A Goodness-of-fit Test For Linearity Of A Stochastic Regression Model With Ranked Set Sample

This article investigates the test for hnearity of a stochastic regression model based on ranked-set sample. The use of simple random sample for developing regression diagnostics has been the subject of several recent research efforts. However, there are abundant situlations where, in context of regression, the measurement of the response variable is costly or time consuming but the measurement of the predictor variable can be obtained easily with relatively negligible cost. Sampling strategies that can reduce cost and increase efficiency are highly desirable in these cases. We in this article suggest a new statistic based on projection technique, kernel method and ranked set sampling technique. The test proposed are consistent against all fixed smooth alternatives to linearity and are asymptotically distribution-free for the distribution of the error. Furthermore, some simulated data sets and comparison of power between tests based on RSS and SRS to demonstrate the efficiency and availability of the test proposed.