scholarly journals On the Degrees of Freedom of Mixed Matrix Regression

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Pan Shang ◽  
Lingchen Kong
Keyword(s):  
Regression Model ◽  
Degrees Of Freedom ◽  
Modern Science ◽  
Model Fit ◽  
Vector Data ◽  
Mixed Matrix ◽  
Science Data ◽  
Adaptive Selection ◽  
Nuclear Norm Regularization ◽  
Consistent Property

With the increasing prominence of big data in modern science, data of interest are more complex and stochastic. To deal with the complex matrix and vector data, this paper focuses on the mixed matrix regression model. We mainly establish the degrees of freedom of the underlying stochastic model, which is one of the important topics to construct adaptive selection criteria for efficiently selecting the optimal model fit. Under some mild conditions, we prove that the degrees of freedom of mixed matrix regression model are the sum of the degrees of freedom of Lasso and regularized matrix regression. Moreover, we establish the degrees of freedom of nuclear-norm regularization multivariate regression. Furthermore, we prove that the estimates of the degrees of freedom of the underlying models process the consistent property.

Evaluating SEM Model Fit with Small Degrees of Freedom

2021 ◽  
pp. 1-36
Author(s):  
Dexin Shi ◽  
Christine DiStefano ◽  
Alberto Maydeu-Olivares ◽  
Taehun Lee
Keyword(s):  
Degrees Of Freedom ◽  
Model Fit

scholarly journals Nuclear data adjustment using Bayesian inference, diagnostics for model fit and influence of model parameters

2020 ◽  
Vol 239 ◽  
pp. 13003
Author(s):  
D. Kumar ◽  
S. B. Alam ◽  
H. Sjöstrand ◽  
J.M. Palau ◽  
C. De Saint Jean
Keyword(s):  
Bayesian Inference ◽  
Degrees Of Freedom ◽  
Nuclear Data ◽  
Information Criteria ◽  
Least Square ◽  
Model Fit ◽  
Adjustment Process ◽  
Model Parameters ◽  
Test Case ◽  
Bayesian Approximation

The mathematical models used for nuclear data evaluations contain a large number of theoretical parameters that are usually uncertain. These parameters can be calibrated (or improved) by the information collected from integral/differential experiments. The Bayesian inference technique is used to utilize measurements for data assimilation. The Bayesian approximation is based on the least-square or Monte-Carlo approaches. In this process, the model parameters are optimized. In the adjustment process, it is essential to include the analysis related to the influence of model parameters on the adjusted data. In this work, some statistical indicators such as the concept of Cook’s distance; Akaike, Bayesian and deviance information criteria; effective degrees of freedom are developed within the CONRAD platform. Further, these indicators are applied to a test case of 155Gd to evaluate and compare the influence of resonance parameters.

Experimental Evaluation of Identification Schemes on a Direct Drive Robot

Robotica ◽  
1997 ◽  
Vol 15 (5) ◽  
pp. 563-571 ◽  
Author(s):  
Fernando Reyes ◽  
Rafael Kelly
Keyword(s):  
Regression Model ◽  
Experimental Evaluation ◽  
Regression Models ◽  
Degrees Of Freedom ◽  
Dynamic Parameter ◽  
Direct Drive ◽  
Identification Schemes ◽  
Inertial Parameters ◽  
Dynamic Regression Model ◽  
Recursive Parameter Estimator

This paper describes the experimental evaluation of three identification schemes to determine the dynamic parameters of a two degrees of freedom direct-drive robot. These schemes involve a recursive estimator while the regression models are formulated in continuous time. The fact that the total energy of robot manipulators can be represented as a linear relation in the inertial parameters, has motivated the suggestion in the literature of several regression models which are linear in a common dynamic parameter vector. Among them, in this paper we consider the schemes based on the filtered dynamic regression model, the supplied energy regression model and a new one proposed in this paper: the filtered power regression model. The underling recursive parameter estimator used in the experimental evaluation is the standard least-squares.

scholarly journals A vertically resolved, global, gap-free ozone database for assessing or constraining global climate model simulations

2012 ◽  
Vol 5 (2) ◽  
pp. 999-1033 ◽  
Author(s):  
G. E. Bodeker ◽  
B. Hassler ◽  
P. J. Young ◽  
R. W. Portmann
Keyword(s):  
Regression Model ◽  
Climate Model ◽  
Global Climate ◽  
Global Climate Model ◽  
Initial Guess ◽  
Model Fit ◽  
Total Column Ozone ◽  
Model Simulations ◽  
Climate Model Simulations ◽  
Vertical Level

Abstract. High vertical resolution ozone measurements from eight different satellite-based instruments have been merged with data from the global ozonesonde network to calculate monthly mean ozone values in 5° latitude zones. These "Tier 0" ozone number densities and ozone mixing ratios are provided on 70 altitude levels (1 to 70 km) and on 70 pressure levels spaced ~1 km apart (878.4 hPa to 0.046 hPa). The Tier 0 data are sparse and do not cover the entire globe or altitude range. To provide a gap-free database, a least squares regression model is fitted to the Tier 0 data and then evaluated globally. The regression model fit coefficients are expanded in Legendre polynomials to account for latitudinal structure, and in Fourier series to account for seasonality. Regression model fit coefficient patterns, which are two dimensional fields indexed by latitude and month of the year, from the N-th vertical level serve as an initial guess for the fit at the N+1th vertical level. The initial guess field for the first fit level (20 km/58.2 hPa) was derived by applying the regression model to total column ozone fields. Perturbations away from the initial guess are captured through the Legendre and Fourier expansions. By applying a single fit at each level, and using the approach of allowing the regression fits to change only slightly from one level to the next, the regression is less sensitive to measurement anomalies at individual stations or to individual satellite-based instruments. Particular attention is paid to ensuring that the low ozone abundances in the polar regions are captured. By summing different combinations of contributions from different regression model basis functions, four different "Tier 1" databases have been compiled for different intended uses. This database is suitable for assessing ozone fields from chemistry-climate model simulations or for providing the ozone boundary conditions for global climate model simulations that do not treat stratospheric chemistry interactively.

Regression Analysis

2018 ◽  
pp. 170-205
Author(s):  
Quan Li
Keyword(s):  
Economic Growth ◽  
Regression Analysis ◽  
Statistical Model ◽  
Regression Model ◽  
Ordinary Least Squares ◽  
Theory And Practice ◽  
Model Fit ◽  
Theoretical Argument ◽  
Markov Theorem ◽  
The Relationship

This chapter teaches how to use R to conduct regression analysis to answer the question: Does trade promote economic growth? It demonstrates how to specify a statistical model from a theoretical argument, prepare data, estimate and interpret the statistical model, and use the estimated results to make inferences and answer the question of interest. More specifically, it discusses the logic of regression analysis, the relationship between population and sample regression models, how to estimate a regression model in theory and practice, the estimation of sample regression model using OLS (ordinary least squares), the interpretation of estimation results, the statistical inference in regression analysis using hypothesis testing and confidence interval, the types of sum of squares and overall model fit, and how to report the model results. The validity of regression analysis is contingent upon the assumptions of the Gauss-Markov theorem being met.

scholarly journals Methodological aspects of a pattern-scaling approach to produce global fields of monthly means of daily maximum and minimum temperature

2013 ◽  
Vol 6 (3) ◽  
pp. 4833-4882
Author(s):  
S. Kremser ◽  
G. E. Bodeker ◽  
J. Lewis
Keyword(s):  
Time Series ◽  
Regression Model ◽  
Climate Model ◽  
Ghg Emissions ◽  
Model Fit ◽  
Daily Maximum ◽  
Statistical Relationship ◽  
Climate Variable ◽  
Methodological Aspects ◽  
Emissions Scenario

Abstract. A Climate Pattern-Scaling Model (CPSM) that simulates global patterns of climate change, for a prescribed emissions scenario, is described. A CPSM works by quantitatively establishing the statistical relationship between a climate variable at a specific location (e.g. daily maximum surface temperature, Tmax) and one or more predictor time series (e.g. global mean surface temperature, Tglobal) – referred to as the "training" of the CPSM. This training uses a regression model to derive fit-coefficients that describe the statistical relationship between the predictor time series and the target climate variable time series. Once that relationship has been determined, and given the predictor time series for any greenhouse gas (GHG) emissions scenario, the change in the climate variable of interest can be reconstructed – referred to as the "application" of the CPSM. The advantage of using a CPSM rather than a typical atmosphere-ocean global climate model (AOGCM) is that the predictor time series required by the CPSM can usually be generated quickly using a simple climate model (SCM) for any prescribed GHG emissions scenario and then applied to generate global fields of the climate variable of interest. The training can be performed either on historical measurements or on output from an AOGCM. Using model output from 21st century simulations has the advantage that the climate change signal is more pronounced than in historical data and therefore a more robust statistical relationship is obtained. The disadvantage of using AOGCM output is that the CPSM training might be compromised by any AOGCM inadequacies. For the purposes of exploring the various methodological aspects of the CPSM approach, AOGCM output was used in this study to train the CPSM. These investigations of the CPSM methodology focus on monthly mean fields of daily temperature extremes (Tmax and Tmin). Key conclusions are: (1) overall, the CPSM trained on simulations based on the Representative Concentration Pathway (RCP) 8.5 emissions scenario is able to reproduce AOGCM simulations of Tmax and Tmin based on predictor time series from an RCP 4.5 emissions scenario; (2) access to hemisphere average land and ocean temperatures as predictors improves the variance that can be explained, particularly over the oceans; (3) regression model fit-coefficients derived from individual simulations based on the RCP 2.6, 4.5 and 8.5 emissions scenarios agree well over most regions of the globe (the Arctic is the exception); (4) training the CPSM on concatenated time series from an ensemble of simulations does not result in fit-coefficients that explain significantly more of the variance than an approach that weights results based on single simulation fits; and (5) the inclusion of a linear time dependence in the regression model fit-coefficients improves the variance explained, primarily over the oceans.

scholarly journals Landsat 8 Lake Water Clarity Empirical Algorithms: Large-Scale Calibration and Validation Using Government and Citizen Science Data from across Canada

2021 ◽  
Vol 13 (7) ◽  
pp. 1257
Author(s):  
Eliza S. Deutsch ◽  
Jeffrey A. Cardille ◽  
Talia Koll-Egyed ◽  
Marie-Josée Fortin
Keyword(s):  
Large Scale ◽  
Median Filter ◽  
Empirical Relationship ◽  
Water Clarity ◽  
Model Fit ◽  
Landsat 8 ◽  
Science Data ◽  
Band Ratio ◽  
Empirical Algorithms

Water clarity has been extensively assessed in Landsat-based remote sensing studies of inland waters, regularly relying on locally calibrated empirical algorithms, and close temporal matching between field data and satellite overpass. As more satellite data and faster data processing systems become readily accessible, new opportunities are emerging to revisit traditional assumptions concerning empirical calibration methodologies. Using Landsat 8 images with large water clarity datasets from southern Canada, we assess: (1) whether clear regional differences in water clarity algorithm coefficients exist and (2) whether model fit can be improved by expanding temporal matching windows. We found that a single global algorithm effectively represents the empirical relationship between in situ Secchi disk depth (SDD) and the Landsat 8 Blue/Red band ratio across diverse lake types in Canada. We also found that the model fit improved significantly when applying a median filter on data from ever-wider time windows between the date of in situ SDD sample and the date of satellite overpass. The median filter effectively removed the outliers that were likely caused by atmospheric artifacts in the available imagery. Our findings open new discussions on the ability of large datasets and temporal averaging methods to better elucidate the true relationships between in situ water clarity and satellite reflectance data.

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