Orientation relationship in finite dimensional space

In the present article, we discuss the regression of a point on the surface of a unit sphere in d dimensions given a point on the surface of a unit sphere in p dimensions, where p may not be equal to d. Point projection is added to the rotation and linear transformation for regression link function. The identifiability of the model is proved. Then, parameter estimation in this set up is discussed. Simulation studies and data analyses are done to illustrate the model.     

Negative and Positive Partial Mobility: A Study of the Relative Changes in Human Development

In this paper, we have considered the issues concerning dynamic changes in HDI and its various components from a relative standpoint. The analysis of HDI mobility should entail directional movement introduced by Fields (in Distribution and development: a new look at the developing world. MIT Press, Cambridge, 2001). However, Fields’ analysis was in the space of absolute values. Here, we will try to extend this exercise to the positional mobility index by considering the question of improvement and deterioration in relative positions. This requires the concept of partial mobility where mobility is judged from the viewpoint of a particular group. We then try to introduce directional changes in partial mobility through axiomatic framework. Finally, we provide an illustrative example from the Indian data.     

Measures of association for nominal categorical variables

This paper reviews existing measures of association for nominal categorical variables, and presents some alternative measures of association, which are symmetric and flexible enough to find partial and multiple association.     

A general adaptive allocation design for continuous responses in the presence of covariates

Several adaptive allocation designs are available in the clinical trial literature for allocating the entering patients among two competing treatments, having binary responses and skewing the allocation in favor of the better treatment. No adaptive design is available for continuous responses in the presence of prognostic factors, which is not model based. In the present paper, a general allocation design is introduced which assumes no specific regression model or distribution of responses. Some performance characteristics of the design are studied. Some related inference, following the allocation, is also studied. The proposed procedure is compared with some possible competitors. A real data set is used to illustrate the applicability of the proposed design.     

Sequential-type nonparametric test using Mann-Whitney statistics

The paper provides a nonparametric test for the identity of two continuous univariate distribution functions when observations are drawn in pairs from the populations, by adopting a sampling scheme which, using Mann-Whitney scores, generalizes the existing inverse binomial sampling technique. Some exact performance characteristics of the proposed test are formulated and compared numerically with existing competitors of the proposed test. The applicability of the proposed test is illustrated using real-life data.     

A RANDOMIZED LONGITUDINAL PLAY-THE-WINNER DESIGN FOR REPEATED BINARY DATA

In some clinical trials with two treatment arms, the patients enter the study at different times and are then allocated to one of two treatment groups. It is important for ethical reasons that there is greater probability of allocating a patient to the group that has displayed more favourable responses up to the patient's entry time. There are many adaptive designs in the literature to meet this ethical constraint, but most have a single binary response. Often the binary response is longitudinal in nature, being observed repeatedly over different monitoring times. This paper develops a randomized longitudinal play‐the‐winner design for such binary responses which meets the ethical constraint. Some performance characteristics of this design have been studied. It has been implemented in a trial of pulsed electro‐magnetic field therapy with rheumatoid arthritis patients.     

Controlling Type-I Error Rate in Monitoring Structural Changes Using Partially Sequential Procedures

In the present article, we develop some asymptotically power on partially sequential nonparametric tests for monitoring structural changes. Our test procedures are based on Wilcoxon score. We use the idea of curved stopping boundaries. We derive some exact results and perform simulation studies to provide various properties of the tests. We see that one of the proposed procedures significantly controls the Type I error rate. This procedure may be very effective for fluctuation monitoring. We illustrate the procedures by using real life data from the stock market.     

A response-adaptive design in crossover trial

In the present work, whenever the response variables are binary, we frame an adaptive allocation rule for a two-treatment two-period crossover design in the presence of possible carry-over effects. The proposed rule is a combination of the play-the-winner and randomized play-the-winner rules. We study various properties of the proposed rule through asymptotics and simulations. Some related inferential problems are also considered. The proposed procedure is compared with some possible competitor.     

Time series analysis of categorical data using auto-odds ratio function

In this paper, we consider the auto-odds ratio function (AORF) as a measure of serial association for a stationary time series process of categorical data at two different time points. Numerical measures such as the autocorrelation function (ACF) have no meaningful interpretation, unless the time series data are numerical. Instead, we use the AORF as a measure of association to study the serial dependency of the categorical time series for both ordinal and nominal categories. Biswas and Song [Discrete-valued ARMA processes. Stat Probab Lett. 2009;79(17):1884–1889] provided some results on this measure for Pegram's operator-based AR(1) process with binary responses. Here, we extend this measure to more general set-ups, i.e. for AR(p) and MA(q) processes and for a general number of categories. We discuss how this method can effectively be used in parameter estimation and model selection. Following Weiß [Empirical measures of signed serial dependence in categorical time series. J Stat Comput Simul. 2011;81(4):411–429], we derive the large sample distribution of the estimator of the AORF under independent and identically distributed (iid) set-up. Some simulation results and two categorical data examples (one is ordinal and other nominal) are presented to illustrate the proposed method.