scholarly journals Optimal Detection of Bilinear Dependence in Short Panels of Regression Data

2020 ◽  
Vol 43 (2) ◽  
pp. 143-171
Author(s):  
Aziz Lmakri ◽  
Abdelhadi Akharif ◽  
Amal Mellouk
Keyword(s):  
Null Hypothesis ◽  
Regression Models ◽  
Scale Parameter ◽  
Regression Coefficient ◽  
Monte Carlo Study ◽  
Test Statistics ◽  
Bilinear Model ◽  
Large N ◽  
Optimal Tests ◽  
Error Terms

In this paper, we propose parametric and nonparametric locally andasymptotically optimal tests for regression models with superdiagonal bilinear time series errors in short panel data (large n, small T). We establish a local asymptotic normality property– with respect to intercept μ, regression coefficient β, the scale parameter σ of the error, and the parameter b of panel superdiagonal bilinear model (which is the parameter of interest)– for a given density f1 of the error terms. Rank-based versions of optimal parametric tests are provided. This result, which allows, by Hájek’s representation theorem, the construction of locally asymptotically optimal rank-based tests for the null hypothesis b = 0 (absence of panel superdiagonal bilinear model). These tests –at specified innovation densities f1– are optimal (most stringent), but remain valid under any actual underlying density. From contiguity, we obtain the limiting distribution of our test statistics under the null and local sequences of alternatives. The asymptotic relative efficiencies, with respect to the pseudo-Gaussian parametric tests, are derived. A Monte Carlo study confirms the good performance of the proposed tests.

Test Statistics for Simple MARKOV Chains. A Monte Carlo Study

1978 ◽  
Vol 20 (1) ◽  
pp. 41-49 ◽  
Author(s):  
Fritz K. Bedall
Keyword(s):  
Monte Carlo ◽  
Markov Chains ◽  
Monte Carlo Study ◽  
Test Statistics

scholarly journals Robust Statistical Inference in Generalized Linear Models Based on Minimum Renyi’s Pseudodistance Estimators

Entropy ◽  
2022 ◽  
Vol 24 (1) ◽  
pp. 123
Author(s):  
María Jaenada ◽  
Leandro Pardo
Keyword(s):  
Generalized Linear Models ◽  
Influence Function ◽  
Regression Models ◽  
Linear Models ◽  
Asymptotic Properties ◽  
Significant Loss ◽  
Superior Performance ◽  
Test Statistics ◽  
Linear Regression Models ◽  
Type Test

Minimum Renyi’s pseudodistance estimators (MRPEs) enjoy good robustness properties without a significant loss of efficiency in general statistical models, and, in particular, for linear regression models (LRMs). In this line, Castilla et al. considered robust Wald-type test statistics in LRMs based on these MRPEs. In this paper, we extend the theory of MRPEs to Generalized Linear Models (GLMs) using independent and nonidentically distributed observations (INIDO). We derive asymptotic properties of the proposed estimators and analyze their influence function to asses their robustness properties. Additionally, we define robust Wald-type test statistics for testing linear hypothesis and theoretically study their asymptotic distribution, as well as their influence function. The performance of the proposed MRPEs and Wald-type test statistics are empirically examined for the Poisson Regression models through a simulation study, focusing on their robustness properties. We finally test the proposed methods in a real dataset related to the treatment of epilepsy, illustrating the superior performance of the robust MRPEs as well as Wald-type tests.

Evaluating the Statistical Significance of Models Developed by Stepwise Regression

1983 ◽  
Vol 20 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Shelby H. McIntyre ◽  
David B. Montgomery ◽  
V. Srinivasan ◽  
Barton A. Weitz
Keyword(s):  
Monte Carlo ◽  
Null Hypothesis ◽  
Regression Models ◽  
Stepwise Regression ◽  
Statistical Significance ◽  
Selection Procedure ◽  
Coefficient Of Determination ◽  
Forward Selection ◽  
Monte Carlo Simulation Study ◽  
Independent Variables

Information for evaluating the statistical significance of stepwise regression models developed with a forward selection procedure is presented. Cumulative distributions of the adjusted coefficient of determination ([Formula: see text]) under the null hypothesis of no relationship between the dependent variable and m potential independent variables are derived from a Monté Carlo simulation study. The study design included sample sizes of 25, 50, and 100, available independent variables of 10, 20, and 40, and three criteria for including variables in the regression model. The results reveal that the biases involved in testing statistical significance by two well-known rules are very large, thus demonstrating the desirability of using the Monté Carlo cumulative [Formula: see text] distributions developed by the authors. Although the results were derived under the assumption of uncorrelated predictors, the authors show that the results continue to be useful for the correlated predictor case.

TESTING CHAOS OF TIME SERIES: PORTMANTEAU STATISTICS UNDER AN ORDER TRANSFORMATION

2001 ◽  
Vol 11 (06) ◽  
pp. 1761-1769 ◽  
Author(s):  
DEJIAN LAI
Keyword(s):  
Time Series ◽  
Null Hypothesis ◽  
Random Variable ◽  
Asymptotic Distributions ◽  
Test Statistics ◽  
Chi Square ◽  
Gaussian Series ◽  
Low Dimensional ◽  
Portmanteau Statistics ◽  
Direct Use

This paper studies several portmanteau test statistics with a nonparametric order transformation for distinguishing independent and identically distributed (i.i.d.) random processes from noisy chaotic time series. These portmanteau test statistics are asymptotically distributed as a chi-square random variable under the null hypothesis of i.i.d. Gaussian series. In this Letter, we show that the asymptotic distributions of these portmanteau test statistics on the transformed series are still chi-square under the null hypothesis. The simulations indicate that direct use of these portmanteau test statistics yields low power in identifying chaos. However, with the proposed order transformation, the simulations show that these test statistics are still effective for identifying noisy low dimensional chaos in some cases.

Penalized regression models with autoregressive error terms

2013 ◽  
Vol 83 (9) ◽  
pp. 1756-1772 ◽  
Author(s):  
Young Joo Yoon ◽  
Cheolwoo Park ◽  
Taewook Lee
Keyword(s):  
Regression Models ◽  
Penalized Regression ◽  
Error Terms
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