A histogram sieve estimator of the drift function in Ito processes and some semimartingales is constructed. It is proved that the estimator is pointwise and L¹ consistent and its finite-dimensional distributions are asymptotically normal. Our approach extends the results of Leśkow and Różański (1989a).
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.
The aim of the paper is estimation of the generalized variance of a bivariate normal distribution in the case of a sample with missing observations. The estimator based on all available observations is compared with the estimator based only on complete pairs of observations.
We consider a failure hazard function, conditional on a time-independent covariate Z, given by . The baseline hazard function and the relative risk both belong to parametric families with . 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 . 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...
In the article, we propose a new estimator of the hazard rate function in the framework of the multiplicative point process intensity model. The technique combines the reflection method and the method of transformation. The new method eliminates the boundary effect for suitably selected transformations reducing the bias at the boundary and keeping the asymptotics of the variance. The transformation depends on a pre-estimate of the logarithmic derivative of the hazard function at the boundary.
In this paper the Kronecker and inner products of mean vectorsof two different populations are considered. Using the generalized jackknife approach, estimators for these products are constructed which turn out to be unbiased, provided one can assume multinormal distribution.
The main aim is to estimate the noncentrality matrix of a noncentral Wishart distribution. The method used is Leung's but generalized to a matrix loss function. Parallelly Leung's scalar noncentral Wishart identity is generalized to become a matrix identity. The concept of Löwner partial ordering of symmetric matrices is used.
Numerical evaluation of the optimal nonlinear robust control requires estimating the impact of parameter uncertainties on the system output. The main goal of the paper is to propose a method for estimating the norm of an output trajectory deviation from the nominal trajectory for nonlinear uncertain, discrete-time systems. The measure of the deviation allows us to evaluate the robustness of any designed controller. The first part of the paper concerns uncertainty modelling for nonlinear systems...
The minimum variance linear unbiased estimators (MVLUE), the best linear invariant estimators (BLIE) and the maximum likelihood estimators (MLE) based on m selected kth record values are presented for the parameters of the Gumbel and Burr distributions.
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...
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...
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.