A note on the asymptotic distribution of the parameter estimates for the harmonic regression model

Biometrika ◽  
1990 ◽  
Vol 77 (3) ◽  
pp. 653-656 ◽  
Author(s):  
EMERY BROWN
Keyword(s):  
Regression Model ◽  
Asymptotic Distribution ◽  
Parameter Estimates ◽  
Harmonic Regression

scholarly journals Analysis of Severe Injury Accident Rates on Interstate Highways Using a Random Parameter Tobit Model

2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Minho Park ◽  
Dongmin Lee
Keyword(s):  
Regression Model ◽  
Unobserved Heterogeneity ◽  
Random Parameter ◽  
Tobit Model ◽  
Severe Injury ◽  
Parameter Estimates ◽  
Random Parameters ◽  
Tobit Regression ◽  
Accident Rates ◽  
Tobit Regression Model

In this study, a random parameter Tobit regression model approach was used to account for the distinct censoring problem and unobserved heterogeneity in accident data. We used accident rate data (continuous data) instead of accident frequency data (discrete count data) to address the zero cell problems from data where roadway segments do not have any recorded accidents over the observed time period. The unobserved heterogeneity problem is also considered by using random parameters, which are parameter estimates that vary across observations instead of fixed parameters, which are parameter estimates that are fixed/constant over observations. Nine years (1999–2007) of panel data related to severe injury accidents in Washington State, USA, were used to develop the random parameter Tobit model. The results showed that the Tobit regression model with random parameters is a better approach to explore factors influencing severe injury accident rates on roadway segments under consideration of unobserved heterogeneity problems.

Multilevel Zero-inflated Censored Beta Regression Modeling for Proportions and Rate Data with Extra-zeros

2019 ◽  
Author(s):  
Leili Tapak ◽  
Omid Hamidi ◽  
Majid Sadeghifar ◽  
Hassan Doosti ◽  
Ghobad Moradi
Keyword(s):  
Regression Model ◽  
Simulation Study ◽  
Real Data ◽  
P Value ◽  
Parameter Estimates ◽  
Beta Regression ◽  
Rate Data ◽  
Data Set ◽  
Proposed Model ◽  
Beta Regression Model

Abstract Objectives Zero-inflated proportion or rate data nested in clusters due to the sampling structure can be found in many disciplines. Sometimes, the rate response may not be observed for some study units because of some limitations (false negative) like failure in recording data and the zeros are observed instead of the actual value of the rate/proportions (low incidence). In this study, we proposed a multilevel zero-inflated censored Beta regression model that can address zero-inflation rate data with low incidence.Methods We assumed that the random effects are independent and normally distributed. The performance of the proposed approach was evaluated by application on a three level real data set and a simulation study. We applied the proposed model to analyze brucellosis diagnosis rate data and investigate the effects of climatic and geographical position. For comparison, we also applied the standard zero-inflated censored Beta regression model that does not account for correlation.Results Results showed the proposed model performed better than zero-inflated censored Beta based on AIC criterion. Height (p-value <0.0001), temperature (p-value <0.0001) and precipitation (p-value = 0.0006) significantly affected brucellosis rates. While, precipitation in ZICBETA model was not statistically significant (p-value =0.385). Simulation study also showed that the estimations obtained by maximum likelihood approach had reasonable in terms of mean square error.Conclusions The results showed that the proposed method can capture the correlations in the real data set and yields accurate parameter estimates.

scholarly journals A Monograph on Nonlinear Regression Models

2018 ◽  
Vol 7 (4.10) ◽  
pp. 543
Author(s):  
B. Mahaboob ◽  
B. Venkateswarlu ◽  
C. Narayana ◽  
J. Ravi sankar ◽  
P. Balasiddamuni
Keyword(s):  
Regression Model ◽  
Least Squares ◽  
Nonlinear Regression ◽  
Nonlinear Models ◽  
Nonlinear Least Squares ◽  
Error Variance ◽  
Ordinary Least Squares ◽  
Parameter Estimates ◽  
Nonlinear Regression Model ◽  
Nonlinear Regression Models

This research article uses Matrix Calculus techniques to study least squares application of nonlinear regression model, sampling distributions of nonlinear least squares estimators of regression parametric vector and error variance and testing of general nonlinear hypothesis on parameters of nonlinear regression model. Arthipova Irina et.al [1], in this paper, discussed some examples of different nonlinear models and the application of OLS (Ordinary Least Squares). MA Tabati et.al (2), proposed a robust alternative technique to OLS nonlinear regression method which provide accurate parameter estimates when outliers and/or influential observations are present. Xu Zheng et.al [3] presented new parametric tests for heteroscedasticity in nonlinear and nonparametric models.  

A spatial, climate-determined risk rating for Scleroderris disease of pines in Ontario

1998 ◽  
Vol 28 (9) ◽  
pp. 1398-1404 ◽  
Author(s):  
L A Venier ◽  
A A Hopkin ◽  
D W McKenney ◽  
Y. Wang
Keyword(s):  
Logistic Regression ◽  
Regression Model ◽  
Classification Accuracy ◽  
Logistic Regression Model ◽  
Distribution Data ◽  
Parameter Estimates ◽  
Final Model ◽  
Probability Of Occurrence ◽  
Model Classification ◽  
Historical Distribution

We used historical distribution data of Scleroderris disease (caused by the fungus Gremmeniella abietina var. abietina (Lagerb.) Morelet) in Ontario to model its probability of occurrence as a function of climate factors. A logistic regression model of the probability of occurrence as a function of the mean temperature of the coldest quarter and the precipitation of the coldest quarter was a very good fit. The concordance (index of classification accuracy) of the model was 84%. We subsampled the data repeatedly, generated new parameter estimates, and tested the predictions against data not included in the model. Classification accuracy was similar for each subsample model; therefore, we concluded that the final model is stable. Gridded estimates of the climate variables were used to spatially extend the two-variable logistic regression model and produce a probability of occurrence map for Scleroderris disease across Ontario. The predicted map of probability of occurrence fits well with the map of the observed locations of the disease. These results lend credence to previous work that suggests that distribution of Scleroderris disease is strongly influenced by climate. The classification results also suggest that this model is a useful tool for assessing the risk of Scleroderris disease throughout Ontario.

scholarly journals Estimation of Impedance and Susceptance Parameters of a 3-Phase Cable System Using PMU Data

Energies ◽  
2019 ◽  
Vol 12 (23) ◽  
pp. 4573 ◽  
Author(s):  
Ravi Shankar Singh ◽  
Helko van den Brom ◽  
Stanislav Babaev ◽  
Sjef Cobben ◽  
Vladimir Ćuk
Keyword(s):  
Regression Model ◽  
Measurement System ◽  
Measurement Errors ◽  
Measurement Unit ◽  
Parameter Estimates ◽  
Total Uncertainty ◽  
Measured Current ◽  
Estimated Parameters ◽  
Unknown Bias ◽  
Cable Segment

This paper proposes a new regression-based method to estimate resistance, reactance, and susceptance parameters of a 3-phase cable segment using phasor measurement unit (PMU) data. The novelty of this method is that it gives accurate parameter estimates in the presence of unknown bias errors in the measurements. Bias errors are fixed errors present in the measurement equipment and have been neglected in previous such attempts of estimating parameters of a 3-phase line or cable segment. In power system networks, the sensors used for current and voltage measurements have inherent magnitude and phase errors whose measurements need to be corrected using calibrated correction coefficients. Neglecting or using wrong error correction coefficients causes fixed bias errors in the measured current and voltage signals. Measured current and voltage signals at different time instances are the variables in the regression model used to estimate the cable parameters. Thus, the bias errors in the sensors become fixed errors in the variables. This error in variables leads to inaccuracy in the estimated parameters. To avoid this, the proposed method uses a new regression model using extra parameters which facilitate the modeling of present but unknown bias errors in the measurement system. These added parameters account for the errors present in the non- or wrongly calibrated sensors. Apart from the measurement bias, random measurement errors also contribute to the total uncertainty of the estimated parameters. This paper also presents and compares methods to estimate the total uncertainty in the estimated parameters caused by the bias and random errors present in the measurement system. Results from simulation-based and laboratory experiments are presented to show the efficacy of the proposed method. A discussion about analyzing the obtained results is also presented.

Parameter estimation for finite-parameter stationary random fields

1986 ◽  
Vol 23 (A) ◽  
pp. 311-318
Author(s):  
M. Rosenblatt
Keyword(s):  
Parameter Estimation ◽  
Asymptotic Distribution ◽  
Random Fields ◽  
Strong Mixing ◽  
Parameter Estimates ◽  
Stationary Sequences ◽  
Linear Processes ◽  
Stationary Random Fields

The concept of strong mixing is used to obtain a generalization of results on the asymptotic distribution of finite-parameter estimates of linear processes and extend them for stationary sequences and random fields.

Least Squares Regression with Integrated or Dynamic Regressors under Weak Error Assumptions

1987 ◽  
Vol 3 (1) ◽  
pp. 98-116 ◽  
Author(s):  
Donald W. K. Andrews
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Least Squares ◽  
Asymptotic Distribution ◽  
Linear Regression Model ◽  
Multiple Regression Model ◽  
Least Squares Regression ◽  
Least Squares Estimators ◽  
Integrated Or ◽  
Weak Error

This paper establishes consistency of least squares estimators in (i) a multiple regression model with integrated regressors and explosive, non-mixing errors, and (ii) a dynamic linear regression model with regressors and errors that may have infinite variances. In the former context, the asymptotic distribution of the least squares estimator also is obtained, in certain cases.

scholarly journals SPECIFICATION TESTS FOR LATTICE PROCESSES

2014 ◽  
Vol 31 (2) ◽  
pp. 294-336 ◽  
Author(s):  
Javier Hidalgo ◽  
Myung Hwan Seo
Keyword(s):  
Regression Model ◽  
Asymptotic Distribution ◽  
Nuisance Parameters ◽  
Monte Carlo Experiment ◽  
Finite Sample ◽  
Omnibus Test ◽  
Unknown Parameters ◽  
Specification Tests ◽  
Image Position ◽  
Lattice Processes

We consider an omnibus test for the correct specification of the dynamics of a sequence $\left\{ {x\left( t \right)} \right\}_{t \in Z^d } $ in a lattice. As it happens with causal models and d = 1, its asymptotic distribution is not pivotal and depends on the estimator of the unknown parameters of the model under the null hypothesis. One first main goal of the paper is to provide a transformation to obtain an asymptotic distribution that is free of nuisance parameters. Secondly, we propose a bootstrap analog of the transformation and show its validity. Thirdly, we discuss the results when $\left\{ {x\left( t \right)} \right\}_{t \in Z^d } $ are the errors of a parametric regression model. As a by product, we also discuss the asymptotic normality of the least squares estimator of the parameters of the regression model under very mild conditions. Finally, we present a small Monte Carlo experiment to shed some light on the finite sample behavior of our test.

A Three-Dimensional Approach to Multistream Migration Modelling: Local-Level Flows in Hereford and Worcester

1993 ◽  
Vol 25 (9) ◽  
pp. 1279-1293 ◽  
Author(s):  
P Boyle
Keyword(s):  
Regression Model ◽  
Local Level ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Population Migration ◽  
Parameter Estimates ◽  
Dimensional Approach ◽  
Population Densities ◽  
Homogeneous Groups ◽  
Migration System

Population migration occurs for many reasons, or combinations of reasons. Subsequently, it is often useful to distinguish streams of migrants, within a given migration system, which are likely to exhibit similar characteristics in their pattern of search and choice of residential destination. This has often been achieved by using distance cutoffs to delimit the various flows into categories. In this paper, an approach is suggested which does not disaggregate migrant flows by distance criteria alone, but incorporates measures relating to the nature of the origins and of the destinations. Relatively homogeneous groups of migrants are therefore distinguished within the county of Hereford and Worcester with information from three dimensions rather than one. In comparison with a standard single-stream regression model this method improves the fit substantially, and the variability in the resulting parameter estimates for each of the eight streams supports the need for identification of distinct migrant streams. In particular, flows over short distances between wards with high population densities are estimated more effectively.

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