scholarly journals The Empirical Cressie-Read Test Statistics for Longitudinal Generalized Linear Models

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Junhua Zhang ◽  
Ruiqin Tian ◽  
Suigen Yang ◽  
Sanying Feng
Keyword(s):  
Generalized Linear Models ◽  
Correlation Matrix ◽  
Linear Models ◽  
Real Data ◽  
Regularity Conditions ◽  
Finite Sample ◽  
Test Statistic ◽  
Quadratic Inference Function ◽  
Working Correlation ◽  
Statistic Approach

For the marginal longitudinal generalized linear models (GLMs), we develop the empirical Cressie-Read (ECR) test statistic approach which has been proposed for the independent identically distributed (i.i.d.) case. The ECR test statistic includes empirical likelihood as a special case. By adopting this ECR test statistic approach and taking into account the within-subject correlation, the efficiency theory results of estimation and testing based on ECR are established under some regularity conditions. Although a working correlation matrix is assumed, there is no need to estimate the nuisance parameters in the working correlation matrix based on the quadratic inference function (QIF). Therefore, the proposed ECR test statistic is asymptotically a standardχ2limit under the null hypothesis. It is shown that the proposed method is more efficient even when the working correlation matrix is misspecified. We also evaluate the finite sample performance of the proposed methods via simulation studies and a real data analysis.

scholarly journals Penalized Quadratic Inference Function-Based Variable Selection for Generalized Partially Linear Varying Coefficient Models with Longitudinal Data

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Jinghua Zhang ◽  
Liugen Xue
Keyword(s):  
Variable Selection ◽  
Longitudinal Data ◽  
Linear Models ◽  
Selection Procedure ◽  
Real Data ◽  
Finite Sample ◽  
Varying Coefficient ◽  
Partially Linear ◽  
Quadratic Inference Function ◽  
Quadratic Inference Functions

Semiparametric generalized varying coefficient partially linear models with longitudinal data arise in contemporary biology, medicine, and life science. In this paper, we consider a variable selection procedure based on the combination of the basis function approximations and quadratic inference functions with SCAD penalty. The proposed procedure simultaneously selects significant variables in the parametric components and the nonparametric components. With appropriate selection of the tuning parameters, we establish the consistency, sparsity, and asymptotic normality of the resulting estimators. The finite sample performance of the proposed methods is evaluated through extensive simulation studies and a real data analysis.

scholarly journals Testing for treatment effect in covariate-adaptive randomized trials with generalized linear models and omitted covariates

2021 ◽  
pp. 096228022110082
Author(s):  
Yang Li ◽  
Wei Ma ◽  
Yichen Qin ◽  
Feifang Hu
Keyword(s):  
Generalized Linear Models ◽  
Treatment Effect ◽  
Linear Models ◽  
Type I Error ◽  
Type I ◽  
Test Statistic ◽  
Asymptotic Results ◽  
Adaptive Randomization ◽  
Adjustment Method ◽  
Inflated Type

Concerns have been expressed over the validity of statistical inference under covariate-adaptive randomization despite the extensive use in clinical trials. In the literature, the inferential properties under covariate-adaptive randomization have been mainly studied for continuous responses; in particular, it is well known that the usual two-sample t-test for treatment effect is typically conservative. This phenomenon of invalid tests has also been found for generalized linear models without adjusting for the covariates and are sometimes more worrisome due to inflated Type I error. The purpose of this study is to examine the unadjusted test for treatment effect under generalized linear models and covariate-adaptive randomization. For a large class of covariate-adaptive randomization methods, we obtain the asymptotic distribution of the test statistic under the null hypothesis and derive the conditions under which the test is conservative, valid, or anti-conservative. Several commonly used generalized linear models, such as logistic regression and Poisson regression, are discussed in detail. An adjustment method is also proposed to achieve a valid size based on the asymptotic results. Numerical studies confirm the theoretical findings and demonstrate the effectiveness of the proposed adjustment method.

scholarly journals Monitoring Persistence Change in Heavy-Tailed Observations

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 936
Author(s):  
Dan Wang
Keyword(s):  
Kernel Method ◽  
Alternative Hypothesis ◽  
Null Distribution ◽  
Real Data ◽  
Ratio Test ◽  
Finite Sample ◽  
Test Statistic ◽  
Bootstrap Approximation ◽  
Heavy Tailed ◽  
Better Than

In this paper, a ratio test based on bootstrap approximation is proposed to detect the persistence change in heavy-tailed observations. This paper focuses on the symmetry testing problems of I(1)-to-I(0) and I(0)-to-I(1). On the basis of residual CUSUM, the test statistic is constructed in a ratio form. I prove the null distribution of the test statistic. The consistency under alternative hypothesis is also discussed. However, the null distribution of the test statistic contains an unknown tail index. To address this challenge, I present a bootstrap approximation method for determining the rejection region of this test. Simulation studies of artificial data are conducted to assess the finite sample performance, which shows that our method is better than the kernel method in all listed cases. The analysis of real data also demonstrates the excellent performance of this method.

PERFORMANCE OF MIXED EFFECTS FOR CLUSTERED COUNTING DATA MODELS

2020 ◽  
Vol 3 (2) ◽  
pp. 34-41
Author(s):  
Intesar N. El-Saeiti ◽  
Khalil Mostafa ALsawi
Keyword(s):  
Generalized Linear Models ◽  
Standard Error ◽  
Mixed Models ◽  
Linear Models ◽  
Generalized Linear Mixed Models ◽  
Linear Mixed Models ◽  
Likelihood Estimation ◽  
Real Data ◽  
Estimation Technique ◽  
Counting Data

This article is concerned with hierarchical generalized linear models. It includes generalized linear models and generalized linear mixed models, which are related to linear models. In generalized linear mixed models, the dependent variable and the standard error follow any distribution from the exponential family, e.g. normal, Poisson, binomial, gamma, etc. We studied counting data, and then use the Poisson-gamma model,where the dependentvariable follows the Poisson distribution and the standard error follow the gamma distribution. Several estimation techniques can be used for generalized linear mixed model. In this paperthe hierarchical likelihood estimation technique was used to prove the performance of H-likelihood methodwhen thecounting data were balanced or unbalanced. Real data were used to test the performance of Poisson-gamma H-likelihood estimation method in case of balanced and unbalanced counting data.When real data used in the past research for another problem, it was noticed that the performance of the hierarchical likelihood estimation technique gave a close approximations in the event of balanced and unbalanced counting data, and the output of the technique was approximately equivalent in both instances.

scholarly journals TESTING FOR A GENERAL CLASS OF FUNCTIONAL INEQUALITIES

2017 ◽  
Vol 34 (5) ◽  
pp. 1018-1064 ◽  
Author(s):  
Sokbae Lee ◽  
Kyungchul Song ◽  
Yoon-Jae Whang
Keyword(s):  
Wage Inequality ◽  
Bootstrap Method ◽  
Real Data ◽  
Regularity Conditions ◽  
Revealed Preferences ◽  
Unified Framework ◽  
Test Statistic ◽  
Nonparametric Bootstrap ◽  
Bootstrap Test ◽  
Auction Models

In this article, we propose a general method for testing inequality restrictions on nonparametric functions. Our framework includes many nonparametric testing problems in a unified framework, with a number of possible applications in auction models, game theoretic models, wage inequality, and revealed preferences. Our test involves a one-sided version ofLpfunctionals of kernel-type estimators (1 ≤p < ∞) and is easy to implement in general, mainly due to its recourse to the bootstrap method. The bootstrap procedure is based on the nonparametric bootstrap applied to kernel-based test statistics, with an option of estimating “contact sets.” We provide regularity conditions under which the bootstrap test is asymptotically valid uniformly over a large class of distributions, including cases where the limiting distribution of the test statistic is degenerate. Our bootstrap test is shown to exhibit good power properties in Monte Carlo experiments, and we provide a general form of the local power function. As an illustration, we consider testing implications from auction theory, provide primitive conditions for our test, and demonstrate its usefulness by applying our test to real data. We supplement this example with the second empirical illustration in the context of wage inequality.

scholarly journals TESTING FOR NEGLECTED NONLINEARITY USING EXTREME LEARNING MACHINES

2013 ◽  
Vol 21 (supp02) ◽  
pp. 117-129
Author(s):  
KYULEE SHIN ◽  
JIN SEO CHO
Keyword(s):  
Monte Carlo ◽  
Sample Size ◽  
Linear Models ◽  
Regularity Conditions ◽  
Extreme Learning Machines ◽  
Test Statistic ◽  
Learning Machines ◽  
Monte Carlo Experiments ◽  
Chi Squared ◽  
Chi Squared Distribution

We introduce a statistic testing for neglected nonlinearity using extreme learning machines and call it ELMNN test. The ELMNN test is very convenient and can be widely applied because it is obtained as a by-product of estimating linear models. For the proposed test statistic, we provide a set of regularity conditions under which it asymptotically follows a chi-squared distribution under the null. We conduct Monte Carlo experiments and examine how it behaves when the sample size is finite. Our experiment shows that the test exhibits the properties desired by our theory.

Generalized Estimating Equations

2010 ◽  
Vol 49 (05) ◽  
pp. 421-425 ◽  
Author(s):  
M. Vens ◽  
A. Ziegler
Keyword(s):  
Correlation Matrix ◽  
Generalized Estimating Equations ◽  
Linear Models ◽  
Estimating Equations ◽  
Optimal Choice ◽  
Range Restriction ◽  
Dependent Variables ◽  
Mean Structure ◽  
Working Correlation ◽  
Generalized Estimating

Summary Background: Generalized estimating equations (GEE) are an extension of generalized linear models (GLM) in that they allow adjusting for correlations between observations. A major strength of GEE is that they do not require the correct specification of the multivariate distribution but only of the mean structure. Objectives: Several concerns have been raised about the validity of GEE when applied to dichotomous dependent variables. In this contribution, we summarize the theoretical findings concerning efficiency and validity of GEE. Methods: We introduce the GEE in a formal way, summarize general findings on the choice of the working correlation matrix, and show the existence of a dilemma for the optimal choice of the working correlation matrix for dichotomous dependent variables. Results: Biological and statistical arguments for choosing a specific working correlation matrix are given. Three approaches are described for overcoming the range restriction of the correlation coefficient. Conclusions: The three approaches described in this article for overcoming the range restrictions for dichotomous dependent variables in GEE models provide a simple and practical way for use in applications.

scholarly journals Instability and change detection in exponential families and generalized linear models, with a study of Atlantic tropical storms

2014 ◽  
Vol 1 (1) ◽  
pp. 371-401
Author(s):  
Y. Lu ◽  
S. Chatterjee
Keyword(s):  
Change Detection ◽  
Generalized Linear Models ◽  
Exponential Family ◽  
Linear Models ◽  
Exponential Families ◽  
Tropical Storms ◽  
Ratio Test ◽  
Test Statistic ◽  
Distributional Assumption ◽  
Data Collection Process

Abstract. Exponential family statistical distributions, including the well-known Normal, Binomial, Poisson, and exponential distributions, are overwhelmingly used in data analysis. In the presence of covariates, an exponential family distributional assumption for the response random variables results in a generalized linear model. However, it is rarely ensured that the parameters of the assumed distributions are stable through the entire duration of data collection process. A failure of stability leads to nonsmoothness and nonlinearity in the physical processes that drive the data under. In this paper, we propose testing for stability of parameters of exponential family distributions and generalized linear models. A rejection of the hypothesis of stable parameters leads to change detection. We derive the related likelihood ratio test statistic. We compare the performance of this test statistic to the popular Normal distributional assumption dependent cumulative sum (Gaussian-CUSUM) statistic in change detection problems. We study Atlantic tropical storms using the techniques developed here, to understand whether the nature of these tropical storms has remained stable over the last few decades.

scholarly journals Fisher information exponential dispersion family and applications

2013 ◽  
Vol 29 (2) ◽  
pp. 209-216
Author(s):  
ION MIHOC ◽  
◽  
CRISTINA-IOANA FATU ◽  
Keyword(s):  
Fisher Information ◽  
Generalized Linear Models ◽  
Exponential Family ◽  
Linear Models ◽  
Regularity Conditions

In this article we discuss some aspects of the Fisher information, under certain regularity conditions, then we have in view a very important exponential family, namely, the exponential dispersion family. Also, we study some implications of this last family in the case of the univaried generalized linear models.

scholarly journals Instability and change detection in exponential families and generalized linear models, with a study of Atlantic tropical storms

2014 ◽  
Vol 21 (6) ◽  
pp. 1133-1143
Author(s):  
Y. Lu ◽  
S. Chatterjee
Keyword(s):  
Change Detection ◽  
Generalized Linear Models ◽  
Exponential Family ◽  
Linear Models ◽  
Exponential Families ◽  
Tropical Storms ◽  
Ratio Test ◽  
Test Statistic ◽  
Distributional Assumption ◽  
Data Collection Process

Abstract. Exponential family statistical distributions, including the well-known normal, binomial, Poisson, and exponential distributions, are overwhelmingly used in data analysis. In the presence of covariates, an exponential family distributional assumption for the response random variables results in a generalized linear model. However, it is rarely ensured that the parameters of the assumed distributions are stable through the entire duration of the data collection process. A failure of stability leads to nonsmoothness and nonlinearity in the physical processes that result in the data. In this paper, we propose testing for stability of parameters of exponential family distributions and generalized linear models. A rejection of the hypothesis of stable parameters leads to change detection. We derive the related likelihood ratio test statistic. We compare the performance of this test statistic to the popular normal distributional assumption dependent cumulative sum (Gaussian CUSUM) statistic in change detection problems. We study Atlantic tropical storms using the techniques developed here, so to understand whether the nature of these tropical storms has remained stable over the last few decades.

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