Smoothing Framework Research Articles

Optimal smoothing in visual motion perception.

When a flash is aligned with a moving object, subjects perceive the flash to lag behind the moving object. Two different models have been proposed to explain this "flash-lag" effect. In the motion extrapolation model, the visual system extrapolates the location of the moving object to counteract neural propagation delays, whereas in the latency difference model, it is hypothesized that moving objects are processed and perceived more quickly than flashed objects. However, recent psychophysical experiments suggest that neither of these interpretations is feasible (Eagleman & Sejnowski, 2000a, 2000b, 2000c), hypothesizing instead that the visual system uses data from the future of an event before committing to an interpretation. We formalize this idea in terms of the statistical framework of optimal smoothing and show that a model based on smoothing accounts for the shape of psychometric curves from a flash-lag experiment involving random reversals of motion direction. The smoothing model demonstrates how the visual system may enhance perceptual accuracy by relying not only on data from the past but also on data collected from the immediate future of an event.

Imperfect Competition, Returns To Scale and Productivity Growth In Australian Manufacturing: A Smooth Transition Approach To Trade Liberalisation

This Paper examines the relationship between trade liberalization and productivity growth for Australian manufacturing. An imperfect competition, non-CRS, smooth transition empirical framework is employed for analysis. GMM estimates of the logistic smooth transition model imply that trade reform impacts take approximately four years to complete, but do not occur over the same time period for all industries. In response to trade reforms, for most industries a significant improvement in productivity is estimated, these improvements are associated with lower mark-ups and falling scale parameters. A minority of industries however, experienced no change or falling productivity growth in response to reforms, these industries tended to have the highest absolute protection levels. [D24, F12, C52, L60]

By how much can residual minimization accelerate the convergence of orthogonal residual methods

We capitalize upon the known relationship between pairs of orthogonal and minimal residual methods (or, biorthogonal and quasi-minimal residual methods) in order to estimate how much smaller the residuals or quasi-residuals of the minimizing methods can be compared to those of the corresponding Galerkin or Petrov–Galerkin method. Examples of such pairs are the conjugate gradient (CG) and the conjugate residual (CR) methods, the full orthogonalization method (FOM) and the generalized minimal residual (GMRES) method, the CGNE and BiCG versions of applying CG to the normal equations, as well as the biconjugate gradient (BiCG) and the quasi-minimal residual (QMR) methods. Also the pairs consisting of the (bi)conjugate gradient squared (CGS) and the transpose-free QMR (TFQMR) methods can be added to this list if the residuals at half-steps are included, and further examples can be created easily. The analysis is more generally applicable to the minimal residual (MR) and quasi-minimal residual (QMR) smoothing processes, which are known to provide the transition from the results of the first method of such a pair to those of the second one. By an interpretation of these smoothing processes in coordinate space we deepen the understanding of some of the underlying relationships and introduce a unifying framework for minimal residual and quasi-minimal residual smoothing. This framework includes the general notion of QMR-type methods.

Descriptor Kalman estimators

A unifying framework of steady-state Kalman filtering, smoothing and prediction for descriptor systems is presented by using the innovation analysis method in the time domain. The descriptor Kalman estimators are presented on the basis of the autoregressive moving-average innovation model and white-noise estimators. The new algorithms of steady-state descriptor Kalman estimators gains are given. The solution of the Riccati equation is avoided. To ensure the asymptotic stability of descriptor Kalman estimators with respect to the initial values of innovation process, formulae for selecting their initial values are given. A simulation example shows the usefulness of the proposed results.

Pension Fund Asset Valuation and Investment

ABSTRACTThe theoretical basis for, and practical application of, the discounted income method for valuing UK pension fund assets is discussed, with particular reference to the widely adopted application to variable income (equity type) assets, as proposed by Day & McKelvey (1964), in the context of both the management and compliance objectives of pension fund valuation. An alternative methodology is proposed in which consistency with assets, liabilities, and market values is demanded, with smoothing of the valuation result achieved on an explicit rather than implicit basis. It is then demonstrated that the explicit smoothing parameter can be set so as to achieve the historic smoothness framework for establishing pension fund investment policy.In conclusion the paper suggests greater emphasis on market-related methodologies for compliance valuations and leaves open the choice of methodology for management valuations and monitoring purposes, on the grounds that there is a large subjective element in any realistic basis. However, it is demonstrated that while smoother than unadjusted market-related methods, other aspects of the dynamics of the funding level under the method of Day & McKelvey can be perverse and it is suggested that this method should not be allowed to dictate investment decisions.

Robustness of multi-grid applied to anisotropic equations on convex domains and on domains with re-entrant corners

We analyse multi-grid applied to anisotropic equations within the framework of smoothing and approximation-properties developed by Hack busch. For a model anisotropic equation on a square, we give an up-till-now missing proof of an estimate concerning the approximation property which is essential to show robustness. Furthermore, we show a corresponding estimate for a model anisotropic equation on an L-shaped domain. The existing estimates for the smoothing property are not suitable to prove robustness for either 2-cyclic Gauss-Seidel smoothers or for less regular problems such as our second model equation. For both cases, we give sharper estimates. By combination of our results concerning smoothing- and approximation-properties, robustness of W-cycle multi-grid applied to both our model equations will follow for a number of smoothers.

Some problems of exponential smoothing

The paper deals with some practical problems connected with the classical exponential smoothing in time series. The fundamental theorem of the exponential smoothing is extended to the case with missing observations and an interpolation procedure in the framework of the exponential smoothing is described. A simple method of the exponential smoothing for multivariate time series is suggested.

Can the Production Smoothing Model of Inventory Behavior be Saved?

The production smoothing model of inventory behavior has a long and venerable history and theoretical foundations that seem very strong. Yet certain overwhelming facts seem not only to defy explanation within the production smoothing framework, but actually to argue that the basic idea of production smoothing is all wrong. Most prominent among these is the fact that the variance of detrended production exceeds the variance of detrended sales. This paper first documents the stylized facts. Then it derives the production smoothing model rigorously and explains how the model can be amended to make it consistent with the facts. Finally, it reviews the theoretical and empirical evidence and tries to draw some tentative conclusions.

On dual regularity and value convergence theorems

We deal with the Value Convergence Problem in the piecewise smooth framework including the rates of convergence and the number of (symmetric) value allocations. In this connection, we also discuss the concept of dual regularity and give several equivalent ways of formulating the regularity conditions.

Moser's implicit function theorem in the framework of analytic smoothing

Moser's implicit function theorem in the framework of analytic smoothing

A unifying framework for linear estimation: Generalized partitioned algorithms

In this paper, generalized partitioned algorithms are presented that serve as the unifying framework for linear filtering and smoothing. The fundamental and all encompassing nature of the generalized partitioned algorithms (hereon denoted GPA) is clearly demonstrated by showing that the GPA contain as special cases important generalizations of past wellknown linear estimation algorithms, as well as whole families of such algorithms, of which all previously obtained major filtering and smoothing algorithms are special cases. Specifically, generalized partitioned filtering and smoothing algorithms are given in terms of integral expressions, that are theoretically interesting, computationally attractive, as well as provide a unification of all previous approaches to linear filtering and smoothing, and clear delineation of their inter-relationships. In particular, the GPA for filtering are shown to contain as special cases families of filtering algorithms which constitute generalizations of the Kalman-Bucy, and Chandrasekhar algorithms as well as of the previously obtained partitioned algorithms of Lainiotis. These generalizations pertain to arbitrary initial conditions and time-varying models. Further, the GPA for smoothing are shown to contain two families of generalized backward and forward smoothing algorithms valid for arbitrary boundary conditions, of which all previous backward and forward algorithms are special cases. It is also shown that the GPA may also be given in terms of an imbedded generalized Chandrasekhar algorithm with the consequent computational advantages. Furthermore, the GPA are shown to serve as the basis of computationally effective, fast, and numerically robust algorithms for the numerical implementation of the estimation formulas. A particularly effective doubling algorithm is also given for calculating the steady-state filter. The partitioned numerical algorithms are given exactly in terms of a set of elemental solutions which are both simple as well as completely decoupled, and as such computable in either a parallel or serial processing mode. Moreover, the overall solution is given by a simple recursive operation on the elemental solutions.

A unifying framework for linear estimation: Generalized partitioned algorithms

In this paper, generalized partitioned algorithms are presented that serve as the unifying framework for linear filtering and smoothing. The fundamental and all encompassing nature of the generalized partitioned algorithms (hereon denoted GPA) is clearly demonstrated by showing that the GPA contain as special cases important generalizations of past well-known linear estimation algorithms, as well as whole families of such algorithms, of which all previously obtained major filtering and smoothing algorithms are special cases. Specifically, generalized partitioned filtering and smoothing algorithms are given in terms of integral expressions, that are theoretically interesting, computationally attractive, as well as provide a unification of all previous approaches to linear filtering and smoothing, and clear delineation of their inter-relationships. In particular, the GPA for filtering are shown to contain as special cases families of filtering algorithms which constitute generalizations of the Kalman-Bucy, and Chandrasekhar algorithms as well as of the previously obtained partitioned algorithms of Lainiotis. These generalizations pertain to arbitrary initial conditions and time-varying models. Further, the GPA for smoothing are shown to contain two families of generalized backward and forward smoothing algorithms valid for arbitrary boundary conditions, of which all previous backward and forward algorithms are special cases. It is also shown that the GPA may also be given in terms of an imbedded generalized Chandrasekhar algorithm with the consequent computational advantages. Furthermore, the GPA are shown to serve as the basis of computationally effective, fast, and numerically robust algorithms for the numerical implementation of the estimation formulas. A particularly effective doubling algorithm is also given for calculating the steady-state filter. The partitioned numerical algorithms are given exactly in terms of a set of elemental solutions which are both simple as well as completely decoupled, and as such computable in either a parallel or serial processing mode. Moreover, the overall solution is given by a simple recursive operation on the elemental solutions.