scholarly journals Penaksiran Parameter dan Pengujian Hipotesis Model Regresi Weibull Univariat

2017 ◽  
Vol 8 (2) ◽  
pp. 179 ◽  
Author(s):  
Suyitno Suyitno
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Regression Model ◽  
Likelihood Ratio ◽  
Model Parameters ◽  
Ratio Test ◽  
Test Statistic ◽  
Chi Square ◽  
Weibull Regression ◽  
Regression Parameters

In this study, a univariate Weibull regression model is discussed. The Weibull regression is a regression model developed from the Weibull distribution, that is the Weibull distribution depending on the covariates or the regression parameters. The univariate Weibull regression (UWR) model can involve the survival function model and the mean model of the response variable with the scale parameter stated in the terms of the regression parameters. The aim of this study is to estimate the UWR model parameters using the maximum likelihood estimation (MLE) method, and to test the regression parameters. The result shows that the closed form of the maximum likelihood estimator can not be found analytically, and it can be approximed by using the Newton-Raphson iterative method. The regression parameters testing involves simultaneous and partial test. The test statistic for simultaneous test is Wilk's likelihood ratio. Wilk statistic follows Chi-square distribution, which can be derived from the likelihood ratio test (LRT) method. The test statistic for partial test is Wald and it follows standard normal distribution. The alternative test statistik for partial test is squared of Wald statistic, where it follows Chi-square distribution with one degree of freedom.

scholarly journals A New Quantile Regression Model and Its Diagnostic Analytics for a Weibull Distributed Response with Applications

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2768
Author(s):  
Luis Sánchez ◽  
Víctor Leiva ◽  
Helton Saulo ◽  
Carolina Marchant ◽  
José M. Sarabia
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Quantile Regression ◽  
Regression Model ◽  
Likelihood Method ◽  
Model Parameters ◽  
Distributed Data ◽  
Quantile Regression Model ◽  
The Mean ◽  
Asymmetrically Distributed

Standard regression models focus on the mean response based on covariates. Quantile regression describes the quantile for a response conditioned to values of covariates. The relevance of quantile regression is even greater when the response follows an asymmetrical distribution. This relevance is because the mean is not a good centrality measure to resume asymmetrically distributed data. In such a scenario, the median is a better measure of the central tendency. Quantile regression, which includes median modeling, is a better alternative to describe asymmetrically distributed data. The Weibull distribution is asymmetrical, has positive support, and has been extensively studied. In this work, we propose a new approach to quantile regression based on the Weibull distribution parameterized by its quantiles. We estimate the model parameters using the maximum likelihood method, discuss their asymptotic properties, and develop hypothesis tests. Two types of residuals are presented to evaluate the model fitting to data. We conduct Monte Carlo simulations to assess the performance of the maximum likelihood estimators and residuals. Local influence techniques are also derived to analyze the impact of perturbations on the estimated parameters, allowing us to detect potentially influential observations. We apply the obtained results to a real-world data set to show how helpful this type of quantile regression model is.

scholarly journals Anti-clutter Gaussian Inverse Wishart PHD Filter for Extended Target Tracking

Sensors ◽  
2019 ◽  
Vol 19 (23) ◽  
pp. 5140
Author(s):  
Yuan Huang ◽  
Liping Wang ◽  
Xueying Wang ◽  
Wei An
Keyword(s):  
Hypothesis Testing ◽  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Likelihood Ratio Test Statistic ◽  
Ratio Test ◽  
Test Statistic ◽  
Chi Square ◽  
Probability Hypothesis Density ◽  
Extended Target ◽  
Correction Step

The extended target Gaussian inverse Wishart probability hypothesis density (ET-GIW-PHD) filter overestimates the number of targets under high clutter density. The reason for this is that the source of measurements cannot be determined correctly if only the number of measurements is used. To address this problem, we proposed an anti-clutter filter with hypothesis testing, we take into account the number of measurements in cells, the target state and spatial distribution of clutter to decide whether the measurements in cell are clutter. Specifically, the hypothesis testing method is adopted to determine the origination of the measurements. Then, the likelihood functions of targets and clutter are deduced based on the information mentioned above, resulting in the likelihood ratio test statistic. Next, the likelihood ratio test statistic is proved to be subject to a chi-square distribution and a threshold corresponding to the confidence coefficient is introduced and the measurements below this threshold are considered as clutter. Then the correction step of ET-GIW-PHD is revised based on hypothesis testing results. Extensive experiments have demonstrated the significant performance improvement of our proposed method.

scholarly journals Parameter estimation and hypothesis testing of geographically and temporally weighted bivariate Gamma regression model

2021 ◽  
Vol 880 (1) ◽  
pp. 012044
Author(s):  
Desy Wasani ◽  
Purhadi ◽  
Sutikno
Keyword(s):  
Maximum Likelihood ◽  
Panel Data ◽  
Gamma Distribution ◽  
Likelihood Estimation ◽  
Complete Information ◽  
Model Parameters ◽  
Large Sample Size ◽  
Ratio Test ◽  
Spatial Effects ◽  
Test Statistic

Abstract Geographically Weighted Regression (GWR) study potential relationships in regression models that distinguish geographic spaces using non-stationary parameters to overcome spatial effects. The use of gamma regression, namely regression with the dependent variable with a gamma distribution, can be an alternative if the data do not follow a normal distribution. Gamma distribution is a continuous set of non-negative values, generally skewed to the right or positive skewness. Gamma regression is developed to be Bivariate Gamma Regression (BGR) when there are two dependent variables with gamma distribution. If the observation units are location points, spatial effects may occur. The Geographically Weighted Bivariate Gamma Regression (GWBGR) model can be a solution for spatial heterogeneity. However, during its development, many cases require information from panel data. Using panel data can provide complete information because it covers several periods, but it allows for temporal effects. This study developed a Geographically and Temporally Weighted Bivariate Gamma Regression (GTWBGR) model to handle spatial and temporal heterogeneity simultaneously. The estimation of the GTWBGR model parameters uses the Maximum Likelihood Estimation (MLE) method that followed by the numerical iteration of Berndt Hall Hall Hausman (BHHH). The simultaneous testing uses the Maximum Likelihood Ratio Test (MLRT) method to get a test statistic. With a large sample size, the distribution of the test statistic approaches chi-square. Meanwhile, partial testing uses the Z test statistic.

A Note on the Asymptotic Distribution of Likelihood Ratio Tests to Test Variance Components

2006 ◽  
Vol 9 (4) ◽  
pp. 490-495 ◽  
Author(s):  
Peter M. Visscher
Keyword(s):  
Maximum Likelihood ◽  
Asymptotic Distribution ◽  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Variance Components ◽  
Degrees Of Freedom ◽  
Likelihood Ratio Tests ◽  
Likelihood Ratio Test Statistic ◽  
Ratio Test ◽  
Test Statistic

AbstractWhen using maximum likelihood methods to estimate genetic and environmental components of (co)variance, it is common to test hypotheses using likelihood ratio tests, since such tests have desirable asymptotic properties. In particular, the standard likelihood ratio test statistic is assumed asymptotically to follow a χ2 distribution with degrees of freedom equal to the number of parameters tested. Using the relationship between least squares and maximum likelihood estimators for balanced designs, it is shown why the asymptotic distribution of the likelihood ratio test for variance components does not follow a χ2 distribution with degrees of freedom equal to the number of parameters tested when the null hypothesis is true. Instead, the distribution of the likelihood ratio test is a mixture of χ2 distributions with different degrees of freedom. Implications for testing variance components in twin designs and for quantitative trait loci mapping are discussed. The appropriate distribution of the likelihood ratio test statistic should be used in hypothesis testing and model selection.

scholarly journals Detecting Differential Item Functioning Using the Logistic Regression Procedure in Small Samples

2016 ◽  
Vol 41 (1) ◽  
pp. 30-43 ◽  
Author(s):  
Sunbok Lee
Keyword(s):  
Logistic Regression ◽  
Maximum Likelihood ◽  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Wald Test ◽  
Small Samples ◽  
Ratio Test ◽  
Chi Square ◽  
Ml Estimation ◽  
Item Functioning

The logistic regression (LR) procedure for testing differential item functioning (DIF) typically depends on the asymptotic sampling distributions. The likelihood ratio test (LRT) usually relies on the asymptotic chi-square distribution. Also, the Wald test is typically based on the asymptotic normality of the maximum likelihood (ML) estimation, and the Wald statistic is tested using the asymptotic chi-square distribution. However, in small samples, the asymptotic assumptions may not work well. The penalized maximum likelihood (PML) estimation removes the first-order finite sample bias from the ML estimation, and the bootstrap method constructs the empirical sampling distribution. This study compares the performances of the LR procedures based on the LRT, Wald test, penalized likelihood ratio test (PLRT), and bootstrap likelihood ratio test (BLRT) in terms of the statistical power and type I error for testing uniform and non-uniform DIF. The result of the simulation study shows that the LRT with the asymptotic chi-square distribution works well even in small samples.

EXACT PROPERTIES OF THE CONDITIONAL LIKELIHOOD RATIO TEST IN AN IV REGRESSION MODEL

2009 ◽  
Vol 25 (4) ◽  
pp. 915-957 ◽  
Author(s):  
Grant Hillier
Keyword(s):  
Distribution Function ◽  
Regression Model ◽  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Critical Value ◽  
The Other ◽  
Ratio Test ◽  
Conditional Likelihood ◽  
Power Functions ◽  
Test Statistic

For a simplified structural equation/IV regression model with one right-side endogenous variable, we derive the exact conditional distribution function of Moreira's (2003) conditional likelihood ratio (CLR) test statistic. This is used to obtain the critical value function needed to implement the CLR test, and reasonably comprehensive graphical versions of this function are provided for practical use. The analogous functions are also obtained for the case of testing more than one right-side endogenous coefficient, but in this case for a similar test motivated by, but not generally the same as, the likelihood ratio test. Next, the exact power functions of the CLR test, the Anderson-Rubin test, and the Lagrange multiplier test suggested by Kleibergen (2002) are derived and studied. The CLR test is shown to clearly conditionally dominate the other two tests for virtually all parameter configurations, but no test considered is either inadmissable or uniformly superior to the other two. The unconditional distribution function of the likelihood ratio test statistic is also derived using the same argument. This shows that both exactly, and under Staiger/Stock weak-instrument asymptotics, the test based on the usual asymptotic critical value is always oversized and can be very seriously so when the number of instruments is large.

scholarly journals Regresi Logistik untuk Pemodelan Indeks Pembangunan Kesehatan Masyarakat Kabupaten/Kota di Pulau Kalimantan

2018 ◽  
Author(s):  
Muhammad Fathurahman
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Likelihood Estimation ◽  
Ratio Test ◽  
Chi Square ◽  
Fisher Scoring

Regresi logistik merupakan model regresi yang paling sering digunakan untuk pemodelan data kategorik. Pada penelitian ini dilakukan pemodelan regresi logistik dan penerapannya pada Indeks Pembangunan Kesehatan Masyarakat (IPKM) kabupaten/kota di Pulau Kalimantan tahun 2013. Metode Maximum Likelihood Estimation (MLE) digunakan untuk penaksiran parameter. Metode Likelihood Ratio Test (LRT) dan uji Wald digunakan untuk pengujian parameter. Hasil penelitian menunjukkan bahwa penaksir parameter dengan metode MLE berbentuk fungsi yang tidak eksplisit. Sehingga digunakan pendekatan numerik dengan metode Fisher Scoring. Berdasarkan metode LRT dan uji Wald, statistik uji untuk pengujian parameter mendekati distribusi chi-square dan distribusi normal standar. Berdasarkan model regresi logistik terbaik, faktor-faktor yang berpengaruh terhadap IPKM kabupaten/kota di Pulau Kalimantan tahun 2013 adalah Indeks Pembangunan Manusia (IPM), tingkat kepadatan penduduk dan persentase penduduk miskin.

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