Combining Alternative Rank Tests for the Multiple Regression Problem

1986 ◽  
Vol 35 (3-4) ◽  
pp. 169-188 ◽  
Author(s):  
Shoutir Kishore Chatterjee ◽  
Tathagata Banerjee
Keyword(s):  
Multiple Regression ◽  
Quadratic Forms ◽  
Null Distribution ◽  
Test Statistic ◽  
Rank Tests ◽  
Asymptotic Power ◽  
Regression Problem ◽  
Test Criterion ◽  
Simultaneous Choice ◽  
Set Up

In this paper we consider the problem of testing absence of regression under the nonparametric multiple regression set up with m predictors. Usual rank tests for this problem are based on particular systems of scores, the test criteria being quadratic forms in m linear rank statistics. Different standard tests correspond to different choices of the system of scores. In this paper we have proposed a test statistic which is based on the simultaneous choice of more than one system of scores. Asymptotic null distribution of the test criterion is a chisquare with m df as in the case of the usual tests. However, the use of several systems of scores results in the improvement of the asymptotic power over the test based on any one of the systems. Ofcourse the use of the test criterion in practice involves the estimation of indices involving the parent density f( . ). Certain standard estimates of these indices are noted in the last section.

Non-Parametric Tests for Multiple Regression Under Permutation Symmetry

1989 ◽  
Vol 38 (1-2) ◽  
pp. 93-114
Author(s):  
Indranil Mukhopadhyay
Keyword(s):  
Multiple Regression ◽  
Null Hypothesis ◽  
Permutation Symmetry ◽  
Special Situation ◽  
Regression Problem ◽  
Set Up ◽  
Nonparametric Procedure ◽  
Non Parametric

In this paper non-parametric tests for the multiple resrcssion set up which take into account the known permutation symmetry of the variates under the null hypothesis, are suggested. It bas been shown that under permutation symmetry the proposed procedure is more efficient than the standard nonparametric procedure for the multiple regression problem (see e.g. Puri and Sen (1985) ). A special situation where it is further known in advance that the regressions are identical is also considered briefly.

A NONPARAMETRIC TEST OF SIGNIFICANT VARIABLES IN GRADIENTS

2020 ◽  
pp. 1-45
Author(s):  
Feng Yao ◽  
Taining Wang
Keyword(s):  
Null Distribution ◽  
Monte Carlo Study ◽  
Nonparametric Test ◽  
Hedonic Price ◽  
Finite Sample ◽  
Test Statistic ◽  
Bootstrap Test ◽  
Local Polynomial Estimation ◽  
Polynomial Estimation ◽  
Mean Function

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.

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.

scholarly journals PENGARUH LATIHAN TERPUSAT DAN LATIHAN ACAK TERHADAP HASIL PENGUASAAN TEKNIK DASAR BOLA BASKET

KINESTETIK ◽  
2018 ◽  
Vol 2 (1) ◽  
pp. 36-43
Author(s):  
Setiana Wati ◽  
Tono Sugihartono ◽  
Sugiyanto Sugiyanto
Keyword(s):  
Statistical Analysis ◽  
Experimental Methods ◽  
Statistical Test ◽  
T Test ◽  
Distributed Data ◽  
Statistical Calculation ◽  
Test Statistic ◽  
Basic Technique ◽  
Test Criterion ◽  
Experimental Group

Abstrak Penelitian ini bertujuan untuk mengetahui pengaruh antara latihan terpusat dan latihan acak terhadap hasil penguasaan teknik dasar bola basket. Penelitian ini menggunakan metode eksperimen yang dilakukan terhadap dua kelompok, yaitu kelompok eksperimen satu yang di beri perlakuan latihan terpusat dan kelompok eksperimen dua di beri perlakuan latihan acak. Penelitian dilakukan di Klub Basket Poltekkes Kemenkes Bengkulu dengan sampel yang di pilih berdasarkan karakteristik tertentu. Analisis statistik yang di gunakan dalam penelitian ini adalah Uji t untuk menguji hipotesis bahwa “latihan acak memberikan pengaruh lebih baik dibandingkan dengan latihan terpusat dalam meningkatkan keterampilan teknik dasar bola basket”. Uji syarat statistik t telah memenuhi syarat homogen dan data berdistribusi normal berdasarkan perhitungan statistik dan pengujian kriteria uji statistic di dapat hasil bahwa latihan terpusat dan latihan acak memberikan pengaruh terhadap hasil penguasaan teknik dasar bola basket. Hal ini diketahui dari data thitung = -5,11 > ttabel = 2,11 dengan taraf ?=0,05. Kesimpulan dari penelitian ini dilihat dari hasil uji signifikan perbedaan peningkatan latihan kedua kelompok menunjukkan bahwa latihan acak memberikan pengaruh yang lebih signifikan terhadap hasil  penguasaan teknik dasar bola basket. Kata Kunci: Latihan terpusat, Latihan acak, Teknik Dasar Bola Basket.Abstract This study aims to determine the effect of centralized training and random exercise on the results of mastery of basic techniques of basketball. This study used experimental methods conducted on two groups, namely the experimental group one which was given the treatment of centralized exercise and the experimental group of two in the treatment of random treatment. The research was conducted at Club Basket Poltekkes Kemenkes Bengkulu with selected samples based on certain characteristics. The statistical analysis used in this study is t-test to test the hypothesis that "randomized exercise gives better effect than centralized training in improving basic basketball technique skills". Test statistic requirement t has complied with homogeneous requirements and normal distributed data based on statistical calculation and statistical test criterion test in can result that centralized exercise and random exercise have an effect on the result of mastery of basic technique of basketball. It is known from thitung = -5,11> ttable = 2,11 with ? = 0,05. The conclusions of this study seen from the results of significant test differences in the improvement of the two groups showed that the random exercise gives a more significant effect on the results of mastery of basic techniques of basketball. Keywords: Centralized exercise, Random exercise, Basic Basketball Technique.

Testing for individual sphericity in heterogeneous panels

Biometrika ◽  
2019 ◽  
Vol 106 (3) ◽  
pp. 740-747
Author(s):  
Simon A Broda
Keyword(s):  
Distribution Function ◽  
Normal Approximation ◽  
Empirical Work ◽  
Null Distribution ◽  
Saddlepoint Approximation ◽  
Test Statistic ◽  
Cross Sectional ◽  
P Values ◽  
Cross Sectional Dimension ◽  
Heterogeneous Panels

Summary This manuscript considers locally best invariant tests for sphericity in heterogeneous panels. A new integral representation for the characteristic function of the test statistic under the null is presented, along with an algorithm for inverting it to obtain the distribution function. A saddlepoint approximation to the null distribution addresses the need to quickly compute approximate $p$-values in empirical work. The approximation shows substantial improvements over the normal approximation when the cross-sectional dimension is small.

scholarly journals A novel gene-set association test based on variance-gamma distribution

2018 ◽  
Vol 28 (9) ◽  
pp. 2868-2875
Author(s):  
Zhongxue Chen ◽  
Qingzhong Liu ◽  
Kai Wang
Keyword(s):  
Gamma Distribution ◽  
Type I Error ◽  
Null Distribution ◽  
Real Data ◽  
Association Test ◽  
P Value ◽  
Type I ◽  
Test Statistic ◽  
Data Set ◽  
Variance Gamma

Several gene- or set-based association tests have been proposed recently in the literature. Powerful statistical approaches are still highly desirable in this area. In this paper we propose a novel statistical association test, which uses information of the burden component and its complement from the genotypes. This new test statistic has a simple null distribution, which is a special and simplified variance-gamma distribution, and its p-value can be easily calculated. Through a comprehensive simulation study, we show that the new test can control type I error rate and has superior detecting power compared with some popular existing methods. We also apply the new approach to a real data set; the results demonstrate that this test is promising.

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