Consistency conditions on the least squares estimator in single common factor analysis model

Summary This paper is concerned with the consistency of estimators in a single common factor analysis model when the dimension of the observed vector is not fixed. In the model several conditions on the sample sizen and the dimensionp are established for the least squares estimator (L.S.E.) to be consistent. Under some assumptions,p/n→0 is a necessary and sufficient condition that the L.S.E. converges in probability to the true value. A sufficient condition for almost sure convergence is also given.     

All Admissible Linear Estimators under Quadratic Loss in Multivariate Model

§ 1.Introduction and Notations　In this paper,for any given matrices A and B,A B denotes the Kronecker productof A and B,A is a vector formed by stacking the columns of A under each other,μ(A)is a space generated by the columns of A,and PA=A(A′A) - A′. Fourthmore,if A andB are square matrices,then A>B and A≥ B mean that A-B is a symmetrical positiveand nonnegative matrix,respectively,andλi(A) is the i-th largest eigenvalue of A.　Consider general multivariate linear modelY …     

Parameter estimation for stochastic equations with additive fractional Brownian sheet

We study the maximum likelihood estimator for stochastic equations with additive fractional Brownian sheet. We use the Girsanov transform for the the two-parameter fractional Brownian motion, as well as the Malliavin calculus and Gaussian regularity theory.      

Strong convergence rates for the estimation of a covariance operator for associated samples

Let X _n , n ≥ 1, be a strictly stationary associated sequence of random variables, with common continuous distribution function F. Using histogram type estimators we consider the estimation of the two-dimensional distribution function of (X ₁,X _k+1) as well as the estimation of the covariance function of the limit empirical process induced by the sequence X _n , n ≥ 1. Assuming a convenient decrease rate of the covariances Cov(X ₁,X _n+1), n ≥ 1, we derive uniform strong convergence rates for these estimators. The condition on the covariance structure of the variables is satisfied either if Cov(X ₁,X _n+1) decreases polynomially or if it decreases geometrically, but as we could expect, under the latter condition we are able to establish faster convergence rates. For the two-dimensional distribution function the rate of convergence derived under a geometrical decrease of the covariances is close to the optimal rate for independent samples.      

A Test of Multivariate Independence Based on a Single Factor Model

A test of the independence of two sets of variables is developed to have high power against a special family of dependence. In this each set of variables has the structure of a single factor model and the dependence is solely via the correlation γ between the underlying latent variables. This is a model with only one nonzero canonical correlation. It is shown that a test based on the maximum likelihood estimate of γ is appreciably more powerful than that based on r₁, the largest sample canonical correlation. If, however, the model is used, not just as a family of alternatives but as the basis for interpretation, and if substantial cross-correlation is present then the procedure is essentially equivalent to the use of r₁.     

On Distribution of Error of Linear Wavelet Estimator of Probability Density

We establish the asymptotic normality of the squared L ²-norm of the approximation error of a linear wavelet estimator of the density of a distribution. The calculations are based on the smallness of correlations between the coefficients of the high-frequency part of the multiresolution expansion of the estimator.Supported by the FCT Foundation (Portugal) in the framework of the project Probability and Statistics (2000–2002), Centro de Matematica, Universidade da Beira Interior.__________Translated from Lietuvos Matematikos Rinkinys, Vol. 45, No. 2, pp. 184–207, April–June, 2005.     

NA样本的递归密度估计

设$\{X_n,n\geq 1\}$是一个严平稳的负相协的随机变量序列, 其概率密度函数为$f(x)$.本文讨论了$f(x)$的递归核估计量的联合渐近正态性.     

Estimating the covariance matrix and the generalized variance under a symmetric loss

For estimating the power of a generalized variance under a multivariate normal distribution with unknown means, the inadmissibility of the best affine equivariant estimator relative to the symmetric loss is shown, and a class of improved estimators is given. The problem of estimating the covariance matrix is also discussed.     

Estimation of Feeding Composition of Industrial Process Based on Data Reconciliation

For an industrial process, the estimation of feeding composition is important for analyzing production status and making control decisions. However, random errors or even gross ones inevitably contaminate the actual measurements. Feeding composition is conventionally obtained via discrete and low-rate artificial testing. To address these problems, a feeding composition estimation approach based on data reconciliation procedure is developed. To improve the variable accuracy, a novel robust M-estimator is first proposed. Then, an iterative robust hierarchical data reconciliation and estimation strategy is applied to estimate the feeding composition. The feasibility and effectiveness of the estimation approach are verified on a fluidized bed roaster. The proposed M-estimator showed better overall performance.     

Minimum Divergence Estimators,Maximum Likelihood and the Generalized Bootstrap

This paper states that most commonly used minimum divergence estimators are MLEs for suited generalized bootstrapped sampling schemes. Optimality in the sense of Bahadur for associated tests of fit under such sampling is considered.