Generalized solutions of a nonlinear parabolic equation with generalized functions as initial data

In [H. Brezis, A. Friedman, Nonlinear parabolic equations involving measures as initial conditions, J. Math. Pure Appl. (9) (1983) 73-97.] Brezis and Friedman prove that certain nonlinear parabolic equations, with the delta-measure as initial data, have no solution. However in [J.F. Colombeau, M. Langlais, Generalized solutions of nonlinear parabolic equations with distributions as initial conditions, J. Math. Anal. Appl (1990) 186-196.] Colombeau and Langlais prove that these equations have a unique solution even if the delta-measure is substituted by any Colombeau generalized function of compact support. Here we generalize Colombeau and Langlais` result proving that we may take any generalized function as the initial data. Our approach relies on recent algebraic and topological developments of the theory of Colombeau generalized functions and results from [J. Aragona, Colombeau generalized functions on quasi-regular sets, Publ. Math. Debrecen (2006) 371-399.]. (C) 2009 Elsevier Ltd. All rights reserved.

On the Multiplicity of Orthogonal Geodesics in Riemannian Manifold With Concave Boundary. Applications to Brake Orbits and Homoclinics

Let (M, g) be a complete Riemannian Manifold, Omega subset of M an open subset whose closure is diffeomorphic to an annulus. If partial derivative Omega is smooth and it satisfies a strong concavity assumption, then it is possible to prove that there are at least two geometrically distinct geodesics in (Omega) over bar = Omega boolean OR partial derivative Omega starting orthogonally to one connected component of partial derivative Omega and arriving orthogonally onto the other one. The results given in [6] allow to obtain a proof of the existence of two distinct homoclinic orbits for an autonomous Lagrangian system emanating from a nondegenerate maximum point of the potential energy, and a proof of the existence of two distinct brake orbits for a. class of Hamiltonian systems. Under a further symmetry assumption, it is possible to show the existence of at least dim(M) pairs of geometrically distinct geodesics as above, brake orbits and homoclinics.

A matrix formula for the skewness of maximum likelihood estimators

We give a general matrix formula for computing the second-order skewness of maximum likelihood estimators. The formula was firstly presented in a tensorial version by Bowman and Shenton (1998). Our matrix formulation has numerical advantages, since it requires only simple operations on matrices and vectors. We apply the second-order skewness formula to a normal model with a generalized parametrization and to an ARMA model. (c) 2010 Elsevier B.V. All rights reserved.

Bias-corrected estimators for dispersion models with dispersion covariates

In this paper we discuss bias-corrected estimators for the regression and the dispersion parameters in an extended class of dispersion models (Jorgensen, 1997b). This class extends the regular dispersion models by letting the dispersion parameter vary throughout the observations, and contains the dispersion models as particular case. General formulae for the O(n(-1)) bias are obtained explicitly in dispersion models with dispersion covariates, which generalize previous results obtained by Botter and Cordeiro (1998), Cordeiro and McCullagh (1991), Cordeiro and Vasconcellos (1999), and Paula (1992). The practical use of the formulae is that we can derive closed-form expressions for the O(n(-1)) biases of the maximum likelihood estimators of the regression and dispersion parameters when the information matrix has a closed-form. Various expressions for the O(n(-1)) biases are given for special models. The formulae have advantages for numerical purposes because they require only a supplementary weighted linear regression. We also compare these bias-corrected estimators with two different estimators which are also bias-free to order O(n(-1)) that are based on bootstrap methods. These estimators are compared by simulation. (C) 2011 Elsevier B.V. All rights reserved.

A note on influence diagnostics in nonlinear mixed-effects elliptical models

This paper provides general matrix formulas for computing the score function, the (expected and observed) Fisher information and the A matrices (required for the assessment of local influence) for a quite general model which includes the one proposed by Russo et al. (2009). Additionally, we also present an expression for the generalized leverage on fixed and random effects. The matrix formulation has notational advantages, since despite the complexity of the postulated model, all general formulas are compact, clear and have nice forms. (C) 2010 Elsevier B.V. All rights reserved.

Bias correction in a multivariate normal regression model with general parameterization

This paper derives the second-order biases Of maximum likelihood estimates from a multivariate normal model where the mean vector and the covariance matrix have parameters in common. We show that the second order bias can always be obtained by means of ordinary weighted least-squares regressions. We conduct simulation studies which indicate that the bias correction scheme yields nearly unbiased estimators. (C) 2009 Elsevier B.V. All rights reserved.

Local power of some tests in exponential family nonlinear models

In this paper we obtain asymptotic expansions up to order n(-1/2) for the nonnull distribution functions of the likelihood ratio, Wald, score and gradient test statistics in exponential family nonlinear models (Cordeiro and Paula, 1989), under a sequence of Pitman alternatives. The asymptotic distributions of all four statistics are obtained for testing a subset of regression parameters and for testing the dispersion parameter, thus generalising the results given in Cordeiro et al. (1994) and Ferrari et al. (1997). We also present Monte Carlo simulations in order to compare the finite-sample performance of these tests. (C) 2010 Elsevier B.V. All rights reserved.

Residual-based test for Nonlinear Cointegration with application in PPPs

Nested by linear cointegration first provided in Granger (1981), the definition of nonlinear cointegration is presented in this paper. Sequentially, a nonlinear cointegrated economic system is introduced. What we mainly study is testing no nonlinear cointegration against nonlinear cointegration by residual-based test, which is ready for detecting stochastic trend in nonlinear autoregression models. We construct cointegrating regression along with smooth transition components from smooth transition autoregression model. Some properties are analyzed and discussed during the estimation procedure for cointegrating regression, including description of transition variable. Autoregression of order one is considered as the model of estimated residuals for residual-based test, from which the teststatistic is obtained. Critical values and asymptotic distribution of the test statistic that we request for different cointegrating regressions with different sample sizes are derived based on Monte Carlo simulation. The proposed theoretical methods and models are illustrated by an empirical example, comparing the results with linear cointegration application in Hamilton (1994). It is concluded that there exists nonlinear cointegration in our system in the final results.

Elbesparing med pelletkaminer och solvärme i direktelvärmda småhus

The aim of this study was to investigate how electricallyheated houses can be converted to using wood pellet and solarheating. There are a large number of wood pellet stoves on themarket. Many stoves have a water jacket, which gives anopportunity to distribute the heat to domestic hot water and aradiator heating system. Three typical Swedish houses with electric resistanceheating have been studied. Fourteen different system conceptsusing wood pellet stoves and solar heating systems have beenevaluated. The systems and the houses have been simulated indetail using TRNSYS. The houses have been divided in up to 10different zones and heat transfer by air circulation throughdoorways and open doors have been simulated. The pellet stoveswere simulated using a recently developed TRNSYS component,which models the start- and stop phases, emissions and thedynamic behaviour of the stoves. The model also calculates theCO-emissions. Simulations were made with one stove without awater jacket and two stoves with different fractions of thegenerated heat distributed in the water circuit. Simulations show that the electricity savings using a pelletstove are greatly affected by the house plan, the systemchoice, if the internal doors are open or closed and thedesired level of comfort. Installing a stove with awater-jacket connected to a radiator system and a hot waterstorage has the advantage that heat can be transferred todomestic hot water and be distributed to other rooms. Suchsystems lead to greater electricity savings, especially inhouses having a traditional layout. It was found that not allrooms needed radiators and that it was more effective in mostcases t use a stove with a higher fraction of the heatdistributed by the water circuit. The economic investigation shows that installing a woodpellet stove without a water jacket gives the lowest totalenergy- and capital costs in the house with an open plan (fortoday's energy prices and the simulated comfort criteria). Inthe houses with a traditional layout a pellet stove givesslightly higher costs than the reference house having onlyelectrical resistance heating due to the fact that less heatingcan be replaced. The concepts including stoves with a waterjacket all give higher costs than the reference system, but theconcept closest to be economical is a system with a bufferstore, a stove with a high fraction of the heat distributed bythe water circuit, a new water radiator heating system and asolar collector. Losses from stoves can be divided into: flue gas lossesincluding leakage air flow when the stove is not in operation;losses during start and stop phases; and losses due to a highair factor. An increased efficiency of the stoves is importantboth from a private economical point of view, but also from theperspective that there can be a lack of bio fuel in the nearfuture also in Sweden. From this point of view it is alsoimportant to utilize as much solar heat as possible. Theutilization of solar heat is low in the simulated systems,depending on the lack of space for a large buffer store. The simulations have shown that the annual efficiency ismuch lower that the nominal efficiency at full power. Thesimulations have also shown that changing the control principlefor the stove can improve efficiency and reduce theCO-emissions. Today's most common control principle for stovesis the on/off control, which results in many starts and stopsand thereby high CO-emissions. A more advanced control varyingthe heating rate from maximum to minimum to keep a constantroom temperature reduces the number of starts and stops andthereby the emissions. Also the efficiency can be higher withsuch a control, and the room temperature will be kept at a moreconstant temperature providing a higher comfort.

Testing common nonlinear features in vector nonlinear autoregressive models

This paper studies a special class of vector smooth-transition autoregressive (VSTAR) models that contains common nonlinear features (CNFs), for which we proposed a triangular representation and developed a procedure of testing CNFs in a VSTAR model. We first test a unit root against a stable STAR process for each individual time series and then examine whether CNFs exist in the system by Lagrange Multiplier (LM) test if unit root is rejected in the first step. The LM test has standard Chi-squared asymptotic distribution. The critical values of our unit root tests and small-sample properties of the F form of our LM test are studied by Monte Carlo simulations. We illustrate how to test and model CNFs using the monthly growth of consumption and income data of United States (1985:1 to 2011:11).

Forecasting with Vector Nonlinear Time Series Models

This work concerns forecasting with vector nonlinear time series models when errorsare correlated. Point forecasts are numerically obtained using bootstrap methods andillustrated by two examples. Evaluation concentrates on studying forecast equality andencompassing. Nonlinear impulse responses are further considered and graphically sum-marized by highest density region. Finally, two macroeconomic data sets are used toillustrate our work. The forecasts from linear or nonlinear model could contribute usefulinformation absent in the forecasts form the other model.

Residual-based Inference for Common Nonlinear Features

This paper investigates common nonlinear features in multivariate nonlinear autore-gressive models via testing the estimated residuals. A Wald-type test is proposed and itis asymptotically Chi-squared distributed. Simulation studies are given to examine thefinite-sample properties of the proposed test.