This paper provides further contributions to the theory of linear sufficiency and linear completeness. The notion of linear sufficiency was introduced by Baksalary and Kala (1981 , Ann. Statist. 9 , 913–916) and Dryg...
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This paper provides further contributions to the theory of linear sufficiency and linear completeness. The notion of linear sufficiency was introduced by Baksalary and Kala (1981 , Ann. Statist. 9 , 913–916) and Drygas (in press, Sankhya ) with respect to the linear model Ey = Xβ , var y = V . In addition to correcting an inadequate proof of [8], the relationship to an earlier definition and to the theory of linear prediction is also demonstrated. Moreover, the notion is extended to the model Ey = Xβ , var y = δ 2 V . Its connection with sufficiency under normality is investigated. An example illustrates the results.
A linear model for the genotypic covariance between relatives under assortative mating comprising the “classical linear model” and the model of “selective assortative mating” is proposed. The general conditions on...
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A linear model for the genotypic covariance between relatives under assortative mating comprising the “classical linear model” and the model of “selective assortative mating” is proposed. The general conditions on the genetical and developmental mechanisms of quantitative characters, as well as on selection and the mating system, on which the model is based, are explicitly stated and discussed. A classification of different relationships is presented and it is shown that these conditions are sufficient to obtain the genotypic covariance between relatives only if the relationship is a combination of descendant-ancestor, full sib, Type 1 and Nth uncle-niece relationships. All the “traditional” relationships, i.e., those for which the covariances of the relatives have been obtained in the literature, fall into this category. These conditions also ensure that the regression of the individual's genotypic value on the genotypic value or phenotype of any of its ancestors is always linear.
Based upon the computed values of the Kullback-Leibler divergence, the relative advantage of an optimal prediction density for the normal linear model over three well-known competitors is displayed and discussed.
Based upon the computed values of the Kullback-Leibler divergence, the relative advantage of an optimal prediction density for the normal linear model over three well-known competitors is displayed and discussed.
This essay discusses the strength and weaknesses of the so-called linear model (LM) of innovation. It is a reaction to the habit of criticising it as over simplistic, mechanistic, or simply blatantly wrong. We argue t...
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This essay discusses the strength and weaknesses of the so-called linear model (LM) of innovation. It is a reaction to the habit of criticising it as over simplistic, mechanistic, or simply blatantly wrong. We argue that, while some criticisms are of course well grounded, many others are instead based on loose interpretations and unwarranted assumptions. In order to separate the wheat from the chaff, this essay first presents a comprehensive description of the linear model and differentiates it from the caricature many refer to. Second, we discuss the main criticisms put forward and argue that many of them are not at all destructive, but can be easily accepted within a refined version of the LM. Third, we discuss the policy implications often derived (or said to derive) from the LM to argue that the LM itself is distinctively policy-neutral. Other assumptions have to be added to justify alternative policy implications. (C) 2009 Elsevier B.V. All rights reserved.
BackgroundCosts for the provision of regional hospital care depend, among other things, on the population density and the maximum reasonable distance to the nearest hospital. In regions with a low population density, ...
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BackgroundCosts for the provision of regional hospital care depend, among other things, on the population density and the maximum reasonable distance to the nearest hospital. In regions with a low population density, it is a challenge to plan the number and location of hospitals with respect both to economic efficiency and to the availability of hospital care close to residential *** examined whether the hospital landscape in rural regions can be planned on the basis of a regional economic model using the example which number of paediatric and obstetric wards in a region in the Northeast of Germany is economically efficient and what would be the consequences for the accessibility when one or more of the three current locations would be *** model of linear programming was developed to estimate the costs and revenues under different scenarios with up to three hospitals with both a paediatric and an obstetric ward in the investigation region. To calculate accessibility of the wards, geographic analyses were *** three hospitals in the study region, there is a financial gap of Euro3.6 million. To get a positive contribution margin for all three hospitals, more cases have to be treated than the region can deliver. Closing hospitals in the parts of the region with the smallest population density would lead to reduced accessibility for about 8% of the population under *** modelling of the costs of regional hospital care provides a basis for planning. A qualitative discussion to the locations of the remaining departments and the implementation of alternative healthcare concepts should follow.
We consider equalities between the ordinary least squares estimator (), the best linear unbiased estimator () and the best linear unbiased predictor () in the general linear model extended with the new unobservable fu...
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We consider equalities between the ordinary least squares estimator (), the best linear unbiased estimator () and the best linear unbiased predictor () in the general linear model extended with the new unobservable future value of the response whose expectation is . Our aim is to provide some new insight and new proofs for the equalities under consideration. We also collect together various expressions, without rank assumptions, for the and provide new results giving upper bounds for the Euclidean norm of the difference between the and and between the and . A remark is made on the application to small area estimation.
We consider the least squares estimation of a linear regression model in transformed variables from a data set that has been microaggregated by means of the individual ranking method. It is shown that the least square...
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We consider the least squares estimation of a linear regression model in transformed variables from a data set that has been microaggregated by means of the individual ranking method. It is shown that the least squares estimators are consistent even in the case where variable transformations are carried out after microaggregation. Applying individual ranking techniques to a data set thus guarantees the analytical validity of the microaggregated data for a wide class of statistical models.
In clinical trials carried out to assess the efficacy of different drugs in reducing the frequency of occlusion after coronary artery bypass, the ratio of the number of patients with at least one occluded anastomosis ...
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In clinical trials carried out to assess the efficacy of different drugs in reducing the frequency of occlusion after coronary artery bypass, the ratio of the number of patients with at least one occluded anastomosis to the number of patients catheterized up to a given day is a widely adopted statistic. In the early evaluation (at 1 or 2 months after surgery), this is affected by the distribution of timing of angiography and it tends to underestimate the cumulative probability of occlusion because patients whose anastomoses are all patent at angiography and occlude between angiography and the day at which the ratio is estimated do not contribute their events to the numerator of the ratio. One may sensibly assume that this underestimate does not affect the evaluation of the efficacy of treatments tested "within" the trial. In contrast, since the distributions of the timing of angiography vary substantially from trial to trial, it can make comparisons "between" trials unclear and possibly biased. The aim of this article is to suggest an alternative approach of statistical analysis in terms of logistic regression. By modeling the dichotomous response given by each patient in function of time at angiography, type of treatment, and other possible covariates, asymptotically unbiased estimates of the cumulative probability of occlusion are attained. Furthermore, the pertinent hazard function can be estimated. The main features of the model are discussed and the results obtained by fitting early data collected in the Studio Indobufen Nel Bypass Aortocoronarico (SINBA) are given.
In the linear model X n × 1 = C n × p θ p × 1 + E n × 1 , Huber's theory of robust estimation of the regression vector θ p × 1 is adapted for two models for the partially specified commo...
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In the linear model X n × 1 = C n × p θ p × 1 + E n × 1 , Huber's theory of robust estimation of the regression vector θ p × 1 is adapted for two models for the partially specified common distribution F of the i.i.d. components of the error vector E n × 1 . In the first model considered, the restriction of F to a set [− a 0 , b 0 ] is a standard normal distribution contaminated, with probability ε, by an unknown distribution symmetric about 0. In the second model, the restriction of F to [− a 0 , b 0 ] is completely specified (and perhaps asymmetrical). In both models, the distribution of F outside the set [− a 0 , b 0 ] is completely unspecified. For both models, consistent and asymptotically normal M -estimators of θ p × 1 are constructed, under mild regularity conditions on the sequence of design matrices { C n × p }. Also, in both models, M -estimators are found which minimize the maximal mean-squared error. The optimal M -estimators have influence curves which vanish off compact sets.
The asymptotic behavior of S-estimators in a random design linear model with long-range-dependent Gaussian errors is considered. It turns out that the S-estimators of regression parameter and error variance are strong...
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The asymptotic behavior of S-estimators in a random design linear model with long-range-dependent Gaussian errors is considered. It turns out that the S-estimators of regression parameter and error variance are strongly consistent under mild conditions. Furthermore, the asymptotic distribution of the S-estimator of regression parameter is normal if the design vectors are i.i.d. and is non-normal if the design vectors are long-range dependent Gaussian vectors. We also show that the asymptotic distribution of S-estimator of the error variance is non-normal since the errors are long-range dependent.
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