The Play-the-Winner (PW) rule is an important method in clinical trials for patient allocation with two treatments, in which the probability a treatment is assigned to the coming patient depends upon the response of the previous patient. In this paper, we consider a general kind of PW rule for multi-treatment adaptive designs, in which the probability a treatment is assigned to the coming patie...

It may be downloaded, printed and reproduced only for personal or classroom use. Absolutely no downloading or copying may be done for, or on behalf of, any for‐profit commercial firm or other commercial purpose without the explicit permission of the Econometric Society. For this purpose, contact Claire Sashi, General Manager, at [email protected]. This paper provides a simulated mome...

This paper investigates the asymptotic theory for a factor GARCH model. Sufficient conditions for strict stationarity, existence of certain moments, geometric ergodicity and βmixing with exponential decay rates are established. These conditions allow for volatility spill-over and integrated GARCH. We then show the strong consistency and asymptotic normality of the quasi-maximum likelihood estim...

We establish a characterization of adequate knots in terms of the degree of their colored Jones polynomial. We show that, assuming the Strong Slope conjecture, our characterization can be reformulated in terms of “Jones slopes” of knots and the essential surfaces that realize the slopes. For alternating knots the reformulated characterization follows by recent work of J. Greene and J. Howie. 20...

This paper establishes the strong consistency and asymptotic normality of the quasi-maximum likelihood estimator (QMLE) for a GARCH process with periodically time-varying parameters. We first give a necessary and sufficient condition for the existence of a strictly periodically stationary solution for the periodic GARCH (P -GARCH) equation. As a result, it is shown that the moment of some posit...

We describe some of the basic ideas of Galois theory for commutative S-algebras originally formulated by John Rognes. We restrict attention to the case of finite Galois groups. We describe the general framework developed by Rognes. Central rôles are played by the notion of strong duality and a trace or norm mapping constructed by Greenlees and May in the context of generalized Tate cohomology. ...

The strong consistency and asymptotic normality of the maximum likelihood estimator in observation-driven models usually requires the study of the model both as a filter for the time-varying parameter and as a data generating process (DGP) for observed data. The probabilistic properties of the filter can be substantially different from those of the DGP. This difference is particularly relevant ...

In this paper, we obtain the strong consistency and asymptotic distribution of the Theil-Sen estimator in simple linear regression models with arbitrary error distributions. We show that the Theil-Sen estimator is super-efficient when the error distribution is discontinuous and that its asymptotic distribution may or may not be normal when the error distribution is continuous. We give an exampl...

On primitive roots of 1 mod p k , divisors of p ± 1, Wieferich primes, and quadratic analysis mod p Abstract Primitive roots of 1 mod p k (k > 2 and odd prime p) are sought, in cyclic units group G k ≡ A k B k mod p k , coprime to p, of order (p − 1)p k−1. 'Core' subgroup A k has order p − 1 independent of precision k, and 'extension' subgroup B k of all p k−1 residues 1 mod p is generated by p...

Urn models are very popular and useful for adaptive designs in clinical studies. Among various urn models, the drop-the-loser rule is an efficient adaptive treatment allocation scheme, recently proposed for comparing different treatments in clinical trials. This rule is superior to other randomization schemes in terms of variability and power. In this paper, the drop-the-loser rule is generaliz...