Grigory Kosenok

AN ALTERNATIVE TO MAXIMUM LIKELIHOOD BASED ON SPACINGS

In the statistics literature, asymptotic properties of the Maximum Product of Spacings estimator are derived from first principles. We propose an alternative derivation based on the comparison between its objective function and that of the Maximum Likelihood estimator. 1. MOTIVATION Consider a scalar continuously distributed random variable x with probability density function (p.d.f.) f(x) f(x, 0) and corresponding cumulative distribution function (c.d.f.) F(x) F(x, 6) known up to a possibly multidimensional parameter 0 E ?. Denote the true value of the parameter by 00. Suppose that a random sample xl,..., x, is available. To estimate 00, one usually uses the maximum likelihood (ML) estimator

Individually Rational, Balanced-Budget Bayesian Mechanisms and the Informed Principal Problem

We investigate the issue of implementation via individually rational ex-post budget-balanced Bayesian mechanisms. We demonstrate that all social choice rules that generate a nonnegative ex-ante surplus, including ex-post efficient ones, can generically be implemented via such mechanisms for any profile of the utility functions. The aggregate expected surplus in these mechanisms can be distributed in an arbitrary way. Also generically, any ex-post efficient social choice rule can be implemented in an informed principal framework, i.e. when the mechanism is offered by one of the informed parties. Only ex-post efficient social choice rules that allocate all surplus to the party designing the mechanism are both sequential equilibrium outcomes and neutral optima, i.e. outcomes that can never be blocked. This result implies that even an informed principal can extract all surplus from players in a Bayesian mechanism

ANOTHER NUMERICAL METHOD OF FINDING CRITICAL VALUES FOR THE ANDREWS STABILITY TEST

We propose a method, alternative to that of Estrella (2003, Econometric Theory 19, 1128–1143), of obtaining exact asymptotic p-values and critical values for the popular Andrews (1993, Econometrica 61, 821–856) test for structural stability. The method is based on inverting an integral equation that determines the intensity of crossing a boundary by the asymptotic process underlying the test statistic. Further integration of the crossing intensity yields a p-value. The proposed method can potentially be applied to other stability tests that employ the supremum functional.

Tests in Contingency Tables as Regression Tests

Applied researchers often use tests based on contingency tables, especially in preliminary data analysis and diagnostic testing. We show that many such tests may be alternatively implemented by testing for coefficient restrictions in linear regression systems.

Sequential Testing with Uniformly Distributed Size

Sequential procedures of testing for structural stability do not provide enough guidance on the shape of boundaries that are used to decide on acceptance or rejection, requiring only that the overall size of the test is asymptotically controlled. We introduce and motivate a reasonable criterion for a shape of boundaries which requires that the test size be uniformly distributed over the testing period. Under this criterion, we numerically construct boundaries for most popular sequential tests that are characterized by a test statistic behaving asymptotically either as a Wiener process or Brownian bridge. We handle this problem both in a context of retrospecting a historical sample and in a context of monitoring newly arriving data. We tabulate the boundaries by tting them to certain exible but parsimonious functional forms. Interesting patterns emerge in an illustrative application of sequential tests to the Phillips curve model.