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Estimation of polynomials in the regression model

Júlia Volaufová (1982)

Aplikace matematiky

Let 𝐘 be an n -dimensional random vector which is N n ( 𝐀 0 , 𝐊 ) distributed. A minimum variance unbiased estimator is given for f ( o ) provided f is an unbiasedly estimable functional of an unknown k -dimensional parameter 0 .

Estimation of the first order parameters in the twoepoch linear model

Karel Hron (2007)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The linear regression model, where the mean value parameters are divided into stable and nonstable part in each of both epochs of measurement, is considered in this paper. Then, equivalent formulas of the best linear unbiased estimators of this parameters in both epochs using partitioned matrix inverse are derived.

Estimation of the hazard function in a semiparametric model with covariate measurement error

Marie-Laure Martin-Magniette, Marie-Luce Taupin (2009)

ESAIM: Probability and Statistics

We consider a failure hazard function, conditional on a time-independent covariate Z, given by η γ 0 ( t ) f β 0 ( Z ) . The baseline hazard function η γ 0 and the relative risk f β 0 both belong to parametric families with θ 0 = ( β 0 , γ 0 ) ⊤ ∈ ℝ m + p . The covariate Z has an unknown density and is measured with an error through an additive error model U = Z + ε where ε is a random variable, independent from Z, with known density f ε . We observe a n-sample (Xi, Di, Ui), i = 1, ..., n, where Xi is the minimum between the failure time and the censoring time, and...

Estimation of the parameters of the mixture k ≥ 2 of logarithmic-normal distributions.

Mariusz J. Wasilewski (1988)

Trabajos de Estadística

In the mixture k ≥ 2 of logarithmic-normal distributions, with density function (1), the parameters μ1, ..., μk satisfying conditions (2) and the parameters p1, ..., pk satisfying conditions (3) are unknown. Using moments of orders r = -k, -k+1, ..., 0, 1, ..., k-1 we get a system of 2k equations (8), an equivalent of matrix equation (10). The equation (13) has exactly one solution with regard to A. If in the equation (13) we substitute the unbiased and consistent estimators D'r for the coefficients...

Estimation of the size of a closed population

S. Sengupta (2010)

Applicationes Mathematicae

The problem considered is that of estimation of the size (N) of a closed population under three sampling schemes admitting unbiased estimation of N. It is proved that for each of these schemes, the uniformly minimum variance unbiased estimator (UMVUE) of N is inadmissible under square error loss function. For the first scheme, the UMVUE is also the maximum likelihood estimator (MLE) of N. For the second scheme and a special case of the third, it is shown respectively that an MLE and an estimator...

Estimation of the spectral moment by means of the extrema.

Enrique M. Cabaña (1985)

Trabajos de Estadística e Investigación Operativa

An estimator of the standard deviation of the first derivative of a stationary Gaussian process with known variance and two continuous derivatives, based on the values of the relative maxima and minima, is proposed, and some of its properties are considered.

Estimation of variance components in mixed linear models

Júlia Volaufová, Viktor Witkovský (1992)

Applications of Mathematics

The MINQUE of the linear function ∫ ' ϑ of the unknown variance-components parameter ϑ in mixed linear model under linear restrictions of the type 𝐑 ϑ = c is defined and derived. As an illustration of this estimator the example of the one-way classification model with the restrictions ϑ 1 = k ϑ 2 , where k ≥ 0 , is given.

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