Misspecification and Conditional Maximum Likelihood Estimation

Recently White (1982) studied the properties of Maximum Likelihood estimation of possibly misspecified models. The present paper extends Andersen (1970) results on Conditional Maximum Likelihood estimators (CMLE) to such a situation. In particular, the asymptotic properties of CMLE's are derived under correct and incorrect specification of the conditional model. Robustness of conditional inferences and estimation with respect to misspecification of the model for the conditioning variables is emphasized. Conditions for asymptotic efficiency of CMLE's are obtained, and specification tests a la Hausman (1978) and White (1982) are derived. Examples are also given to illustrate the use of CMLE's properties. These examples include the simple linear model, the multinomial logit model, the simple Tobit model, and the multivariate logit model

Théorie des contextes et relations internationales : Départ de la première guerre d’Indochine

Bateson's "Eurêka" has been his application of Russell and Whitehead's theory of types to the social sciences. They had postulated a discontinuity between the levels of the members of a class and a class of classes and so on. Hence a class may not be a member of itself. The cat scratches and the word "cat" does not bite. Confusion between levels, or the signifier and the signified, or the map and the territory, or the menu and the meal, is a sign of disorder. Having been introduced to Bateson's ecology, Anthony Wilden has formulated a theory of contexts, already present in "System and Structure". In order to avoid simplicity through the flattening of social and organic levels into inorganic levels of matter-energy, the theory of contexts suggest the organisation of constraints, complexites, or levels of reality into levels of logical types, using the rule of extinction. It goes on to suggest the use of the rule of commutation to eliminate spurious similarities and inappropriate symmetries which lead to oppositions and Imaginary "contradictions". It is suggested to use Korzybski and Hayakawa's rule of communication in order to get over conflicts due to misperception. To illustrate all of this, we propose to dismanthe the processes which have led to the misunderstanding behind the first Indochinese war of 1946-1954. From one misunderstanding to another, the VPA (Vietnam People's Army), in the 1980's, mobilised at the Kmer-Siamese border, at the door of Thailand who since 1939 has claimed to be the land of the Thais and heir to the Champa empire which was established in 192 and, soon after 1471, was dissolved by the "gnawing" of the Vietnamese peasants in their "long march" towards the South. The most revolting of working, conjugal and international disputes is that which emerge from misperceptions where each party is convinced of its own good will and of the foul bad will of the other. A mutual consent regarding the context, that of metacommunication, may lead to a common signification (consensus) of beings, events and objects

Stratégies technico-commerciales asiatiques

John Foster Dulles, then Secretary of State under the presidency of Eisenhower, once said there are two ways to conquer: by the clash of arms or through the economic control. The motto of the former WWII British SBS Commandos (Special Boat Service)used to be "United we conquer" and the one from the SAS (Special Air Service) used to be "Who dare win ", both of these commando troops or irregulars were in tactical competition framed by strategic cooperation where the light forces overcame heavier and overnumbering forces. Unity and daringness seem to be their secret weapon, but neither so secret nor so exclusive, comparatively to the recipe of tactical competition framed by strategic co-operation and coordination. "Superior numbers on the battlefield are an undoubted advantage, but skill, better organization, and training, and above all a firmer determination in all ranks to conquer at any cost, are the chief factors of success. Half-hearted measures never attain success in war and lack of determination is the most fruitful source of defeat" wrote Anthony Wilden1. The Chinese "Chii" (close to the latin "anima": heart, mind, courage) may be translated to "determination" and not by "energy" as it uses to be with the western obsession and compulsion of matter, energy and big power at the expense of high determination or "Tai Chi". The Chinese "Lii" - though its primal senses are "Law", "Rationality" and "Reason", "Rite" and "Harmony" - may be viewed as "Skill". Here, Asia is the Far East and mainly Japan, the "mother tiger" and her "baby tigers ", namely Korea (South), Hong Kong, Singapore and Taiwan. The ride of the dragon is oriented elsewhere and devastated Viet Nam (the smaller dragon) - by its independence wars and communist insulation and isolation - is not yet in the game. Strategy is both an organizational level of action and a type of action based on disguise, deception, uncertainty, flexibility and adaptation

Generalized Inverses and Asymptotic Properties of Wald Tests

We consider Wald tests based on consistent estimators of g-inverses of the asymptotic covariance matrix ∑ of a statistic that is n^1/2-asymptotically normal distributed under the null hypothesis. Under the null hypothesis and under any sequence of local alternatives in the column space of ∑, these tests are asymptotically equivalent for any choice of g-inverses. For sequences of local alternatives not in the column space of ∑ and for a suitable choice of g- inverse, the asymptotic power of the corresponding Wald test can be made equal to zero or arbitrarily large. In particular, the test based on a consistent estimator of the Moore-Penrose inverse of ∑ has zero asymptotic power against sequences of local alternatives in the orthogonal complement to the column space of ∑

Cramer-Rao Bounds for Misspecified Models

In this paper, we derive some lower bounds of the Cramer-Rao type for the covariance matrix of any unbiased estimator of the pseudo-true parameters in a parametric model that may be misspecified. We obtain some lower bounds when the true distribution belongs either to a parametric model that may differ from the specified parametric model or to the class of all distributions with respect to which the model is regular. As an illustration, we apply our results to the normal linear regression model. In particular, we extend the Gauss-Markov Theorem by showing that the OLS estimator has minimum variance in the entire class of unbiased estimators of the pseudo-true parameters when the mean and the distribution of the errors are both misspecified

Probability Feedback in a Recursive System of Probability Models

This paper presents a general model for qualitative endogenous variables that is defined by a recursive system of conditional probability models in which the probabilities of some outcomes may depend on the probabilities of posterior outcomes. The model is related to, but conceptually different from C. D. Mallar's (1977) simultaneous probability model. It has as special cases the multivariate logit model (M. Nerlove and S. J. Press (1973, 1976)) and the constrained nested logit model (D. McFadden (1981)). The model can also be used to analyze outcomes of some game situations. Two examples are in particular considered: a game against Nature and a Stackelberg game under uncertainty. Identification of the structural parameters in the first example is seen to be related to the classical problem of stochastic revealed preference as studied by M. K. Richter and L. Shapiro (1978)