Robust inference from multiple test statistics via permutations: a better alternative to the single test statistic approach for randomized trials

2013 ◽  
Vol 12 (5) ◽  
pp. 282-290 ◽  
Author(s):  
Jitendra Ganju ◽  
Xinxin Yu ◽  
Guoguang Julie Ma
Keyword(s):  
Randomized Trials ◽  
Robust Inference ◽  
Test Statistics ◽  
Single Test ◽  
Test Statistic ◽  
Multiple Test ◽  
Statistic Approach

scholarly journals Confidence intervals for policy evaluation in adaptive experiments

2021 ◽  
Vol 118 (15) ◽  
pp. e2014602118
Author(s):  
Vitor Hadad ◽  
David A. Hirshberg ◽  
Ruohan Zhan ◽  
Stefan Wager ◽  
Susan Athey
Keyword(s):  
Randomized Trials ◽  
Mean Squared Error ◽  
Test Statistics ◽  
Test Statistic ◽  
Asymptotically Normal ◽  
Squared Error ◽  
Normal Test ◽  
Weighted Means ◽  
Heavy Tailed ◽  
Inverse Propensity Weighting

Adaptive experimental designs can dramatically improve efficiency in randomized trials. But with adaptively collected data, common estimators based on sample means and inverse propensity-weighted means can be biased or heavy-tailed. This poses statistical challenges, in particular when the experimenter would like to test hypotheses about parameters that were not targeted by the data-collection mechanism. In this paper, we present a class of test statistics that can handle these challenges. Our approach is to adaptively reweight the terms of an augmented inverse propensity-weighting estimator to control the contribution of each term to the estimator’s variance. This scheme reduces overall variance and yields an asymptotically normal test statistic. We validate the accuracy of the resulting estimates and their CIs in numerical experiments and show that our methods compare favorably to existing alternatives in terms of mean squared error, coverage, and CI size.

OPTIMALITY FOR THE INTEGRATED CONDITIONAL MOMENT TEST

1999 ◽  
Vol 15 (5) ◽  
pp. 710-718 ◽  
Author(s):  
Wm. Brent Boning ◽  
Fallaw Sowell
Keyword(s):  
Function Space ◽  
Random Function ◽  
Test Statistics ◽  
Single Test ◽  
Test Statistic ◽  
Conditional Moment ◽  
Conditional Mean ◽  
Basis Element

This paper proposes a version of the integrated conditional moment (ICM) test that is optimal for a class of composite alternatives. The ICM test is built on the fact that a random function based on a correctly specified model should have zero mean, whereas any misspecification in the conditional mean implies a divergent mean for the random function. We derive test statistics that are optimal for each basis element of an orthonormal decomposition of the function space for which the random function is an element. We then use a weighted summation of these test statistics to compose the single test statistic that is optimal for any pair of alternatives that are symmetric about zero. This test is equivalent to using a particular measure in the ICM test of Bierens and Ploberger (1997, Econometrica 65, 1129–1152).

scholarly journals Effects of kinship correction on inflation of genetic interaction statistics in commonly used mouse populations

2021 ◽  
Author(s):  
Anna L Tyler ◽  
Baha El Kassaby ◽  
Georgi Kolishovski ◽  
Jake Emerson ◽  
Ann E Wells ◽  
...  
Keyword(s):  
Mixed Model ◽  
Linear Mixed Model ◽  
Genetic Interaction ◽  
Recombinant Inbred Lines ◽  
Test Statistics ◽  
Test Statistic ◽  
Kinship Matrix ◽  
Main Effect ◽  
Main Effects ◽  
Interaction Test

Abstract It is well understood that variation in relatedness among individuals, or kinship, can lead to false genetic associations. Multiple methods have been developed to adjust for kinship while maintaining power to detect true associations. However, relatively unstudied, are the effects of kinship on genetic interaction test statistics. Here we performed a survey of kinship effects on studies of six commonly used mouse populations. We measured inflation of main effect test statistics, genetic interaction test statistics, and interaction test statistics reparametrized by the Combined Analysis of Pleiotropy and Epistasis (CAPE). We also performed linear mixed model (LMM) kinship corrections using two types of kinship matrix: an overall kinship matrix calculated from the full set of genotyped markers, and a reduced kinship matrix, which left out markers on the chromosome(s) being tested. We found that test statistic inflation varied across populations and was driven largely by linkage disequilibrium. In contrast, there was no observable inflation in the genetic interaction test statistics. CAPE statistics were inflated at a level in between that of the main effects and the interaction effects. The overall kinship matrix overcorrected the inflation of main effect statistics relative to the reduced kinship matrix. The two types of kinship matrices had similar effects on the interaction statistics and CAPE statistics, although the overall kinship matrix trended toward a more severe correction. In conclusion, we recommend using a LMM kinship correction for both main effects and genetic interactions and further recommend that the kinship matrix be calculated from a reduced set of markers in which the chromosomes being tested are omitted from the calculation. This is particularly important in populations with substantial population structure, such as recombinant inbred lines in which genomic replicates are used.

A test for fuzzy exponentiality based on Kullback-Leibler information

2021 ◽  
pp. 1-8
Author(s):  
Lingtao Kong
Keyword(s):  
Biological Sciences ◽  
Monte Carlo ◽  
Goodness Of Fit ◽  
Experimental Studies ◽  
Real Data ◽  
Test Statistics ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
Higher Power ◽  
Leibler Information

The exponential distribution has been widely used in engineering, social and biological sciences. In this paper, we propose a new goodness-of-fit test for fuzzy exponentiality using α-pessimistic value. The test statistics is established based on Kullback-Leibler information. By using Monte Carlo method, we obtain the empirical critical points of the test statistic at four different significant levels. To evaluate the performance of the proposed test, we compare it with four commonly used tests through some simulations. Experimental studies show that the proposed test has higher power than other tests in most cases. In particular, for the uniform and linear failure rate alternatives, our method has the best performance. A real data example is investigated to show the application of our test.

scholarly journals An approach to gene-based testing accounting for dependence of tests among nearby genes

2021 ◽  
Author(s):  
Ronald J Yurko ◽  
Kathryn Roeder ◽  
Bernie Devlin ◽  
Max G'Sell
Keyword(s):  
Multiple Testing ◽  
Association Studies ◽  
Autism Spectrum ◽  
P Value ◽  
Genome Wide Association Studies ◽  
Strongly Correlated ◽  
Test Statistics ◽  
Test Statistic ◽  
Genome Wide ◽  
Insight Into

In genome-wide association studies (GWAS), it has become commonplace to test millions of SNPs for phenotypic association. Gene-based testing can improve power to detect weak signal by reducing multiple testing and pooling signal strength. While such tests account for linkage disequilibrium (LD) structure of SNP alleles within each gene, current approaches do not capture LD of SNPs falling in different nearby genes, which can induce correlation of gene-based test statistics. We introduce an algorithm to account for this correlation. When a gene's test statistic is independent of others, it is assessed separately; when test statistics for nearby genes are strongly correlated, their SNPs are agglomerated and tested as a locus. To provide insight into SNPs and genes driving association within loci, we develop an interactive visualization tool to explore localized signal. We demonstrate our approach in the context of weakly powered GWAS for autism spectrum disorder, which is contrasted to more highly powered GWAS for schizophrenia and educational attainment. To increase power for these analyses, especially those for autism, we use adaptive p-value thresholding (AdaPT), guided by high-dimensional metadata modeled with gradient boosted trees, highlighting when and how it can be most useful. Notably our workflow is based on summary statistics.

Testing for equality of means with equal and unequal variances

2021 ◽  
Vol 20 (2) ◽  
pp. 51-60
Author(s):  
A.O. Abidoye ◽  
W.A. Lamidi ◽  
M.O. Alabi ◽  
J. Popoola
Keyword(s):  
Agricultural Development ◽  
Secondary Data ◽  
Development Project ◽  
T Test ◽  
Harmonic Mean ◽  
Test Statistics ◽  
Test Statistic ◽  
Unequal Variances ◽  
Equality Of Means ◽  
Pooled Sample

In this paper, we are interested in comparing the conventional t –test with the proposed t – test for testing equality of means with unequal and equal variances. Here, we proposed harmonic mean of variances as an alternative to the pooled sample variance when there is heterogeneity of variances. Two sets of secondary data were obtained from Agricultural Development Project (KWADP) and the Ministry of Agriculture in Ilorin, Kwara State to demonstrate the two test statistics used and the results show that the proposed t – test statistic is found to be appropriate than the conventional t – test statistic when we have unequal variances but the conventional t – test perform better when we have equal variances.

A Bounds Approach to Inference Using the Long Run Multiplier

2019 ◽  
Vol 27 (3) ◽  
pp. 281-301 ◽  
Author(s):  
Clayton Webb ◽  
Suzanna Linn ◽  
Matthew Lebo
Keyword(s):  
Unit Root ◽  
Unit Roots ◽  
Small Sample ◽  
Stochastic Simulations ◽  
Upper And Lower Bounds ◽  
Test Statistics ◽  
Test Statistic ◽  
Independent Variables ◽  
Long Run ◽  
Presidential Success

Pesaran, Shin, and Smith (2001) (PSS) proposed a bounds procedure for testing for the existence of long run cointegrating relationships between a unit root dependent variable ($y_{t}$) and a set of weakly exogenous regressors $\boldsymbol{x}_{t}$ when the analyst does not know whether the independent variables are stationary, unit root, or mutually cointegrated processes. This procedure recognizes the analyst’s uncertainty over the nature of the regressors but not the dependent variable. When the analyst is uncertain whether $y_{t}$ is a stationary or unit root process, the test statistics proposed by PSS are uninformative for inference on the existence of a long run relationship (LRR) between $y_{t}$ and $\boldsymbol{x}_{t}$. We propose the long run multiplier (LRM) test statistic as a means of testing for LRRs without knowing whether the series are stationary or unit roots. Using stochastic simulations, we demonstrate the behavior of the test statistic given uncertainty about the univariate dynamics of both $y_{t}$ and $\boldsymbol{x}_{t}$, illustrate the bounds of the test statistic, and generate small sample and approximate asymptotic critical values for the upper and lower bounds for a range of sample sizes and model specifications. We demonstrate the utility of the bounds framework for testing for LRRs in models of public policy mood and presidential success.

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