Accession Number : ADA186036

Title :   Test of Linearity in General Regression Models.

Descriptive Note : Technical rept.,

Corporate Author : PITTSBURGH UNIV PA CENTER FOR MULTIVARIATE ANALYSIS

Personal Author(s) : Chen, X R ; Krishnaiah, P R

PDF Url : ADA186036

Report Date : Dec 1986

Pagination or Media Count : 32

Abstract : Linear regression models are widely used in statistical analysis of experimental and observational data. Usually the linearity of the model is merely an assumption and cannot be taken for granted. In some planned experiments, repeated measurements on the dependent variable Y can be taken while the independent variable X is held fixed. In such cases standard analysis-of-variance technique can be employed to generate a test for linearity. In many applications, however, the independent variable is observed simultaneously with Y. That is to say, X, as well as Y, is a random variable. Under such circumstances the usual method for testing linearity cannot supply. This paper studies this problem in large-sample context. The authors propose a method to test the linearity hypothesis based on a grouping of the data. The critical value of test-statistic is determined so that the test has a prescribed lever of significant alpha asymptotically as the sample size tends to infinity. The consistency of the test is established, and the asymptotic power is calculated when the distance (in some sense) between the true regression function and the space of linear functions tends to zero in some specific rate.

Descriptors :   *LINEAR REGRESSION ANALYSIS, *LINEARITY, *MATHEMATICAL MODELS, *MODELS, *STATISTICAL TESTS, ASYMPTOTIC SERIES, CONSISTENCY, HYPOTHESES, MULTIVARIATE ANALYSIS, RATES, REGRESSION ANALYSIS, STATISTICAL ANALYSIS

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE