Non-parametric recursive estimates of a probability density function and its derivatives

Recursive estimates of a probability density function (pdf) are known. This paper presents recursive estimates of a derivative of any desired order of a pdf. Let f be a pdf on the real line and p?0 be any desired integer. Based on a random sample of size n from f, estimators f^(p)_n of f^(p), the pth order derivatives of f, are exhibited. These estimators are of the form $\text{n}{}^{\mathrm{?1}}\text{∑n}\text{j=1}\text{δ}{}_{\mathrm{jp}}$, where δ_jp depends only on p and the jth observation in the sample, and hence can be computed recursively as the sample size increases. These estimators are shown to be asymptotically unbiased, mean square consistent and strongly consistent, both at a point and uniformly on the real line. For pointwise properties, the conditions on f^(p) have been weakened with a little stronger assumption on the kernel function.     

Three models of OPEC leadership and policy in the aftermath of Iran

Collapse of the Shah's regime has transformed Iran's attitude regarding oil production policy. The nature of OPEC leadership is changing as well. Three models examine the nature of this leadership inside OPEC: (1) the conventional price leadership model, (2) a model emphasizing a concept of egalitarian leadership, and (3) a team model composed of coalitions. The three models establish the limits within which OPEC leadership is exercised. A composite model drawing upon all three sets of results suggests that Saudi Arabia shapes cartel policy not by itself, but through a dominant coalition of states. For most of the period 1969–1978 this coalition has been stable. Following the unsettling changes of 1973, cooptation of Iran into the dominant coalition in 1974 was an important step in achieving a new level of stability. But during the turbulence of regime transformation in Iran, the nature of the governing coalition appears to have changed. One consequence may be that in the future Saudi Arabia will yield more willingly to arguments heard within OPEC on behalf of upwards price pressure, especially in an atmosphere of growing political isolation and overall tight supply.     

Debt management in a small open economy: A theoretical and an empirical study for Belgium

This article analyzes the effects of debt management and its consequence for the control of base money in a small open economy (Belgium). The study compares the effects obtained from a small theoretical model with the results of a larger empirical model.The theoretical model focuses on the financing of government by money operation, on the bond rate, and on the international reserve of the Central Bank.The empirical model is a medium-term one, including the demand and the supply sectors of the economy and permitting simultaneous analysis of real and financial variables.The effects of an endogeneous or exogenous debt management have been studied by numerical simulation of modification in the public expenditure, the world trade, and the discount rate.     

On UMVU estimators and Bhattacharya bounds in exponential distributions

A subfamily of exponential distributions is considered and it is shown that the variance of the UMVU estimator of an estimable function g(θ) having power series expansion is the limit of Bhattacharya bounds.     

On uniform approximation of Poisson variates by normal ones

In this paper the accuracy of the normal approximation to the Poisson is treated from the viewpoint of direct approximation of Poisson variables by normal ones. The conclusions that are derived on the accuracy of this approximation lead (among others) to very useful results on confidence limits for the mean of a linear combination of independent Poisson variables; these latter are employed in precise determination of the composition of a mixture of radioactive isotopes by means of a scintillation counter.     

À propos de l’article de François-Xavier de Vaujany, « Les figures de la gestion du changement sociotechnique »

The approach adopted by François Xavier de Vaujany draws from “structurationist” research in English-speaking social sciences, a current that shares with the sociology of technology a vision of the contextual and negotiated nature of the links between technical and organizational phenomena. Various trajectories in the way organizations use new information and communication technology can be compared; and the role, examined that specific mediators play in the appropriation process. This approach provides stimulating input in discussions about the impact of new technology on organizational change.     

Asymptotical improvement of maximum likelihood estimators on Kullback–Leibler loss

We discuss the general form of a first-order correction to the maximum likelihood estimator which is expressed in terms of the gradient of a function, which could for example be the logarithm of a prior density function. In terms of Kullback–Leibler divergence, the correction gives an asymptotic improvement over maximum likelihood under rather general conditions. The theory is illustrated for Bayes estimators with conjugate priors. The optimal choice of hyper-parameter to improve the maximum likelihood estimator is discussed. The results based on Kullback–Leibler risk are extended to a wide class of risk functions.     

Note on the Cramér-Rao inequality in the nonregular case: the family of uniform distributions

We consider the family of uniform distributions with range of unit length. The main result of this note asserts that the average variance of any unbiased estimator of the midpoint of the range is not less than (2(n+1))(n+2))^-1 and this lower bound is sharp. The proof is based upon a nonregular version of the Cramér-Rao inequality.     

Conditional inference for subject-specific and marginal agreement: Two families of agreement measures

A two-stage procedure is described for assessing subject-specific and marginal agreement for data from a test-retest reliability study of a binary classification procedure. Subject-specific agreement is parametrized through the log odds ratio, while marginal agreement is reflected by the log ratio of the off-diagonal Poisson means. A family of agreement measures in the interval [-1, 1] is presented for both types of agreement. The conditioning argument described facilitates exact inference. The proposed methodology is demonstrated by way of an example involving hypothetical data chosen for illustrative purposes, and data from a National Health Survey Study (Rogot and Goldberg 1966).     

Estimation of an exponential quantile under pitman's measure of closeness

We consider the problem of estimating a quantile of an exponential distribution with unknown location and scale parameters under Pitman's measure of closeness (PMC). The loss function is required to satisfy some mild conditions but is otherwise arbitrary. An optimal estimator is obtained in the class of location-scale-equivariant estimators, and its admissibility in the sense of PMC is investigated.