Set Of Auxiliary Variables Research Articles

The Role of Auxiliary Variables in Deterministic and Deterministic-Stochastic Spatial Models of Air Temperature in Poland

Our study examines the role of auxiliary variables in the process of spatial modelling and mapping of climatological elements, with air temperature in Poland used as an example. The multivariable algorithms are the most frequently applied for spatialization of air temperature, and their results in many studies are proved to be better in comparison to those obtained by various one-dimensional techniques. In most of the previous studies, two main strategies were used to perform multidimensional spatial interpolation of air temperature. First, it was accepted that all variables significantly correlated with air temperature should be incorporated into the model. Second, it was assumed that the more spatial variation of air temperature was deterministically explained, the better was the quality of spatial interpolation. The main goal of the paper was to examine both above-mentioned assumptions. The analysis was performed using data from 250 meteorological stations and for 69 air temperature cases aggregated on different levels: from daily means to 10-year annual mean. Two cases were considered for detailed analysis. The set of potential auxiliary variables covered 11 environmental predictors of air temperature. Another purpose of the study was to compare the results of interpolation given by various multivariable methods using the same set of explanatory variables. Two regression models: multiple linear (MLR) and geographically weighted (GWR) method, as well as their extensions to the regression-kriging form, MLRK and GWRK, respectively, were examined. Stepwise regression was used to select variables for the individual models and the cross-validation method was used to validate the results with a special attention paid to statistically significant improvement of the model using the mean absolute error (MAE) criterion. The main results of this study led to rejection of both assumptions considered. Usually, including more than two or three of the most significantly correlated auxiliary variables does not improve the quality of the spatial model. The effects of introduction of certain variables into the model were not climatologically justified and were seen on maps as unexpected and undesired artefacts. The results confirm, in accordance with previous studies, that in the case of air temperature distribution, the spatial process is non-stationary; thus, the local GWR model performs better than the global MLR if they are specified using the same set of auxiliary variables. If only GWR residuals are autocorrelated, the geographically weighted regression-kriging (GWRK) model seems to be optimal for air temperature spatial interpolation.

Calibration estimation in dual-frame surveys

Survey statisticians make use of auxiliary information to improve estimates. One important example is calibration estimation, which constructs new weights that match benchmark constraints on auxiliary variables while remaining “close” to the design weights. Multiple-frame surveys are increasingly used by statistical agencies and private organizations to reduce sampling costs and/or avoid frame undercoverage errors. Several ways of combining estimates derived from such frames have been proposed elsewhere; in this paper, we extend the calibration paradigm, previously used for single-frame surveys, to calculate the total value of a variable of interest in a dual-frame survey. Calibration is a general tool that allows to include auxiliary information from two frames. It also incorporates, as a special case, certain dual-frame estimators that have been proposed previously. The theoretical properties of our class of estimators are derived and discussed, and simulation studies conducted to compare the efficiency of the procedure, using different sets of auxiliary variables. Finally, the proposed methodology is applied to real data obtained from the Barometer of Culture of Andalusia survey.

Applications of the generalized Langevin equation: Towards a realistic description of the baths

The Generalised Langevin Equation (GLE) method, as developed in Ref. [Phys. Rev. B 89, 134303 (2014)], is used to calculate the dissipative dynamics of systems described at the atomic level. The GLE scheme goes beyond the commonly used bilinear coupling between the central system and the bath, and permits us to have a realistic description of both the dissipative central system and its surrounding bath. We show how to obtain the vibrational properties of a realistic bath and how to convey such properties into an extended Langevin dynamics by the use of the mapping of the bath vibrational properties onto a set of auxiliary variables. Our calculations for a model of a Lennard-Jones solid show that our GLE scheme provides a stable dynamics, with the dissipative/relaxation processes properly described. The total kinetic energy of the central system always thermalises toward the expected bath temperature, with appropriate fluctuation around the mean value. More importantly, we obtain a velocity distribution for the individual atoms in the central system which follows the expected canonical distribution at the corresponding temperature. This confirms that both our GLE scheme and our mapping procedure onto an extended Langevin dynamics provide the correct thermostat. We also examined the velocity autocorrelation functions and compare our results with more conventional Langevin dynamics.

Study of Periodic Structures at Oblique Incidence by Radial Point Interpolation Meshless Method

This paper presents a novel split-field radial point interpolation meshless (RPIM) scheme for the study of periodic structures under oblique incidence condition. The time delay in the transverse plane is eliminated with the introduction of a set of auxiliary variables. With the application of split-field technique to the standard RPIM method, a leap-frog formulation is derived. Numerical experiment is implemented to demonstrate the effectiveness of the code and the obtained result is compared with result of split-field finite-difference time domain method.

Improving forest field inventories by using remote sensing data in novel sampling designs

It is becoming more common that auxiliary information from remote sensing is available at the planning stage of a forest field inventory. Recent developments in sampling theory allows the inclusion of such information in the sampling design to obtain better samples and, hence, improve estimates of common forest attributes. We explain the methodology and evaluate the possibility of including data from airborne laser scanning in the sampling design. The novel designs that we use can select samples that are balanced on a set of auxiliary variables and (or) well spread in a set of auxiliary variables. The results from a simulation study with real data indicate that significant improvement is achieved.

Bilinear Power System State Estimation

This paper presents a three-stage state estimation methodology based on the sequential solution of two weighted least squares (WLS) linear problems with a nonlinear explicit transformation in between. This requires that appropriate sets of auxiliary variables be introduced so that the resulting measurement models become linear. Simulation results show that the proposed approach yields, in a non-iterative manner, virtually the same solution as that provided by the Gauss-Newton iterative scheme arising in the conventional WLS method.

Regression with imputed covariates: A generalized missing-indicator approach

A common problem in applied regression analysis is that covariate values may be missing for some observations but imputed values may be available. This situation generates a trade-off between bias and precision: the complete cases are often disarmingly few, but replacing the missing observations with the imputed values to gain precision may lead to bias. In this paper, we formalize this trade-off by showing that one can augment the regression model with a set of auxiliary variables so as to obtain, under weak assumptions about the imputations, the same unbiased estimator of the parameters of interest as complete-case analysis. Given this augmented model, the bias-precision trade-off may then be tackled by either model reduction procedures or model averaging methods. We illustrate our approach by considering the problem of estimating the relation between income and the body mass index (BMI) using survey data affected by item non-response, where the missing values on the main covariates are filled in by imputations.

Regression with Imputed Covariates: A Generalized Missing Indicator Approach

A common problem in applied regression analysis is that covariate values may be missing for some observations but imputed values may be available. This situation generates a trade-off between bias and precision: the complete cases are often disarmingly few, but replacing the missing observations with the imputed values to gain precision may lead to bias. In this paper we formalize this trade-off by showing that one can augment the regression model with a set of auxiliary variables so as to obtain, under weak assumptions about the imputations, the same unbiased estimator of the parameters of interest as complete-case analysis. Given this augmented model, the bias-precision trade-off may then be tackled by either model reduction procedures or model averaging methods. We illustrate our approach by considering the problem of estimating the relation between income and the body mass index (BMI) using survey data affected by item non-response, where the missing values on the main covariates are filled in by imputations.

On Pricing Derivatives in the Presence of Auxiliary State Variables

Binomial, trinomial, and other lattice-based option pricing procedures are extremely useful in dealing with early exercise because solution by backward induction is possible. As one rolls back through the tree, the option value at each node depends on the current price for the underlying and the paths that might be followed going forward. But for many kinds of derivatives, the value at a given point in time depends on both the current asset price and the price path that it has followed up to the current point. Derivatives on interest rates in the Heath-Jarrow-Morton (HJM) model are one example. Another is option pricing when the underlying volatility varies over time according to a GARCH model. The most successful technique for adapting a lattice model to a path-dependent process has been to carry along a set of auxiliary variables that summarize (approximately) the necessary path information at each node. These techniques work, but they are typically very time consuming. In this article, Lin and Ritchken present a way to greatly increase the efficiency of this procedure. Some auxiliary path information must still be carried through the tree, but much less is needed. They demonstrate the sharp increase in performance this makes possible in an HJM application and for an underlying that follows a GARCH process. <b>TOPICS:</b>Options, simulations

Calculating Comparable Statistics from Incomparable Surveys, with an Application to Poverty in India

Applied economists are often interested in studying changes over time of important economic indicators, such as inequality or poverty, but such comparisons can be made impossible by changes in data collection methodology. We describe an easily implemented procedure to recover comparability that can be adopted whenever the statistic of interest satisfies a moment condition, when the researcher has available a set of auxiliary variables whose reports are not affected by the different survey design, and whose relation with the main variable of interest is stable over time. We analyze the asymptotic properties of the estimator taking into account the presence of clustering, stratification, and sampling weights, which characterize most household surveys. We use the 1999-2000 Round of the Indian National Sample Survey as an empirical illustration. Due to important changes in the adopted questionnaire, the unadjusted figures are likely to understate poverty relative to the previous rounds. We use previous waves of the same survey to provide evidence supporting the plausibility of the identifying assumptions and conclude that most of the very large reduction in poverty implied by the unadjusted figures is real.

Superparamagnetic segmentation by excitable neural systems.

Magnetic modeling for clustering or segmentation purposes can either associate the image data to external quenched fields or to the interactions among a set of auxiliary variables. The latter gives rise to superparamagnetic segmentation and is usually done with Potts systems. We have used the superparamagnetic clustering technique to segment images, with the aid of different associated systems. Results using Potts model are comparable to those obtained using excitable FitzHugh-Nagumo and Morris-Lecar model neurons. Interactions between the associated system components are a function of the difference of luminosity on a gray scale of neighbor pixels and the difference of membrane potential.

Radiation Pressure Dynamics in Planetary Exospheres II. Closed Solutions for the Evolution of Orbital Elements

We present the exact solutions in three dimensions for the orbital elements of a satellite particle continuously exposed to weak solar radiation. The solutions are obtained from a set of auxiliary variables, which are separable and therefore integrable. We have illustrated various examples of the behavior of the elements as they evolve cyclically. In addition, there are three items worthy of note: (1) The planar case, wherein the orbital plane contains the Sun, has been solved previously; but here a near-planar orbit is shown to evolve away from its original, nearly planar orientation. This consequence of radiation pressure may be contrasted with gravitational perturbation by massive bodies in the orbital plane, which tend to stabilize such orbits. (2) In the general, three-dimensional case the orbital elements not only have components that vary with time, as expected, in a uniform sinusoidal manner. They possess, as well, nonuniform sinusoidal variations that have the same period as the uniform variations. (3) The semimajor axis, a, which is related to the total energy, may be regarded as constant in the first order, on the grounds that a particle returns essentially to its starting point after one orbit. Here we derive the actual time variation of a from the extended Laplace constant. That constant was obtained in Paper I from the separation of variables that is allowed when the perturbed Keplerian problem is formulated in parabolic coordinates, and it remains a valid constant even when the total Keplerian energy is not. The relative amplitude, Δa(t)/a(0) varies as (a/rx)4, where rx is the distance from the planet where the gravitational and radiative acceleration are equal (i.e., the radius of the exosphere). Hence, the variation in a(t) is very small, except for orbits comparable in size to the exosphere itself.

Improved covariant quantization of the heterotic superstring

A generalized lagrangian BRST formalism is developed and used to study the covariant quantization of the heterotic superstring. The quantum action is by construction invariant under the off-shell nilpotent BRST transformations, which is achieved by introducing a minimal set of auxiliary variables with nonzero ghost number. The method relies on the classical gauge structure, and represents a natural lagrangian extension of the ideas existing in the hamiltonian BRST approach.

Periodic inverse problem for a new hierarchy of coupled evolution equations

We study the inverse problem with periodic boundary condition for a new class of integrable nonlinear evolution equations. The multiphase periodic solutions for the nonlinear fields (p, q, r) are expressed in terms of the Riemann theta function, which is obtained via the linearization of the flows of the set of auxiliary variables “μj” on a Riemann surface. An explicit case is evaluated to obtain the form of the algebraic curve on which the variables “μj” move.

Échantillonnage représentatif optimum à probabilités inégales

We propose to use some inequal probability sampling algorithms in order to approach the representativeness of selected samples for a set of auxiliary variables, and to produce jointly optimal probabilities p (s) for sample selection. On French Census datas and for small sample sizes (a few units) in a modest size population (below 100 people), we may use the very simple Horvitz estimator instead of the more complex regression estimator, because we don't take into account the auxiliary information in the estimator formula, but during the procedure of selection.

A Realization Procedure for Systems of Nonlinear Higher-order Differential Equations

Abstract Nonlinear realization theory has ooncentrated so far on the realization of non-linear input-output naps, despite the fact that many (physical) nonlinear systems are more naturally described by a set of algebraic and (higher-order) differential equations involving the external variables (inputs and outputs) of the system. In this paper we deal with the realization problem for this last case. We show that under general conditions the existence of minimal realizations involving a set of auxiliary variables, called driving variables, is guaranteed. In general these extra variables cannot be omitted. Sufficient conditions are given for the existence of realizations involving only the state and the external variables. We give a constructive procedure to obtain realizations with or without driving variables. This realization procedure is also applied to systems given by the interconnection of nonlinear state space systems.

On realization of nonlinear systems described by higher-order differential equations

We consider systems of smooth nonlinear differential and algebraic equations in which some of the variables are distinguished as “external variables.” The realization problem is to replace the higher-order implicit differential equations by first-order explicit differential equations and the algebraic equations by mappings to the external variables. This involves the introduction of “state variables.” We show that under general conditions there exist realizations containing a set of auxiliary variables, called “driving variables.” We give sufficient conditions for the existence of realizations involving only state variables and external variables, which can then be split into input and output variables. It is shown that in general there are structural obstructions for the existence of such realizations. We give a constructive procedure to obtain realizations with or without driving variables. The realization procedure is also applied to systems defined by interconnections of state space systems. Finally, a theory of equivalence transformations of systems of higher-order differential equations is developed.

Design of Machine-Tools: The Random Response Calculations of Machine Tools Subjected to Stochastic Excitations Using Dynamic Condensation Technique

The response spectral density is an important parameter which should be examined by a machine-tool analyst. A new approach for the calculation of response spectral density for a linear stationary random multi-degree-of-freedom system is presented. This method is based on condensing the system matrices and introducing a set of auxiliary variables. The response spectral density matrix obtained by using this new approach contains the spectral densities and the cross-spectral densities of the master degrees-of-freedom chosen. The new method requires significantly less computation time, as compared to conventional methods, for calculating response spectral densities associated with the selected number of degrees of freedom. To compare the computation time, three numerical examples are presented.

Reality constraints for the periodic sine-Gordon equation

A simple method is presented for ensuring the reality of solutions of the periodic sine-Gordon equation. The method consists of forcing a simple polynomial constraint on the initial conditions of a set of auxiliary variables. Numerical results are presented to demonstrate the method's practicality.

A new approach for the calculation of response spectral density of a linear stationary random multidegree of freedom system

A new approach for the calculation of response spectral density for a linear stationary random multidegree of freedom system is presented. The method is based on modifying the stochastic dynamic equations of the system by using a set of auxiliary variables. The response spectral density matrix obtained by using this new approach contains the spectral densities and the cross-spectral densities of the system generalized displacements and velocities. The new method requires significantly less computation time as compared to the conventional method for calculating response spectral densities. Two numerical examples are presented to compare quantitatively the computation time.