Generalized Estimation Method Research Articles

A general estimation method using spacings

Abstract A general parametric estimation method which makes use of the coverage probabilities or spacings is proposed. Under some regularity conditions, it is shown that such estimators are asymptotically normal. This method generalizes the maximum spacing method of estimation that has been discussed in the literature. Furthermore, it is shown that the maximum spacing estimator is asymptotically most efficient within the subclass of spacings-based estimators under consideration.

On the Estimation of Nonstationary Functional Series TARMA Models: An Isomorphic Matrix Algebra Based Method1

Functional Series Time-dependent AutoRegressive Moving Average (TARMA) models form an important class of nonstationary stochastic models offering high parsimony, tracking of “fast” and “slow” variations, high accuracy and resolution, as well as accurate capturing of both resonances and antiresonances. This paper considers the estimation of Functional Series TARMA models with polynomial functional spaces based upon a novel matrix algebra that is isomorphic to that of the noncommutative ring of time-varying polynomial operators expressed in terms of the model’s functional spaces. The Generalized estimation method introduced offers important advantages, such as the use of properly contracted functional spaces that is necessary for the elimination of asymptotic bias errors, the ability to handle AR and MA functional spaces of different dimensionalities, as well as improved accuracy through a streamlined realization. The method’s excellent performance characteristics are confirmed via Monte Carlo experiments and comparisons with an earlier Polynomial-Algebraic approach and the adaptive Recursive Maximum Likelihood ARMA method.

Estimation of genome length

The genome length is a fundamental feature of a species. This note outlined the general concept and estimation method of the physical and genetic length. Some formulae for estimating the genetic length were derived in detail. As examples, the genome genetic length of Pinus pinaster Ait. and the genetic length of chromosome VI ofOryza sativa L. were estimated from partial linkage data.

A note on the geometric interpretation of the EM algorithm in estimating item characteristics and student abilities

This note uses the EM-algorithm in an item response model as an illustration of a general method of parameter estimation, which geometrically can be described as an alternating projection method.

Efficient Estimation of Additive Partially Linear Models

I consider the problem of estimating an additive partially linear model using general series estimation methods with polynomial and splines as two leading cases. I show that the finite‐dimensional parameter is identified under weak conditions. I establish the root‐n‐normality result for the finite‐dimensional parameter in the linear part of the model and show that it is asymptotically more efficient than a semiparametric estimator that ignores the additive structure. When the error is conditional homoskedastic, my finite‐dimensional parameter estimator reaches the semiparametric efficiency bound. Efficient estimation when the error is conditional heteroskedastic is also discussed.

The mathematics of Markov models: what Markov chains can really predict in forest successions

The formalism of Markov chains is presented as a mathematical description of a succession process with a known scheme of successional transitions and their time characteristics. The basic hypotheses and assumptions behind the formalism are formulated and discussed from the viewpoint of the prognostic potential in the resulting models. Fundamental mathematical results from the theory of stochastic processes guarantee the existence of a stationary probability distribution of states in any finite, regular, time-homogeneous Markov chain, and any initial distribution of chain states does converge to some stationary distribution, matching the paradigm of classical succession theory. We propose a general method for estimation of time-homogeneous transition probabilities applicable for any kind of successional scheme, yet with strong requirements to the expert data: average duration times should be known for each specified stage of succession as well as the likelihood proportions among the transitions from the ramifying states of the scheme. Constructed by this method on a single set of data, the discrete- and continuous-time models are proved to converge to the identical distributions, while the average sojourn times in each state are shown to be also the same in the two models. Succession through forest types in a mixed (coniferous–deciduous) forest in Central Russia is considered as an example.

Local generalized method of moments estimation based on kernel weights: An application to panel data

This paper presents and applies a local generalized method of moments (LGMM) estimator for regression functions. The method is an extension of previous results obtained by Gozalo and Linton. The LGMM estimation procedure can be applied to estimate a mean regression function and its derivatives at an interior point x , without making explicit assumptions about its functional form. The method has been applied to estimate dynamic models based on panel data.

M-estimators of structural parameters in pseudolinear models

Real valued M-estimators \(\hat \theta _n : = \min \sum\limits_1^n {\varrho \left( {Y_i - \tau \left(\theta \right)} \right)} \) in a statistical model 1 with observations \(Y_i \sim F_{{\theta }_0 }\) are replaced by \(\mathbb{R}^p \)-valued M-estimators \(\hat \beta _n : = \min \sum\limits_1^n {\varrho \left( {Y_i - \tau \left( {u\left( {z_i^T \beta } \right)} \right)} \right)} \) in a new model with observations \(Y_i \sim F_{u\left( {z_i^t {\beta }}_{0} \right)}\) where \(z_i \in \mathbb{R}^p \) are regressors, \({\beta }_{0} \in \mathbb{R}^p \) is a structural parameter and \(u:\mathbb{R} \to \mathbb{R}\) a structural function of the new model. Sufficient conditions for the consistency of \(\hat \beta _n \) are derived, motivated by the sufficiency conditions for the simpler “parent estimator” \(\hat \theta _n \) The result is a general method of consistent estimation in a class of nonlinear (pseudolinear) statistical problems. If Fθ has a natural exponential density eθx−b( x ) then our pseudolinear model with u = (g o μ)−1 reduces to the well known generalized linear model, provided μ(θ) = db(θ)/dθ and g is the so-called link function of the generalized linear model. General results are illustrated for special pairs ϱ and τ leading to some classical M-estimators of mathematical statistics, as well as to a new class of generalized α-quantile estimators.

A general efficient method for chaotic signal estimation

This article presents a general, computationally efficient method for chaotic signal estimation based on the connection between the symbolic sequence and the initial condition of a chaotic system. The performance of the method in white Gaussian noise is evaluated. The new method is asymptotically unbiased and attains the Cramer-Rao lower bound at high signal-to-noise ratios.

A general method of density estimation for associated random variables

Let {X n ;n ≥1} be a sequence of stationary associated random variables having a common marginal density function f (x). Let , be a sequence of Borel-measurable functions defined on R 2. Let be the empirical density function. Here we study a set of sufficient conditions under which the probability at an exponential rate as n → ∞ where the rate possibly depends on ϵ, δ and f and [a, b] is a finite or an infinite interval.

Nonparametric smoothing estimates of time-varying coefficient models with longitudinal data

This paper considers nonparametric estimation in a varying coefficient model with repeated measurements (Yij, Xij, tij), for i = 1,…, ni and j = 1,…, ni, where Xij=(Xijo,…, xijk)T and (Yij, Xij, tij) denote the jth outcome, covariate and time design points, respectively, of the ith subject. The model considered here is Yij = XijTβ(tij) + +i(tij), where β(t) = (β0(t), …, Bk(t))T, for k ≧ 0, are smooth nonparametric functions of interest and εi(t) is a zero-mean stochastic process. The measurements are assumed to be independent for different subjects but can be correlated at different time points within each subject. Two nonparametric estimators of β(t), namely a smoothing spline and a locally weighted polynomial, are derived for such repeatedly measured data. A crossvalidation criterion is proposed for the selection of the corresponding smoothing parameters. Asymptotic properties, such as consistency, rates of convergence and asymptotic mean squared errors, are established for kernel estimators, a special case of the local polynomials. These asymptotic results give useful insights into the reliability of our general estimation methods. An example of predicting the growth of children born to HIV infected mothers based on gender, HIV status and maternal vitamin A levels shows that this model and the corresponding nonparametric estimators are useful in epidemiological studies.

Model parameter estimation from non-equidistant sampled data sets at low data rates

A general method of model parameter estimation for irregularly sampled data is introduced, with special emphasis on estimation of the power spectral density. The main application is processing of data sets from a laser Doppler anemometer (LDA), for which often the mean data rate is low and the total data set duration is short. It is shown that the model parameter estimation can be quite effective under these conditions, resulting in consistent, bias-free estimates which exhibit very low variance. Simulations and experiments are used to examine the performance of the technique.

Parameter Estimation in Hidden Fuzzy Markov Random Fields and Image Segmentation

This paper proposes a new unsupervised fuzzy Bayesian image segmentation method using a recent model using hidden fuzzy Markov fields. The originality of this model is to use Dirac and Lebesgue measures simultaneously at the class field level, which allows the coexistence of hard and fuzzy pixels in a same picture. We propose to solve the main problem of parameter estimation by using of a recent general method of estimation in the case of hidden data, called iterative conditional estimation (ICE), which has been successfully applied in classical segmentation based on hidden Markov fields. The first part of our work involves estimating the parameters defining the Markovian distribution of the noise-free fuzzy picture. We then combine this algorithm with the ICE method in order to estimate all the parameters of the fuzzy picture corrupted with noise. Last, we combine the parameter estimation step with two segmentation methods, resulting in two unsupervised statistical fuzzy segmentation methods. The efficiency of the proposed methods is tested numerically on synthetic images and a fuzzy segmentation of a real image of clouds is studied.

An empirical investigation of asset pricing models using Japanese stock market data

This article examines the empirical performance of the following asset pricing models: (i) a time-separable model; (ii) Abel's model with a consumption externality; (iii) the time non-separable model; (iv) the consumption-based recursive utility model; and (v) the ad-hoc factor pricing model. The testing framework includes the Hansen-Jagannathan volatility bounds test, the Hansen-Jagannathan specification error test and Euler equation-based generalized method of moments estimation. The test evidence indicates that habit forming preferences are empirically supportable and provide a good characterization of the Japanese security market data.

Parameter estimation for analysis of vapor diffusion in polymers

AbstractThis paper presents a general method for estimation of diffusion coefficient and other relevant parameters for the analysis of vapor diffusion in polymers. Sorption curves generated by the constants estimated using the parameter estimation method presented here are in closer agreement with experimental curves than curves generated by other conventional methods.

Multi-state Markov models for analysing incomplete disease history data with illustrations for HIV disease.

Multi-state Markov models can be useful in analysing disease history data. We apply the general estimation methods of Kalbfleisch and Lawless to panel data in which individuals are viewed over only a portion of their life history and complete information about transition times between states is unavailable. Methods to assess goodness-of-fit are proposed. To illustrate the methods, we consider models of HIV disease relating important immunological marker measurements to the onset of AIDS.

Fiscal Constraints and Electoral Manipulation in American Social Welfare

American social welfare policy involves a politically significant fiscal interaction between short-run, pay-as-you-go constraints and long-run equilibrium constraints motivated by the contributory principle and the concept of actuarial soundness. The fiscal constraints induce conflict between benefit recipients and payroll-tax-payers. To support small election-year reductions in payroll taxes, means-tested program benefits are slightly reduced in election years (compared to non-election-year levels under similar economic conditions). The existence of the constraints and of the election-year changes is tested using a multivariate time series regression model of monthly transfer payments and contributions for social insurance during years 1948–87. Short-run dynamics are found to be weakly incrementalist, but otherwise the results support the argument. Extraordinary manipulations are identified during 1972. Special technical features of the econometric analysis are a nonlinear, dynamic specification; robust generalized method of moments estimation; and near cointegration.

Some general estimation methods for nonlinear mixed-effects models.

A nonlinear mixed-effects model suitable for characterizing repeated measurement data is described. The model allows dependence of random coefficients on covariate information and accommodates general specifications of a common intraindividual covariance structure, such as models for variance within individuals that depend on individual mean response and autocorrelation. Two classes of procedures for estimation in this model are described, which incorporate estimation of unknown parameters in the assumed intraindividual covariance structure. The procedures are straightforward to implement using standard statistical software. The techniques are illustrated by examples in growth analysis and assay development.

Transverse vibration of symmetrically laminated rectangular composite plates

A general numerical method for estimation of the vibrational response of symmetrically laminated rectangular composite plates is presented. This is based on the Rayleigh-Ritz method using the admissible 2-D orthogonal polynomials to derive the governing eigenvalue equation. The natural frequencies and mode shapes for the laminated plates are obtained by solving this governing eigenvalue equation. Several test problems are solved to demonstrate the accuracy and flexibility of the proposed method. The present results, where possible, are verified with those available values from the literature. The effects of the material, number of layers and fibre orientation upon the frequencies and mode shapes are discussed. This study may provide valuable information for researchers and engineers in design applications.

Partitioning in aqueous two-phase systems as a method of estimation of the relative hydrophobicity of solutes

Partitioning of two non-ionic glycosides, 4-nitrophenyl-α-D-mannopyranoside and 4-nitrophenyl-N-acetyl-β-D-glucosaminide, in aqueous dextran–poly(ethylene glycol) and dextran–polyvinylpyrrolidone two-phase systems of different polymer concentrations and various ionic compositions has been studied. The differences in the abilities of the aqueous media in the coexisting phases of the systems used to participate in ionic and hydrophobic hydration interactions with a solute being partitioned have been estimated previously. The relative hydrophobicity of the solutes expressed in equivalent quantity of CH2 groups depends on the composition of the aqueous medium (the nature and concentration of the salts present, the nature of the phase polymers). The difference between the relative hydrophobicities for the non-ionic solutes, however, is independent of the above factors. This indicates that the partition technique can be considered as an adequate general method for estimation of the relative hydrophobicity of solutes.