共查询到20条相似文献,搜索用时 312 毫秒
1.
This paper gives an analytical expression for the best linear unbiased estimator (BLUE) of the unknown parameters in the linear
Haar-wavelet model. From the analytical expression, we solve for the eigenvalues of the covariance matrix of the BLUE in analytical
form. Further, we use these eigenvalues to construct some conventional discrete optimal designs for the model. The equivalences
among these optimal designs are demonstrated and some examples are also given.
相似文献
2.
Shuangzhe Liu 《Metrika》2000,51(2):145-155
We first establish two matrix determinant Kantorovich-type inequalities. Then, based on these two and other inequalities,
we introduce new efficiency criteria and present their upper bounds to make efficiency comparisons between the ordinary least
squares estimator and the best linear unbiased estimator in the general linear model. We provide numerical examples to examine
the upper bounds of some new and old efficiency criteria.
Received: June 1999 相似文献
3.
Yongge Tian 《Revue internationale de statistique》2007,75(2):224-248
We consider in this paper a partitioned linear model { y , X 1 β 1 + X 2 β 2 , σ 2 σ } and two corresponding small models { y , X 1 β 1 , σ 2 σ } and { y , X 2 β 2 , σ 2 σ } . We derive necessary and sufficient conditions for (i) the ordinary least squares estimator under the full model to be the sum of the ordinary least squares estimators under the two small models; (ii) the best linear unbiased estimator under the full model to be the sum of the best linear unbiased estimators under the two small models; (iii) the best linear unbiased estimator under the full model to be the sum of the ordinary least squares estimators under the two small models. The proofs of the main results in this paper also demonstrate how to use the matrix rank method for characterizing various equalities of estimators under general linear models. 相似文献
4.
A general approach for constructing filters to produce trend estimates from a repeated survey is described. This approach accounts for the correlation structure induced by the rotation pattern used in the survey. Different filters are developed depending on whether the trend analysis is based on elementary estimates available for each rotation group or overall estimates obtained by combining the rotation group estimates. The properties of trend estimates obtained directly from the elementary estimates, those obtained from the simple average of the rotation group estimates and trend estimates obtained from the best linear unbiased estimates of the population characteristics of interest are compared. These comparisons are done for a number of rotation pattern, enabling an assessment of the impact of the choice of rotation patterns on trend estimation. 相似文献
5.
Dr. A. Chaudhuri 《Metrika》1992,39(1):341-357
Summary General procedures are described to generate quantitative randomized response (RR) required to estimate the finite population
total of a sensitive variable. Permitting sample selection with arbitrary probabilities a formula for the mean square error
(MSE) of a linear estimator of total based on RR is noted indicating the simple modification over one that might be based
on direct response (DR) if the latter were available. A general formula for an unbiased estimator of the MSE is presented.
A simple approximation is proposed in case the RR ratio estimator is employed based on a simple random sample (SRS) taken
without replacement (WOR). Among sampling strategies employing unbiased but not necessarily linear estimators based on RR,
certain optimal ones are identified under two alternative models analogously to well-known counterparts based on DR, if available.
Unlike Warner’s (1965) treatment of categorical RR we consider quantitative RR here. 相似文献
6.
Sample surveys are widely used to obtain information about totals, means, medians and other parameters of finite populations. In many applications, similar information is desired for subpopulations such as individuals in specific geographic areas and socio‐demographic groups. When the surveys are conducted at national or similarly high levels, a probability sampling can result in just a few sampling units from many unplanned subpopulations at the design stage. Cost considerations may also lead to low sample sizes from individual small areas. Estimating the parameters of these subpopulations with satisfactory precision and evaluating their accuracy are serious challenges for statisticians. To overcome the difficulties, statisticians resort to pooling information across the small areas via suitable model assumptions, administrative archives and census data. In this paper, we develop an array of small area quantile estimators. The novelty is the introduction of a semiparametric density ratio model for the error distribution in the unit‐level nested error regression model. In contrast, the existing methods are usually most effective when the response values are jointly normal. We also propose a resampling procedure for estimating the mean square errors of these estimators. Simulation results indicate that the new methods have superior performance when the population distributions are skewed and remain competitive otherwise. 相似文献
7.
Starting from the one-dimensional results by Wang et al (1994) we consider the performance of the ordinary least squares estimator
in comparison to the best linear unbiased estimator under an error component model with random effects in units and time.
Upper bounds are derived for the first-order approximation to the difference between both estimators and for the spectral
norm of the difference between their dispersion matrices. 相似文献
8.
In the researching of products' reliability, the result of life testing is used as the basis for the evaluation and improvement of reliability. During life testing, however, the future observation in an ordered sample is often expected to be predicted so as to show how long a sample of units might run until all fail in life testing. Therefore, we propose five new pivotal quantities to obtain prediction intervals of future order statistics based on right type II censored samples from the Pareto distribution with known shape parameter, then compares the lengths of the prediction intervals when using the pivotal quantity of Ouyang and Wu (1994) based on best linear unbiased estimator (BLUE) of scale parameter, and these five pivotal quantities. An advantage of these five pivotal quantities is that these are easier to calculate than the pivotal quantity of Ouyang and Wu (1994) based on BLUE of scale parameter, since they need to compute the tables of coefficients of BLUE of scale parameter. 相似文献
9.
The power of each of four tests of first-order autocorrelation in the linear regression model is determined for a simple and multiple regression model whose parameters are presumed to be known. The tests are: Durbin-Watson bounds test, a test based on Theil's best linear unbiased scalar estimator, a test devised by Abrahamse, Koerts and Louter, and an exact test devised by Durbin.For positive values of the coefficient of autocorrelation the Durbin-Watson bounds test is generally better than the tests based on the estimator proposed by Abrahamse, Koerts and Louter, the best linear unbiased scalar estimator, and the Durbin exact test. For negative values of the coefficient of autocorrelation, the pattern of results is mixed for all four test procedures. A byproduct of these experiments is the demonstrated feasibility of enumerating the distribution of the Durbin-Watson test statistic for any regression matrix and thus eliminating the region of indeterminacy from the Durbin-Watson test procedure. 相似文献
10.
F. Pukelshim 《Metrika》1980,27(1):103-113
Summary Estimation of the coefficients of skewness and kurtosis in a classical linear model situation is presented as an application of multilinear algebra and standard theory of mean estimation. The resulting estimators have optimality properties among all estimators that are invariant under mean translations, polynomials of degree three (skewness) or four (kurtosis) in the observations, and unbiased. 相似文献
11.
On random fuzzy variables of second order and their application to linear statistical inference with fuzzy data 总被引:2,自引:0,他引:2
Wolfgang Näther 《Metrika》2000,51(3):201-221
This paper summarizes some results on random fuzzy variables with existing expectation and variance, called random fuzzy
variables of second order. Using the Frechét-principle and – via support functions – the embedding of convex fuzzy sets into
a Banach space of functions it especially presents a unified view on expectation and variance of random fuzzy variables. These
notions are applied in developing linear statistical inference with fuzzy data. Detailed investigations are presented concerning
best linear unbiased estimation in linear regression models with fuzzy observations.
Received: November 1999 相似文献
12.
13.
A broad class of generalized linear mixed models, e.g. variance components models for binary data, percentages or count data, will be introduced by incorporating additional random effects into the linear predictor of a generalized linear model structure. Parameters are estimated by a combination of quasi-likelihood and iterated MINQUE (minimum norm quadratic unbiased estimation), the latter being numerically equivalent to REML (restricted, or residual, maximum likelihood). First, conditional upon the additional random effects, observations on a working variable and weights are derived by quasi-likelihood, using iteratively re-weighted least squares. Second, a linear mixed model is fitted to the working variable, employing the weights for the residual error terms, by iterated MINQUE. The latter may be regarded as a least squares procedure applied to squared and product terms of error contrasts derived from the working variable. No full distributional assumptions are needed for estimation. The model may be fitted with standardly available software for weighted regression and REML. 相似文献
14.
Yongge Tian 《Metrika》2010,72(3):313-330
Estimations of parametric functions under a general linear model and its restricted models involve some complicated operations
of matrices and their generalized inverses. In the past several years, a powerful tool—the matrix rank method was utilized
to manipulate various complicated matrix expressions that involve generalized inverses of matrices. In this paper, we use
this method to derive necessary and sufficient conditions for six equalities of the ordinary least-squares estimators and
the best linear unbiased estimators of parametric functions to equal under a general linear model and its corresponding restricted
model. 相似文献
15.
Dr. Qiqing Yu 《Metrika》1990,37(1):245-252
16.
L.C.A. Corsten 《Statistica Neerlandica》1989,43(2):69-84
This paper is concerned with the interpolation of spatially distributed observations of a quantitative phenomenon, sometimes referred to as kriging. This activity can be understood as a prediction procedure for values of random functions under stationarity assumptions in a polynomial linear regression context. After a heuristic and an exact derivation of the best linear unbiased prediction procedure (and the variance of prediction error) if the covariance function relating covariance between two possible observations to their mutual distance is known, follows the introduction of weaker assumptions admitting the definition of the variance only for increments of a certain order by a pseudoco–variance function. A particular related case is the so–called semivariogram for increments of order one. The prediction procedure turns out to be similar to that in the previous situation. The weaker assumptions allow an unbiased estimation of the unknown pseudocovahance function of polynomial form under restrictions imposed by Fourier transformation. Extension from point–wise observations or predictions to area or volume averages is touched upon. 相似文献
17.
Summary This paper considers the prediction of the sample mean by extreme order statistics when the population distribution is known.
The predictor and its mean square error are found. The problem is studied in details for the normal model. 相似文献
18.
Suppose independent random samples are drawn from k (2) populations with a common location parameter and unequal scale parameters. We consider the problem of estimating simultaneously the hazard rates of these populations. The analogues of the maximum likelihood (ML), uniformly minimum variance unbiased (UMVU) and the best scale equivariant (BSE) estimators for the one population case are improved using Rao‐Blackwellization. The improved version of the BSE estimator is shown to be the best among these estimators. Finally, a class of estimators that dominates this improved estimator is obtained using the differential inequality approach. 相似文献
19.
Claudia Baldermann Nicola Salvati Timo Schmid 《Revue internationale de statistique》2018,86(1):136-159
The effective use of spatial information in a regression‐based approach to small area estimation is an important practical issue. One approach to account for geographic information is by extending the linear mixed model to allow for spatially correlated random area effects. An alternative is to include the spatial information by a non‐parametric mixed models. Another option is geographic weighted regression where the model coefficients vary spatially across the geography of interest. Although these approaches are useful for estimating small area means efficiently under strict parametric assumptions, they can be sensitive to outliers. In this paper, we propose robust extensions of the geographically weighted empirical best linear unbiased predictor. In particular, we introduce robust projective and predictive estimators under spatial non‐stationarity. Mean squared error estimation is performed by two analytic approaches that account for the spatial structure in the data. Model‐based simulations show that the methodology proposed often leads to more efficient estimators. Furthermore, the analytic mean squared error estimators introduced have appealing properties in terms of stability and bias. Finally, we demonstrate in the application that the new methodology is a good choice for producing estimates for average rent prices of apartments in urban planning areas in Berlin. 相似文献
20.
This paper is concerned with the statistical analysis of proportions involving extra-binomial variation. Extra-binomial variation is inherent to experimental situations where experimental units are subject to some source of variation, e.g. biological or environmental variation. A generalized linear model for proportions does not account for random variation between experimental units. In this paper an extended version of the generalized linear model is discussed with special reference to experiments in agricultural research. In this model it is assumed that both treatment effects and random contributions of plots are part of the linear predictor. The methods are applied to results from two agricultural experiments. 相似文献