On the estimation of the general parameter

In this paper, we first discuss the origin, developments and various thoughts by several researchers on the generalized linear regression estimator (GREG) due to Deville and Särndal [Deville, J.C., Särndal, C.E., 1992. Calibration estimators in survey sampling. J. Amer. Statist. Assoc. 87, 376-382]. Then, the problem of estimation of the general parameter of interest considered by Rao [Rao, J.N.K., 1994. Estimating totals and distribution functions using auxiliary information at the estimation stage. J. Official Statist. 10 (2), 153-165], and Singh [Singh, S., 2001. Generalized calibration approach for estimating the variance in survey sampling. Ann. Inst. Statist. Math. 53 (2), 404-417; Singh, S., 2004. Golden and Silver Jubilee Year-2003 of the linear regression estimators. In: Proceedings of the Joint Statistical Meeting, Toronto (Available on the CD), 4382-4380; Singh, S., 2006. Survey statisticians celebrate Golden Jubilee Year-2003 of the linear regression estimator. Metrika 1-18] is further investigated. In addition to that it is shown that the Farrell and Singh [Farrell, P.J., Singh, S., 2005. Model-assisted higher order calibration of estimators of variance. Australian & New Zealand J. Statist. 47 (3), 375-383] estimators are also a special case of the proposed methodology. Interestingly, it has been noted that the single model assisted calibration constraint studied by Farrell and Singh [Farrell, P.J., Singh, S., 2002. Re-calibration of higher order calibration weights. Presented at Statistical Society of Canada conference, Hamilton (Available on CD); Farrell, P.J., Singh, S., 2005. Model-assisted higher order calibration of estimators of variance. Australian & New Zealand J. Statist. 47 (3), 375-383] and Wu [Wu, C., 2003. Optimal calibration estimators in survey sampling. Biometrika 90, 937-951] is not helpful for calibrating the Sen [Sen, A.R., 1953. On the estimate of the variance in sampling with varying probabilities. J. Indian Soc. Agril. Statist. 5, 119-127] and Yates and Grundy [Yates, F., Grundy, P.M., 1953. Selection without replacement from within strata with probability proportional to size. J. Roy. Statist. Soc. Ser. 15, 253-261] estimator of the variance of the linear regression estimator under the optimal designs of Godambe and Joshi [Godambe, V.P., Joshi, V.M., 1965. Admissibility and Bayes estimation in sampling finite populations—I. Ann. Math. Statist. 36, 1707-1722]. Three new estimators of the variance of the proposed linear regression type estimator of the general parameters of interest are introduced and compared with each other. The newly proposed two-dimensional linear regression models are found to be useful, unlike a simulation based on a couple of thousands of random samples, in comparing the estimators of variance. The use of knowledge of the model parameters in assisting the estimators of variance has been found to be beneficial. The most attractive feature is that it has been shown theoretically that the proposed method of calibration always remains more efficient than the GREG estimator.     

A general framework for the evaluation of symbol recognition methods

Performance evaluation is receiving increasing interest in graphics recognition. In this paper, we discuss some questions regarding the definition of a general framework for evaluation of symbol recognition methods. The discussion is centered on three key elements in performance evaluation: test data, evaluation metrics and protocols of evaluation. As a result of this discussion we state some general principles to be taken into account for the definition of such a framework. Finally, we describe the application of this framework to the organization of the first contest on symbol recognition in GREC’03, along with the results obtained by the participants.     

Explicit group versus implicit line iterative methods

In this paper, a new explicit 4 point and 9 point block overrelaxation scheme for the numerical solution of the sparse linear systems derived from the discretisation of self-adjoint elliptic partial differential equations by finite difference/element techniques. A comparison with the implicit 1-line and 2‐line block S.O.R. schemes for the model problem clearly demonstrates the new techniques to be computationally superior.     

A general extending and constraining procedure for linear iterative methods

Algebraic reconstruction techniques (ARTs), on both their successive and simultaneous formulations, have been developed since the early 1970s as efficient ‘row-action methods’ for solving the image-reconstruction problem in computerized tomography. In this respect, two important development directions were concerned with, first, their extension to the inconsistent case of the reconstruction problem and, second, their combination with constraining strategies, imposed by the particularities of the reconstructed image. In the first part of this paper, we introduce extending and constraining procedures for a general iterative method of an ART type and we propose a set of sufficient assumptions that ensure the convergence of the corresponding algorithms. As an application of this approach, we prove that Cimmino's simultaneous reflection method satisfies this set of assumptions, and we derive extended and constrained versions for it. Numerical experiments with all these versions are presented on a head phantom widely used in the image reconstruction literature. We also consider hard thresholding constraining used in sparse approximation problems and apply it successfully to a 3D particle image-reconstruction problem.     

A general compiler for password-authenticated group key exchange protocol

Password-authenticated group key exchange protocols allow that a group of participants who share a human-memorable (short) password can obtain a common session key in a secure way over public networks. In this paper, we design a compiler, which transforms any basic group key exchange protocol (which is only resistant against benign adversaries) into a password-authenticated group key exchange protocol. We prove that the new protocol outputted by the compiler is secure in the random-oracle and ideal-cipher models if the underlying group key exchange protocol is secure. Our compiler is practical since it only needs four more additional rounds of communications, which means that the new protocol still holds constant-round property if the original one is a constant-round scheme.     

On the general problem of pole assignment

Given a linear, time-invariant, minimal and strictly proper system  set of monic polynomials φ _i (s), i = l, 2, [tdot],q, such that φ _i (s) divides φ _i?1 (s), i = 2, 3, [tdot],q a method for finding a proper feedback system  which makes the invariant polynomials of the closed-loop system equal to the φ _i (s) is established and a sufficient condition which ensures the existence of  is determined. This method can also be used to assign the poles of the compensated system provided that certain poles are multiple. The order of the required compensator is generally loss than that of the Luenberger or the Wolovich compensation schemes.     

On the optical-mechanical analogy in general relativity

The existence of a new optical-mechanical analogy is revealed between the equation of rotational motion of a body in the mechanics of general relativity (GR) and the first pair of the Maxwell equations. It is also shown that the equations of rotational motion are a consequence of the equations of translational motion in GR mechanics.     

Two general methods for dynamizing decomposable searching problems

We define two classes of decomposable searching problems and consider ways of efficiently dynamizing them. For the first class, DD, we show that both insertions and deletions can be processed efficiently. For the second class, MD, we exploit a merge technique to obtain better insertion times. We also give a number of examples of problems to which the methods apply, including the dynamic maintenance of quadtrees and of the common intersection of finitely many halfspaces in the plane.     

Probabilistic sensitivity analysis methods for general decision models

Probabilistic sensitivity analysis has previously been described for the special case of dichotomous decision trees. We now generalize these techniques for a wider range of decision problems. These methods of sensitivity analysis allow the analyst to evaluate the impact of the multivariate uncertainty in the data used in the decision model and to gain insight into the probabilistic contribution of each of the variables to the decision outcome. The techniques are illustrated using Monte Carlo simulation on a trichotomous decision tree. Application of these powerful tools permits the decision analyst to investigate the structure and limitations of more complex decision problems with inherent uncertainties in the data upon which the decisions are based. Probabilistic sensitivity measures can provide guidance into the allocation of resources to resolve uncertainty about critical components of medical decisions.     

Unitary representations of the hyperfinite Heisenberg group and the logical extension methods in physics

In order to provide a general framework for applications of nonstandard analysis to quantum physics, the hyperfinite Heisenberg group, which is a finite Heisenberg group in the nonstandard universe, is formulated and its unitary representations are examined. The ordinary Schrödinger representation of the Heisenberg group is obtained by a suitable standardization of its internal representation. As an application, a nonstandard-analytical proof of noncommutative Parseval's identity based on the orthogonality relations for unitary representations of finite groups is shown. This attempt is placed in a general framework, called the logical extension methods in physics, which aims at the systematic applications of methods of foundations of mathematics to extending physical theories. The program and the achievement of the logical extension methods are explained in some detail.Dedicated to Professor Huzihiro Araki on his sixtieth birthday     

On the rational subsets of the free group

 We show that every rational subset of a free group of finite rank is either disjunctive or has finite index. We then generalise this result to virtually free groups: if G is virtually free and R is a rational subset of G, then the syntactic normal subgroup N of R is either finite or has finite index. Received November 25, 1992/February 3, 1995     

Adaptive logarithmic discretization for numerical renormalization group methods

The problem of the logarithmic discretization of an arbitrary positive function (such as the density of states) is studied in general terms. Logarithmic discretization has arbitrary high resolution around some chosen point (such as Fermi level) and it finds application, for example, in the numerical renormalization group (NRG) approach to quantum impurity problems (Kondo model), where the continuum of the conduction band states needs to be reduced to a finite number of levels with good sampling near the Fermi level. The discretization schemes under discussion are required to reproduce the original function after averaging over different interleaved discretization meshes, thus systematic deviations which appear in the conventional logarithmic discretization are eliminated. An improved scheme is proposed in which the discretization-mesh points themselves are determined in an adaptive way; they are denser in the regions where the function has higher values. Such schemes help in reducing the residual numeric artefacts in NRG calculations in situations where the density of states approaches zero over extended intervals. A reference implementation of the solver for the differential equations which determine the full set of discretization coefficients is also described.     

On the symmetry group of the Mollard code

We study the symmetry group of a binary perfect Mollard code M(C,D) of length tm + t + m containing as its subcodes the codes C ¹ and D ² formed from perfect codes C and D of lengths t and m, respectively, by adding an appropriate number of zeros. For the Mollard codes, we generalize the result obtained in [1] for the symmetry group of Vasil’ev codes; namely, we describe the stabilizer

$$Sta{b_{{D^2}}}$$

Sym(M(C,D)) of the subcode D ² in the symmetry group of the code M(C,D) (with the trivial function). Thus we obtain a new lower bound on the order of the symmetry group of the Mollard code. A similar result is established for the automorphism group of Steiner triple systems obtained by the Mollard construction but not necessarily associated with perfect codes. To obtain this result, we essentially use the notions of “linearity” of coordinate positions (points) of a nonlinear perfect code and a nonprojective Steiner triple system.

     

On the problem and methods of corporate choice

The problems of collective and corporate decision-making that arise in corporate systems are considered. To solve them, an axiomatic approach that allows arriving at stable trade-offs is developed. Constructive methods to solve the problems of collective and corporate decision-making are obtained.     

Alternating group explicit (AGE) iterative methods

In this paper the Alternating Group Explicit (AGE) methods, modified analogues of the classical Alternating Direction Implicit (ADI) methods, are introduced. Their explicit nature and their obvious parallelism, in contrast with the inherent parallelism of the ADI methods, makes them most suitable for the solution of the resulting linear systems arising from the discretisation of a class of elliptic PDEs on a Parallel Computer of SIMD (Single Instruction Stream-Multiple Data Stream) type. The determination of optimum sets of acceleration parameters in 2-dimensional problems is discussed and numerical experiments are successfully completed.     

On the convergence of variable-metric methods

In this paper the convergence of variablemetric methods is considered. The minimum of a quadratic function is attained with a number of iterations equal to the rank of the Hessian matrix of the function. Under certain conditions the sequence of variable-metric matrices tends to the pseudoinverse of the Hessian matrix.     

On the classification performance of TAN and general Bayesian networks

Over a decade ago, Friedman et al. introduced the Tree Augmented Naïve Bayes (TAN) classifier, with experiments indicating that it significantly outperformed Naïve Bayes (NB) in terms of classification accuracy, whereas general Bayesian network (GBN) classifiers performed no better than NB. This paper challenges those claims, using a careful experimental analysis to show that GBN classifiers significantly outperform NB on datasets analyzed, and are comparable to TAN performance. It is found that the poor performance reported by Friedman et al. are not attributable to the GBN per se, but rather to their use of simple empirical frequencies to estimate GBN parameters, whereas basic parameter smoothing (used in their TAN analyses but not their GBN analyses) improves GBN performance significantly. It is concluded that, while GBN classifiers may have some limitations, they deserve greater attention, particularly in domains where insight into classification decisions, as well as good accuracy, is required.