Nominal-Level Variables, I

2018 ◽  
pp. 73-138
Author(s):  
Kenneth J. Berry ◽  
Janis E. Johnston ◽  
Paul W. Mielke
Keyword(s):  
Nominal Level

Testing conditional moment restriction models using empirical likelihood

2021 ◽  
Author(s):  
Yves G Berger
Keyword(s):  
Empirical Likelihood ◽  
Model Specification ◽  
Ratio Test ◽  
Conditional Moment ◽  
Nominal Level ◽  
Empirical Likelihood Ratio Test ◽  
Likelihood Model ◽  
Heteroscedastic Errors ◽  
Endogenous Covariates ◽  
The Relationship

Abstract An empirical likelihood test is proposed for parameters of models defined by conditional moment restrictions, such as models with non-linear endogenous covariates, with or without heteroscedastic errors or non-separable transformation models. The number of empirical likelihood constraints is given by the size of the parameter, unlike alternative semi-parametric approaches. We show that the empirical likelihood ratio test is asymptotically pivotal, without explicit studentisation. A simulation study shows that the observed size is close to the nominal level, unlike alternative empirical likelihood approaches. It also offers a major advantages over two-stage least-squares, because the relationship between the endogenous and instrumental variables does not need to be known. An empirical likelihood model specification test is also proposed.

scholarly journals Inference Using Simulated Neural Moments

Econometrics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 35
Author(s):  
Michael Creel
Keyword(s):  
Neural Network ◽  
Confidence Intervals ◽  
Bayesian Methods ◽  
Jump Diffusion ◽  
Nominal Level ◽  
Method Of Simulated Moments ◽  
Mcmc Estimation ◽  
Test Models ◽  
Minimum Number ◽  
Jump Diffusion Model

This paper studies method of simulated moments (MSM) estimators that are implemented using Bayesian methods, specifically Markov chain Monte Carlo (MCMC). Motivation and theory for the methods is provided by Chernozhukov and Hong (2003). The paper shows, experimentally, that confidence intervals using these methods may have coverage which is far from the nominal level, a result which has parallels in the literature that studies overidentified GMM estimators. A neural network may be used to reduce the dimension of an initial set of moments to the minimum number that maintains identification, as in Creel (2017). When MSM-MCMC estimation and inference is based on such moments, and using a continuously updating criteria function, confidence intervals have statistically correct coverage in all cases studied. The methods are illustrated by application to several test models, including a small DSGE model, and to a jump-diffusion model for returns of the S&P 500 index.

scholarly journals A simple non-parametric goodness-of-fit test for elliptical copulas

2017 ◽  
Vol 5 (1) ◽  
pp. 330-353 ◽  
Author(s):  
Miriam Jaser ◽  
Stephan Haug ◽  
Aleksey Min
Keyword(s):  
Monte Carlo ◽  
Goodness Of Fit ◽  
Monte Carlo Study ◽  
Goodness Of Fit Test ◽  
Kendall’S Tau ◽  
Kendall's Tau ◽  
Nominal Level ◽  
Empirical Application ◽  
Non Parametric

AbstractIn this paper, we propose a simple non-parametric goodness-of-fit test for elliptical copulas of any dimension. It is based on the equality of Kendall’s tau and Blomqvist’s beta for all bivariate margins. Nominal level and power of the proposed test are investigated in a Monte Carlo study. An empirical application illustrates our goodness-of-fit test at work.

scholarly journals Bridging observational studies and randomized experiments by embedding the former in the latter

2017 ◽  
Vol 28 (7) ◽  
pp. 1958-1978 ◽  
Author(s):  
Marie-Abele C Bind ◽  
Donald B Rubin
Keyword(s):  
Statistical Analysis ◽  
Outcome Data ◽  
Design Stage ◽  
Randomized Experiment ◽  
Randomized Experiments ◽  
Causal Inferences ◽  
Data Set ◽  
Nominal Level ◽  
Point Estimates ◽  
Stage 1

Consider a statistical analysis that draws causal inferences from an observational dataset, inferences that are presented as being valid in the standard frequentist senses; i.e. the analysis produces: (1) consistent point estimates, (2) valid p-values, valid in the sense of rejecting true null hypotheses at the nominal level or less often, and/or (3) confidence intervals, which are presented as having at least their nominal coverage for their estimands. For the hypothetical validity of these statements, the analysis must embed the observational study in a hypothetical randomized experiment that created the observed data, or a subset of that hypothetical randomized data set. This multistage effort with thought-provoking tasks involves: (1) a purely conceptual stage that precisely formulate the causal question in terms of a hypothetical randomized experiment where the exposure is assigned to units; (2) a design stage that approximates a randomized experiment before any outcome data are observed, (3) a statistical analysis stage comparing the outcomes of interest in the exposed and non-exposed units of the hypothetical randomized experiment, and (4) a summary stage providing conclusions about statistical evidence for the sizes of possible causal effects. Stages 2 and 3 may rely on modern computing to implement the effort, whereas Stage 1 demands careful scientific argumentation to make the embedding plausible to scientific readers of the proffered statistical analysis. Otherwise, the resulting analysis is vulnerable to criticism for being simply a presentation of scientifically meaningless arithmetic calculations. The conceptually most demanding tasks are often the most scientifically interesting to the dedicated researcher and readers of the resulting statistical analyses. This perspective is rarely implemented with any rigor, for example, completely eschewing the first stage. We illustrate our approach using an example examining the effect of parental smoking on children’s lung function collected in families living in East Boston in the 1970s.

scholarly journals An Empirical Evaluation of a Test Procedure for the Median of Symmetrical and Asymmetrical Populations Using an Interpolated Nonparametric Confidence Interval

2020 ◽  
Vol 10 (1) ◽  
pp. 85
Author(s):  
Mohammad Ibrahim Ahmmad Soliman Gaafar
Keyword(s):  
Confidence Interval ◽  
Test Procedure ◽  
Empirical Evaluation ◽  
Empirical Power ◽  
Single Population ◽  
Nominal Level ◽  
Simulation Results ◽  
Heavy Tailed

This paper investigates, evaluates, and highlights the performance of a test procedure for the median of a single population using an old nonparametric interpolated confidence interval. Simulation results show that the test procedure under investigation strictly maintains the size at its nominal level and has generally higher empirical power under both symmetrical heavy-tailed and asymmetrical populations.

scholarly journals A new and intuitive test for zero modification

2018 ◽  
Vol 19 (4) ◽  
pp. 341-361 ◽  
Author(s):  
Paul Wilson ◽  
Jochen Einbeck
Keyword(s):  
Null Hypothesis ◽  
Statistical Tests ◽  
Ratio Test ◽  
Nominal Level ◽  
Number Of Zeros ◽  
Data Regression ◽  
Poisson Binomial Distribution ◽  
The Mean ◽  
Direct Use ◽  
Hybrid Estimator

Abstract: While there do exist several statistical tests for detecting zero modification in count data regression models, these rely on asymptotical results and do not transparently distinguish between zero inflation and zero deflation. In this manuscript, a novel non-asymptotic test is introduced which makes direct use of the fact that the distribution of the number of zeros under the null hypothesis of no zero modification can be described by a Poisson-binomial distribution. The computation of critical values from this distribution requires estimation of the mean parameter under the null hypothesis, for which a hybrid estimator involving a zero-truncated mean estimator is proposed. Power and nominal level attainment rates of the new test are studied, which turn out to be very competitive to those of the likelihood ratio test. Illustrative data examples are provided.

Chi-Square: A Test Commonly Used for Nominal-Level Measures

2020 ◽  
pp. 225-266
Author(s):  
David Weisburd ◽  
Chester Britt ◽  
David B. Wilson ◽  
Alese Wooditch
Keyword(s):  
Chi Square ◽  
Nominal Level

scholarly journals Simultaneous Inference on All Linear Combinations of Means with Heteroscedastic Errors

2011 ◽  
Vol 2011 ◽  
pp. 1-10
Author(s):  
Xin Yan ◽  
Xiaogang Su
Keyword(s):  
Confidence Intervals ◽  
Error Rate ◽  
Pairwise Comparisons ◽  
Simultaneous Inference ◽  
Familywise Error Rate ◽  
Linear Combinations ◽  
Simultaneous Confidence Intervals ◽  
Nominal Level ◽  
Equal Variance ◽  
Heteroscedastic Errors

We proposed a statistical method to construct simultaneous confidence intervals on all linear combinations of means without assuming equal variance where the classical Scheffé's simultaneous confidence intervals no longer preserve the familywise error rate (FWER). The proposed method is useful when the number of comparisons on linear combinations of means is extremely large. The FWERs for proposed simultaneous confidence intervals under various configurations of mean variances are assessed through simulations and are found to preserve the predefined nominal level very well. An example of pairwise comparisons on heteroscedastic means is given to illustrate the proposed method.

scholarly journals Globally Robust Confidence Intervals for Location

2012 ◽  
Vol 60 (1) ◽  
pp. 109-113 ◽  
Author(s):  
M Ershadul Haque ◽  
Jafar A Khan
Keyword(s):  
Sample Size ◽  
Confidence Intervals ◽  
Simulation Study ◽  
Nominal Level ◽  
Sampling Variability ◽  
Extensive Simulation ◽  
Robust Estimates ◽  
Point Estimates ◽  
Classical Inference ◽  
Method Show

Classical inference considers sampling variability to be the only source of uncertainty, and does not address the issue of bias caused by contamination. Naive robust intervals replace the classical estimates by their robust counterparts without considering the possible bias of the robust point estimates. Consequently, the asymptotic coverage proportion of these intervals of any nominal level will invariably tend to zero for any proportion of contamination.In this study, we attempt to achieve reasonable coverage percentages by constructing globally robust confidence intervals that adjust for the bias of the robust point estimates. We improve these globally robust intervals by considering the direction of the bias of the robust estimates used. We compare the proposed intervals with the existing ones through an extensive simulation study. The proposed methods have reasonable coverage percentage while the existing method show very poor coverage as sample size increases.DOI: http://dx.doi.org/10.3329/dujs.v60i1.10347  Dhaka Univ. J. Sci. 60(1): 109-113 2012 (January)

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