variables and the selection of outliers for qualitative analysis; (2) a homogeneity analysis with alternating least squares that results in a two-dimensional picture in which the relationships between categorical variables are graphically presented.

Urbanicity, City Delegations, and Two-Dimensional Liberalism

2018 ◽  
Author(s):  
Thomas K. Ogorzalek
Keyword(s):  
National Level ◽  
Two Dimensions ◽  
Political Order ◽  
Two Dimensional ◽  
Local Institutions ◽  
Horizontal Integration ◽  
National Politics ◽  
United Front ◽  
Strategies For Success

This theoretical chapter develops the argument that the conditions of cities—large, densely populated, heterogeneous communities—generate distinctive governance demands supporting (1) market interventions and (2) group pluralism. Together, these positions constitute the two dimensions of progressive liberalism. Because of the nature of federalism, such policies are often best pursued at higher levels of government, which means that cities must present a united front in support of city-friendly politics. Such unity is far from assured on the national level, however, because of deep divisions between and within cities that undermine cohesive representation. Strategies for success are enhanced by local institutions of horizontal integration developed to address the governance demands of urbanicity, the effects of which are felt both locally and nationally in the development of cohesive city delegations and a unified urban political order capable of contending with other interests and geographical constituencies in national politics.

scholarly journals Three-Dimensional Thematic Map Imaging of the Yacht Port on the Example of the Polish National Sailing Centre Marina in Gdańsk

2021 ◽  
Vol 11 (15) ◽  
pp. 7016
Author(s):  
Pawel S. Dabrowski ◽  
Cezary Specht ◽  
Mariusz Specht ◽  
Artur Makar
Keyword(s):  
Spatial Data ◽  
Convex Surface ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Future Research ◽  
Two Dimensional ◽  
Thematic Maps ◽  
Research Directions ◽  
Future Research Directions ◽  
The Many

The theory of cartographic projections is a tool which can present the convex surface of the Earth on the plane. Of the many types of maps, thematic maps perform an important function due to the wide possibilities of adapting their content to current needs. The limitation of classic maps is their two-dimensional nature. In the era of rapidly growing methods of mass acquisition of spatial data, the use of flat images is often not enough to reveal the level of complexity of certain objects. In this case, it is necessary to use visualization in three-dimensional space. The motivation to conduct the study was the use of cartographic projections methods, spatial transformations, and the possibilities offered by thematic maps to create thematic three-dimensional map imaging (T3DMI). The authors presented a practical verification of the adopted methodology to create a T3DMI visualization of the marina of the National Sailing Centre of the Gdańsk University of Physical Education and Sport (Poland). The profiled characteristics of the object were used to emphasize the key elements of its function. The results confirmed the increase in the interpretative capabilities of the T3DMI method, relative to classic two-dimensional maps. Additionally, the study suggested future research directions of the presented solution.

Turbulent three-dimensional dielectric electrohydrodynamic convection between two plates

2012 ◽  
Vol 696 ◽  
pp. 228-262 ◽  
Author(s):  
A. Kourmatzis ◽  
J. S. Shrimpton
Keyword(s):  
Spatial Data ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Energy Budgets ◽  
Turbulent Regime ◽  
Scalar Flux ◽  
Wide Range ◽  
Scalar Variance

AbstractThe fundamental mechanisms responsible for the creation of electrohydrodynamically driven roll structures in free electroconvection between two plates are analysed with reference to traditional Rayleigh–Bénard convection (RBC). Previously available knowledge limited to two dimensions is extended to three-dimensions, and a wide range of electric Reynolds numbers is analysed, extending into a fully inherently three-dimensional turbulent regime. Results reveal that structures appearing in three-dimensional electrohydrodynamics (EHD) are similar to those observed for RBC, and while two-dimensional EHD results bear some similarities with the three-dimensional results there are distinct differences. Analysis of two-point correlations and integral length scales show that full three-dimensional electroconvection is more chaotic than in two dimensions and this is also noted by qualitatively observing the roll structures that arise for both low (${\mathit{Re}}_{E} = 1$) and high electric Reynolds numbers (up to ${\mathit{Re}}_{E} = 120$). Furthermore, calculations of mean profiles and second-order moments along with energy budgets and spectra have examined the validity of neglecting the fluctuating electric field ${ E}_{i}^{\ensuremath{\prime} } $ in the Reynolds-averaged EHD equations and provide insight into the generation and transport mechanisms of turbulent EHD. Spectral and spatial data clearly indicate how fluctuating energy is transferred from electrical to hydrodynamic forms, on moving through the domain away from the charging electrode. It is shown that ${ E}_{i}^{\ensuremath{\prime} } $ is not negligible close to the walls and terms acting as sources and sinks in the turbulent kinetic energy, turbulent scalar flux and turbulent scalar variance equations are examined. Profiles of hydrodynamic terms in the budgets resemble those in the literature for RBC; however there are terms specific to EHD that are significant, indicating that the transfer of energy in EHD is also attributed to further electrodynamic terms and a strong coupling exists between the charge flux and variance, due to the ionic drift term.

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