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We study the marginal longitudinal nonparametric regression problem and some of its semiparametric extensions. We point out that, while several elaborate proposals for efficient estimation have been proposed, a relative simple and straightforward one, based on penalized splines, has not. After describing our approach we then explain how Gibbs sampling and the BUGS software can be used to achieve quick and effective implementation. Illustrations are provided for nonparametric regression and additive models.

We conclude that MBI is simple, convenient, efficient, gives exact and accurate information about daily activities and ambulation and could be used in inpatient follow up sittings, in the Arab and culturally similar Middle East countries.

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Benefits of using Ranked Set Sampling (RSS) rather than Simple Random Sampling (SRS) are indeed significant when estimating population mean or estimating linear models. Significance of this sampling method clearly appears since it can increase efficiency of the estimated parameters and decrease sampling costs. This paper investigates and introduces RSS method to fit spline and penalized spline models parametrically. It shows that the estimated parameters using RSS are more efficient than the estimated parameters using SRS for both spline and penalized spline models. The superiority of RSS approach is demonstrated using a simulation study as well as the "Air Pollution"environmental real data study. The approach in this paper can be illustrated for general smoothing spline models; for example B-spline,Radial spline etc, straightforwardly.

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In statistics we often experience combining n-independent tests of simple hypothesis, versus a one-tailed alternative as n approaches infinity. In the present study, we consider combining independent tests in case of conditional normal distribution with probability density function Xjh$N ðch; 1Þ; h 2 ½a; 1Þ; a ! 0 when h 1 ; h 2 ; ::: have a distribution function (DF) F h : Four nonparametric combination procedures (Fisher, logistic, sum of p-values and inverse normal) were compared via the exact Bahadur slope. We concluded that the inverse normal procedure is better than the other procedures.