Reconstructing phylogenetic trees using the criterion of minimum evolution requires the use of a formula FT (d) that estimates the total length of a tree T given only the estimated distances d between the leaves of the tree. Let U(T ) be the collection of linear formulas FT (d) that correctly estimate the total length of T whenever d is an additive distance function on T . The current paper cha...

We consider a local least-squares criterion for aligning multiple time series fragments differing by locations and show the consistency of the time-lag estimator and the asymptotic normality of the location estimator. We apply the criterion to the problem of aligning 50 glacial varve fragments and construct a 3000-year surrogate for global temperature. Some key words: Aligning time series; Asym...

In vector autoregressive modeling, the order selected with the Akaike Information Criterion tends to be too high. This effect is called overfit. Finite sample effects are an important cause of overfit. By incorporating finite sample effects, an order selection criterion for vector AR models can be found with an optimal trade-off of underfit and overfit. The finite sample formulae in this paper ...

Approximate model equations often relate given measurements to unknown parameters whose estimate is sought. The Least-Squares (LS) estimation criterion assumes the measured data to be exact, and seeks parameters which minimize the model errors. Existing extensions of LS, such as the Total LS (TLS) and Constrained TLS (CTLS) take the opposite approach, namely assume the model equations to be exa...

With an optimal design one wants to determine the ideal allocation of observations for the estimation of the unknown parameter vector θ of a given model ( ) ( ) θ ; i i x f y E = , with [ ] p T θ θ θ L 1 = , ( ) n T x x X ,..., 1 = , the xi from a given experimental region ER.. Let ( ) X V ; θ be the asymptotical variance-covariance matrix of the least squares estimatorθ̂ of θ . We consider the ...

pedomodels have become a popular topic in soil science and environmentalresearch. they are predictive functions of certain soil properties based on other easily orcheaply measured properties. the common method for fitting pedomodels is to use classicalregression analysis, based on the assumptions of data crispness and deterministic relationsamong variables. in modeling natural systems such as s...

 Abstract: Determination of the diffusion coefficient on the base of solution of a linear inverse problem of the parameter estimation using the Least-square method is presented in this research. For this propose a set of temperature measurements at a single sensor location inside the heat conducting body was considered. The corresponding direct problem was then solved by the application of the ...

Determining the diffusion coefficient based on the solution of the linear inverse problem of the parameter estimation by using the Least-square method is presented. A set of temperature measurements at a single sensor location inside the heat conducting body is required. The corresponding direct problem will be solved by an application of the heat fundamental solution.

The problem of assessing the performance of algorithms used for the minimization of an l1-penalized least-squares functional, for a range of penalization parameters, is investigated. A criterion that uses the idea of ‘approximation isochrones’ is introduced.

In this paper the problem of determining optimal designs for least squares estimation is considered in the common linear regression model with correlated observations. Our approach is based on the determination of ‘nearly’ universally optimal designs, even in the case where the universally optimal design does not exist. For this purpose we introduce a new optimality criterion which reflects the...