Testing the proportionality assumption for specified covariate in the cox model

In this paper, I propose a test for proportional hazards assumption for specified covariates. The testis based on a general alternative in sense that hazards rates under different values of covariates therate is not only constant as in the Cox model, but it may cross, go away, and may be monotonicwith time. The limit distribution of the test statistic is derived. Finite samples properties of thetest power are analyzed by simulation. Application of the proposed test on Real data examples areconsidered.

The Small Number System

I argue that the human mind includes an innate domain-specific system for representing precise small numerical quantities. This theory contrasts with object-tracking theories and with domain-general theories that only make use of mental models. I argue that there is a good amount of evidence for innate representations of small numerical quantities and that such a domain-specific system has explanatory advantages when infants’ poor working memory is taken into account. I also show that the mental models approach requires previously unnoticed domain-specific structure and consequently that there is no domain-general alternative to an innate domain-specific small number system.

Word order and the Final-Over-Final Condition

This chapter develops an antisymmetric view of linearization, along the general lines of Kayne’s antisymmetry theory. A general alternative to earlier accounts of the Final-Over-Final Condition is developed based on Chomsky’s Labelling Algorithm, in particular the proposal that functional heads may vary in their capacity to autonomously label their categories. We propose that ‘weak’ functional categories lack this capacity, and trigger roll-up of their complement in order to effect this. Furthermore, a general version of the Strict Cycle is proposed which is also central to ‘generalized Universal 20 effects’. Finally, we formulate the parameter hierarchy for word-order variation (or, more precisely, for the roll-up movement which is a major determinant of word order across languages) in terms of the labelling-driven account of roll-up. We discuss both how the nature of the macro-, meso-, and microparameters making up that hierarchy can be deduced, and some of the empirical results.