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.

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.

Quantitative Determination of Si, Al, Ti, and Fe in Laterites and Bauxites by X-ray Fluorescence Using a Computer for Correction of Interelement Effects

1979 ◽  
Vol 33 (6) ◽  
pp. 634-637 ◽  
Author(s):  
Hasso Schorin
Keyword(s):  
Regression Analysis ◽  
Quantitative Determination ◽  
Multiple Regression Analysis ◽  
Multiple Regression ◽  
International Standards ◽  
X Ray ◽  
Calibration Curves ◽  
Set Up

A method for the quantitative determination of the major constituents in laterites and bauxites by x-ray fluorescence using fused Na2B4O7 glass discs is presented. The calibration curves were set up employing synthetic mixtures of oxides of Si, Al, Ti, and Fe. The interelement effects were corrected using a multiple regression analysis programed on a PDP 11/45 computer. The precision was determined by preparation and analysis of five synthetic pellets; the accuracy was ascertained by analysis of five international standards.

Utilization of Additional Information in Non-Parametric Tests

1984 ◽  
Vol 33 (1-2) ◽  
pp. 69-84 ◽  
Author(s):  
Tathagata Banerjee
Keyword(s):  
Single Sample ◽  
Sign Test ◽  
Sensitive Test ◽  
Sample Problem ◽  
Test Statistic ◽  
Additional Information ◽  
Set Up ◽  
Single Sample Problem ◽  
Non Parametric

For the single sample problem of testing for location against one-sided alternatives under the non parametric set-up, the question of utilization of additional information is examined. Considering the case of the sign test it is shown that if suitable bounds to the ratio of the densities at the median and the known quantile are available it is possible to construct a more sensitive test by using a combination of the sign test statistic and the number of exceedances above the known quantile.

An Alternative Multicollinearity Approach in Solving Multiple Regression Problem

2011 ◽  
Vol 6 (11) ◽  
pp. 1241-1255 ◽  
Author(s):  
H.J. Zainodin ◽  
A. Noraini ◽  
S.J. Yap
Keyword(s):  
Multiple Regression ◽  
Regression Problem

scholarly journals What Constitutes Science and Scientific Evidence: Roles of Null Hypothesis Testing

2016 ◽  
Vol 77 (3) ◽  
pp. 475-488 ◽  
Author(s):  
Mark Chang
Keyword(s):  
Hypothesis Testing ◽  
Multiple Regression ◽  
Null Hypothesis ◽  
Scientific Discovery ◽  
Scientific Evidence ◽  
Fundamental Principle ◽  
Statistical Testing ◽  
Similarity Principle ◽  
Null Hypothesis Testing ◽  
Null Hypothesis Statistical Testing

We briefly discuss the philosophical basis of science, causality, and scientific evidence, by introducing the hidden but most fundamental principle of science: the similarity principle. The principle’s use in scientific discovery is illustrated with Simpson’s paradox and other examples. In discussing the value of null hypothesis statistical testing, the controversies in multiple regression, and multiplicity issues in statistics, we describe how these difficult issues should be handled based on our interpretation of the similarity principle.

Stereological analysis of particles of varying ellipsoidal shape

1988 ◽  
Vol 25 (2) ◽  
pp. 322-335 ◽  
Author(s):  
J. Møller
Keyword(s):  
Sampling Procedure ◽  
Parametric Models ◽  
Stereological Analysis ◽  
Ellipsoidal Shape ◽  
Particle Aggregates ◽  
Set Up ◽  
Information Combining ◽  
Lower Dimensional ◽  
Non Parametric

Stereological analysis of d-dimensional particles of ellipsoidal shape based on lower-dimensional sections through the particles is discussed. It is proved that the non-void intersections between three parallel hyperplanes and an ellipsoid uniquely determine the ellipsoid, and based on this fact we may reconstruct ellipsoids from sectional information. Combining this reconstruction with a new sampling procedure we obtain a useful tool for non-parametric stereological analysis of particle aggregates of ellipsoids. Finally, parametric models for ellipsoids which are mathematically convenient for the present set up are introduced and discussed.

scholarly journals FORMULATION OF MATHEMATICAL MODEL FOR PRODUCTION TURNOVER OF BIODIESEL PLANT BASED ON DIMENSIONAL ANALYSIS AND MULTIPLE REGRESSION

2012 ◽  
pp. 268-276
Author(s):  
ASHWIN S. CHATPALLIWAR ◽  
DR. VISHWAS S. DESHPANDE ◽  
DR. JAYANT P. MODAK ◽  
DR. NILESHSINGH V. THAKUR
Keyword(s):  
Mathematical Model ◽  
Multiple Regression ◽  
Dimensional Analysis ◽  
Least Square Method ◽  
Least Square ◽  
Design Data ◽  
Dimensionless Equation ◽  
Set Up ◽  
The Mathematical Model ◽  
Data Design

This paper presents the approach for the mathematical modeling of production turnover for the set up of new Biodiesel plant based on the dimensional analysis and multiple regression. Presented production turnover mathematical model is derived based on the generated design data. Design data is generated from the estimated design data. Estimation of design data is carried out based on the assumed plant layouts of different capacities. Dimensional analysis is used to make the independent and dependent variables dimensionless and to get dimensionless equation. Later, multiple regression analysis is applied to this dimensionless equation to obtain the index values based on the least square method. The mathematical model of production turnover is formulated using these obtained index values. Finally, the formulated model is evaluated on the basis of correlation and root mean square error between the computed values by model and the estimated values.

scholarly journals Comparison of Type I Error of some Non-Parametric Tests on Multiple Regression Models Coefficients

2015 ◽  
Vol 11 (7) ◽  
pp. 5426-5443
Author(s):  
Ali Shadrokh
Keyword(s):  
Multiple Regression ◽  
Regression Models ◽  
Type I Error ◽  
Hypothesis Test ◽  
Type I ◽  
Lower Type ◽  
Modified Method ◽  
Higher Power ◽  
Multiple Regression Models ◽  
Non Parametric

Various non-parametric methods have been used to perform hypothesis test on multiple regression coefficients. In this article, at first the most important methods which has been introduced from other statisticians as proper methods, such as Kennedy, Freedman and Lane, and modified Kennedy, are explained and then, Freedman and Lane (Huh-John) method will be modified in the form of Kennedy method; finally, all aforementioned methods will be compared as simulating. At last, we look for a method that done best. So, Huh-John (2001) modify the method of Kennedy which was proposed in 1995 and showed by simulation that is called modified Huh-John method; and it has less type I error. On the other hand, Anderson as simulation (1991) and Schadrekh as theory (2011) had shown that Freedman& Lane method has lower type I error in comparison with Kennedy method. We did some modification on Freedman and Lane method that Huh-John had done on Kennedy method and compared this modified method with Freedman and Lane and Huh-John method. We conclude that Freedman and Lane modified method often has lower type I error estimation and higher power than Freedman& Lane and Huh-John method.

Hypothesis Testing

2005 ◽  
Author(s):  
D. Brynn Hibbert ◽  
J. Justin Gooding
Keyword(s):  
Hypothesis Testing ◽  
Null Hypothesis ◽  
Hypothesis Test ◽  
Significance Test ◽  
Type I ◽  
Test Statistic ◽  
The Difference ◽  
Set Up ◽  
Type Ii Errors ◽  
Normally Distributed

• To understand the concept of the null hypothesis and the role of Type I and Type II errors. • To test that data are normally distributed and whether a datum is an outlier. • To determine whether there is systematic error in the mean of measurement results. • To perform tests to compare the means of two sets of data.… One of the uses to which data analysis is put is to answer questions about the data, or about the system that the data describes. In the former category are ‘‘is the data normally distributed?’’ and ‘‘are there any outliers in the data?’’ (see the discussions in chapter 1). Questions about the system might be ‘‘is the level of alcohol in the suspect’s blood greater than 0.05 g/100 mL?’’ or ‘‘does the new sensor give the same results as the traditional method?’’ In answering these questions we determine the probability of finding the data given the truth of a stated hypothesis—hence ‘‘hypothesis testing.’’ A hypothesis is a statement that might, or might not, be true. Usually the hypothesis is set up in such a way that it is possible to calculate the probability (P) of the data (or the test statistic calculated from the data) given the hypothesis, and then to make a decision about whether the hypothesis is to be accepted (high P) or rejected (low P). A particular case of a hypothesis test is one that determines whether or not the difference between two values is significant—a significance test. For this case we actually put forward the hypothesis that there is no real difference and the observed difference arises from random effects: it is called the null hypothesis (H<sub>0</sub>). If the probability that the data are consistent with the null hypothesis falls below a predetermined low value (say 0.05 or 0.01), then the hypothesis is rejected at that probability. Therefore, p<0.05 means that if the null hypothesis were true we would find the observed data (or more accurately the value of the statistic, or greater, calculated from the data) in less than 5% of repeated experiments.

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