scholarly journals Nonparametric test for spatial geometric anisotropy

2010 ◽  
Vol 51 ◽  
Author(s):  
Kęstutis Dučinskas ◽  
Lina Dreižienė

Paper deals with a problem of testing isotropy against geometric anisotropy for Gaussian spatial data. The original simple test statistic based on directional empirical semivariograms is proposed. Under the assumption of independence of the classical semivariogram estimators and for increasing domain asymptotics, the distribution of test statistics is approximated by chi-squared distribution. The simulation experiments demonstrate the efficacy of the proposed test.

2010 ◽  
Vol 107 (2) ◽  
pp. 501-510 ◽  
Author(s):  
Michael A. Long ◽  
Kenneth J. Berry ◽  
Paul W. Mielke

Monte Carlo resampling methods to obtain probability values for chi-squared and likelihood-ratio test statistics for multiway contingency tables are presented. A resampling algorithm provides random arrangements of cell frequencies in a multiway contingency table, given fixed marginal frequency totals. Probability values are obtained from the proportion of resampled test statistic values equal to or greater than the observed test statistic value.


Biometrika ◽  
1991 ◽  
Vol 78 (3) ◽  
pp. 573 ◽  
Author(s):  
Gauss M. Cordeiro ◽  
Silvia L. de Paula Ferrari

Biometrika ◽  
1991 ◽  
Vol 78 (3) ◽  
pp. 573-582 ◽  
Author(s):  
GAUSS M. CORDEIRO ◽  
SILVIA L. DE PAULA FERRARI

Author(s):  
KYULEE SHIN ◽  
JIN SEO CHO

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.


2009 ◽  
Vol 33 (2) ◽  
pp. 81-86 ◽  
Author(s):  
Douglas Curran-Everett

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This second installment of Explorations in Statistics delves into test statistics and P values, two concepts fundamental to the test of a scientific null hypothesis. The essence of a test statistic is that it compares what we observe in the experiment to what we expect to see if the null hypothesis is true. The P value associated with the magnitude of that test statistic answers this question: if the null hypothesis is true, what proportion of possible values of the test statistic are at least as extreme as the one I got? Although statisticians continue to stress the limitations of hypothesis tests, there are two realities we must acknowledge: hypothesis tests are ingrained within science, and the simple test of a null hypothesis can be useful. As a result, it behooves us to explore the notions of hypothesis tests, test statistics, and P values.


Author(s):  
Anna L Tyler ◽  
Baha El Kassaby ◽  
Georgi Kolishovski ◽  
Jake Emerson ◽  
Ann E Wells ◽  
...  

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.


2020 ◽  
pp. 1-45
Author(s):  
Feng Yao ◽  
Taining Wang

We propose a nonparametric test of significant variables in the partial derivative of a regression mean function. The derivative is estimated by local polynomial estimation and the test statistic is constructed through a variation-based measure of the derivative in the direction of variables of interest. We establish the asymptotic null distribution of the test statistic and demonstrate that it is consistent. Motivated by the null distribution, we propose a wild bootstrap test, and show that it exhibits the same null distribution, whether the null is valid or not. We perform a Monte Carlo study to demonstrate its encouraging finite sample performance. An empirical application is conducted showing how the test can be applied to infer certain aspects of regression structures in a hedonic price model.


1998 ◽  
Vol 30 (3) ◽  
pp. 807-830 ◽  
Author(s):  
Rebecca A. Betensky

Analytic approximations are derived for the distribution of the first crossing time of a straight-line boundary by a d-dimensional Bessel process and its discrete time analogue. The main ingredient for the approximations is the conditional probability that the process crossed the boundary before time m, given its location beneath the boundary at time m. The boundary crossing probability is of interest as the significance level and power of a sequential test comparing d+1 treatments using an O'Brien-Fleming (1979) stopping boundary (see Betensky 1996). Also, it is shown by DeLong (1980) to be the limiting distribution of a nonparametric test statistic for multiple regression. The approximations are compared with exact values from the literature and with values from a Monte Carlo simulation.


Author(s):  
Lingtao Kong

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.


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