1 . Introduction . In his paper [1], Erdös introduced the sequences of positive integers b 1 < b, < . . ., with (b ;, bj ) = 1, for i ~A j, and 'bi 1 < oo . With any such arbitrary sequence of integers, he associated the sequence {di} of all positive integers not divisible by any bj , and he showed that if b1 > 2, there exists a 0 < 1 (independent of the sequence {b i }) such that d i 1 di < d°...

This paper presents a systematic approach for obtaining results from the area of quantitative investigations in logic and type theory. We investigate the proportion between tautologies (inhabited types) of a given length n against the number of all formulas (types) of length n. We investigate an asymptotic behavior of this fraction. Furthermore, we characterize the relation between number of pr...

This article examines the adjustment of normal theory methods for the analysis of covariance structures to make them applicable under the class of elliptical distributions. It is shown that if the model satisfies a mild scale invariance condition and the data have an elliptical distribution, the asymptotic covariance matrix of sample covariances has a structure that results in the retention of ...

A new approach to the derivation of asymptotic conservation laws in field theory is presented. This approach is based upon the explicit construction of a universal spacetime differential form which plays a central role in the general theory of lowerdegree conservation laws. It is shown that this differential form immediately leads to the standard asymptotic conservations laws for both the Einst...

We provide in this paper asymptotic theory for the multivariate GARCH(p, q) process. Strong consistency of the quasi-maximum likelihood estimator (MLE) is established by appealing to conditions given in Jeantheau [19] in conjunction with a result given by Boussama [9] concerning the existence of a stationary and ergodic solution to the multivariate GARCH(p, q) process. We prove asymptotic norma...

This paper proposes and implements a tractable approach to detect group structure in panel data. The mechanism works by means of a panel structure model, which assumes that individuals form a number of homogeneous groups in a heterogeneous population. Within each group, the (linear) regression coefficients are the same, while they may be different across different groups. The econometrician is ...

Traditional methods of estimating the frequency of sinusoids from noisy data include the periodogram maximization and the nonlinear least squares. It is well-known that these methods lead to efficient frequency estimates whose asymptotic standard error is of order O(n−3/2). To actually compute the estimates, some sort of iterative search procedures must be employed in view of the high nonlinear...

We will estimate the size of a random process (X t) t∈T by the size of another (simpler) random process (Y t) t∈T. Define a Gaussian centered process to be when X t is a mean-zero random variable. For a random variable X