Autoregressive error-processes, cubic splines and tridiagonal matrices
In the paper formulate for the inversion of some tridiagonal matrices are given. The results can be applied to the autoregressive processes.
Â?Wahrscheinlichkeitslernen" in der statistischen Lerntheorie.
Bad luck in quadratic improvement of the linear estimator in a special linear model
The paper concludes our investigations in looking for the locally best linear-quadratic estimators of mean value parameters and of the covariance matrix elements in a special structure of the linear model (2 variables case) where the dispersions of the observed quantities depend on the mean value parameters. Unfortunately there exists no linear-quadratic improvement of the linear estimator of mean value parameters in this model.
Bahadur-efficiency of linear rand tests - a survey
Balanced ternary designs with block size three, any ... and any R.
Banach Algebra Methods in Prediction Theory.
Bartlett Corrections for the Weibull Distribution.
Basic bounds of Fréchet classes
Algebraic bounds of Fréchet classes of copulas can be derived from the fundamental attributes of the associated copulas. A minimal system of algebraic bounds and related basic bounds can be defined using properties of pointed convex polyhedral cones and their relationship with non-negative solutions of systems of linear homogeneous Diophantine equations, largely studied in Combinatorics. The basic bounds are an algebraic improving of the Fréchet-Hoeffding bounds. We provide conditions of compatibility...
Bayes and empirical bayes tests for the life parameter
We study the one-sided testing problem for the exponential distribution via the empirical Bayes (EB) approach. Under a weighted linear loss function, a Bayes test is established. Using the past samples, we construct an EB test and exhibit its optimal rate of convergence. When the past samples are not directly observable, we work out an EB test by using the deconvolution kernel method and obtain its asymptotic optimality.
BAYES Estimation for the Variance of a Finite Population.
Bayes estimation of the reliability function and hazard rate of a Weibull failure time distribution.
Given the recorded life times from a Weibull distribution, Bayes estimates of the reliability function and hazard rate are obtained using the posterior distributions and some recent results on Bayesian approximations due to Lindley (1980). Based on a Monte Carlo study, these estimates are compared with their maximum likelihood counterparts.
Bayes optimal stopping of a homogeneous poisson process under linex loss function and variation in the prior
A homogeneous Poisson process (N(t),t ≥ 0) with the intensity function m(t)=θ is observed on the interval [0,T]. The problem consists in estimating θ with balancing the LINEX loss due to an error of estimation and the cost of sampling which depends linearly on T. The optimal T is given when the prior distribution of θ is not uniquely specified.
Bayes robustness via the Kolmogorov metric
An upper bound for the Kolmogorov distance between the posterior distributions in terms of that between the prior distributions is given. For some likelihood functions the inequality is sharp. Applications to assessing Bayes robustness are presented.
Bayes Sequential Estimation for an Exponential Family of Processes: A Discrete Time Approach.
Bayes sequential estimation procedures for exponential-type processes
The Bayesian sequential estimation problem for an exponential family of processes is considered. Using a weighted square error loss and observing cost involving a linear function of the process, the Bayes sequential procedures are derived.
Bayes sharpening of imprecise information
A complete algorithm is presented for the sharpening of imprecise information, based on the methodology of kernel estimators and the Bayes decision rule, including conditioning factors. The use of the Bayes rule with a nonsymmetrical loss function enables the inclusion of different results of an under- and overestimation of a sharp value (real number), as well as minimizing potential losses. A conditional approach allows to obtain a more precise result thanks to using information entered as the...
Bayes unbiased estimation in a model with three variance components
In the paper necessary and sufficient conditions for the existence and an explicit expression for the Bayes invariant quadratic unbiased estimate of the linear function of the variance components are presented for the mixed linear model , , , with three unknown variance components in the normal case. An application to some examples from the analysis of variance is given.
Bayes unbiased estimation in a model with two variance components
In the paper an explicit expression for the Bayes invariant quadratic unbiased estimate of the linear function of the variance components is presented for the mixed linear model , , with the unknown variance componets in the normal case. The matrices , may be singular. Applications to two examples of the analysis of variance are given.
Bayes unbiased estimators of parameters of linear trend with autoregressive errors
The method of least wquares is usually used in a linear regression model for estimating unknown parameters . The case when is an autoregressive process of the first order and the matrix corresponds to a linear trend is studied and the Bayes approach is used for estimating the parameters . Unbiased Bayes estimators are derived for the case of a small number of observations. These estimators are compared with the locally best unbiased ones and with the usual least squares estimators.
Bayesian analysis of structural change in a distributed Lag Model (Koyck Scheme)
Structural change for the Koyck Distributed Lag Model is analyzed through the Bayesian approach. The posterior distribution of the break point is derived with the use of the normal-gamma prior density and the break point, ν, is estimated by the value that attains the Highest Posterior Probability (HPP). Simulation study is done using R. Given the parameter values ϕ = 0.2 and λ = 0.3, the full detection of the structural change when σ² = 1 is generally attained at ν + 1. The after...