On sufficient conditions for the strong consistency of least-squares estimates

The strong consistency of the least-squares estimates in regression models is obtained when the errors are i.i.d. with absolute moment of order r, 0<r? 2. The assumptions presented for the random error sequence will permit us to obtain improvements of the conditions on the regressors in order to obtain the strong consistency of the least-squares estimates in linear and nonlinear regression models.     

Strong consistency of least squares estimates with i.i.d. errors with mean values not necessarily defined

We establish strong consistency of the least squares estimates in multiple regression models discarding the usual assumption of the errors having null mean value. Thus, we required them to be i.i.d. with absolute moment of order r, 0<r<2, and null mean value when r>1. Only moderately restrictive conditions are imposed on the model matrix. In our treatment, we use an extension of the Marcinkiewicz–Zygmund strong law to overcome the errors mean value not being defined. In this way, we get a unified treatment for the case of i.i.d. errors extending the results of some previous papers.     

Religious Cults, the Individual and the Family

Relatively little attention has been paid in the professional literature to the cult phenomenon: what it is, how it attracts converts, what differentiates the vulnerable youth from the non-vulnerable; the effects of cult membership on the convert's family, and, particularly, in what ways the family can be aided during and after involvement with the cult. The authors have drawn on clinical observations, interviews, and extant literature from a variety of disciplines in constructing a portrait of the vulnerable youth; the techniques used by cults to attract, recruit, and convert members; the dynamics of the recruits family; and the most effective modes of therapy for intervening. The intent of the article is to stimulate: 1) professional awareness of and knowledge about the cults, and 2) further research into related family dynamics and therapeutic techniques.     

Measuring values: A conceptual framework for interpreting transactions with special reference to contingent valuation of visibility

People express their value for a good when they pay something for it. Interpretinggood andpayment very broadly, we offer a general analytical framework for characterizing such transactions. This framework is suitable for interpreting actual transactions as well as for creating hypothetical transactions for research purposes. It is described here both in general terms and with special application to one particular kind of transaction, contingent valuation studies in which individuals estimate the value of possible changes in atmospheric visibility. In these transactions, as in many others, risk (of undesired changes in visibility) is one principal feature; at least some uncertainty often surrounds other transaction features as well (For example: How much will visibility really change if I promise to pay for it? Will I really have to pay?). The framework presented here conceptualizes any transaction as involving (a) a good, (b) a payment, and (c) a social context within which the transaction is conducted. Each of these aspects in turn has a variety of features that might and in some cases should affect evaluations. For each such feature, the framework considers first the meaning of alternative specifications and then the difficulties of ensuring that they are understood and evaluated properly. As a whole, the framework provides an integrated approach to designing evaluation studies and interpreting their results.     

On the Strong Consistency of Ridge Estimates

In this article, we establish strong consistency of the ridge estimates using extended results for the strong consistency of the least squares estimates in multiple regression models which discard the usual assumption of null mean value for the errors and only requires them to be i.i.d. with absolute moment of order r (0 < r ? 1).     

Religious Cults: Family Concerns and the Law

The activities of contemporary religious cults cause concern and controversy among parents and mental health practitioners, both because they are perceived as threats to the well-being of their young adult members and because such cults are protected by the First Amendment. The primary issues discussed here are "mind control" and informed consent. Possible bases for legal redress of alleged injuries, as well as possible preventive measures, are suggested.     

VARIABLE SELECTION ALONG CANONICAL VECTORS

When describing and displaying inter-group relationships using canonical variate analysis, the question often arises: which variables contribute most to the group separation along particular canonical vectors? This problem is discussed in the context of an example which uses remotely sensed data to discriminate between cover classes. The appropriate between-groups matrix to be input into subset selection procedures is identified. When combined with subsequent simplification of the vectors, the approach leads to a simpler interpretation of the canonical variate display.     

The Rate of Convergence of some Asymptotic Expansions for Distribution Approximations via an Esseen Type Estimate

Some asymptotic expansions not necessarily related to the central limit theorem are studied. We first observe that the smoothing inequality of Esseen implies the proximity, in the Kolmogorov distance sense, of the distributions of the random variables of two random sequences satisfying a sort of general asymptotic relation. We then present several instances of this observation. A first example, partially motivated by the the statistical theory of high precision measurements, is given by a uniform asymptotic approximation to (g(X + μ _n )) _n∈?, where g is some smooth function, X is a random variable and (μ _n ) _n∈? is a sequence going to infinity; a multivariate version is also stated and proved. We finally present a second class of examples given by a randomization of the interesting parameter in some classical asymptotic formulas; namely, a generic Laplace's type integral, randomized by the sequence (μ _n X) _n∈?, X being a Gamma distributed random variable.