Restricted Linear Model Research Articles

The Relative Efficiency of the Conditional Root Square Estimation of Parameter in Inhomogeneous Equality Restricted Linear Model

This paper made a discuss on the relative efficiency of the generalized conditional root square estimation and the specific conditional root square estimation in paper [1,2] in inhomogeneous equality restricted linear model. It is shown that the generalized conditional root squares estimation has not smaller the relative efficiency than the specific conditional root square estimation, by a constraint condition in root squares parameter, we compare bounds of them, thus, choose appropriate squares parameter, the generalized conditional root square estimation has the good performance on mean squares error.

Conditional weighted combination of wind power forecasts

AbstractThe classical regression model for combined forecasting was reformulated in order to impose restrictions on the combination weights. This restricted linear combination model was then extended to the case where the weights were allowed to be a non‐parametric function of some meteorological variables, yielding the so‐called conditional weighted combination method. The weight functions are estimated with local regression techniques. The conditional weighted combination method was applied to a test case of a wind farm over a period of 10 months. Various combinations of two forecasts out of the three available ones were considered. Analysis of the data suggested that meteorological forecasts of air density and turbulent kinetic energy may be considered as relevant external variables in the combination scheme. A performance comparison showed that the conditional weighted combination method introduced in this paper outperformed the least‐squares combination method for almost all prediction horizons, especially for larger ones. This indicates that further developments based on conditional combination methods, including adaptivity of the weight functions estimation, may significantly enhance forecast accuracy and dampen the risk of large prediction errors. Copyright © 2010 John Wiley & Sons, Ltd.

SPECIFICATION TESTING IN MODELS WITH MANY INSTRUMENTS

This paper studies the asymptotic validity of the Anderson–Rubin (AR) test and the J test for overidentifying restrictions in linear models with many instruments. When the number of instruments increases at the same rate as the sample size, we establish that the conventional AR and J tests are asymptotically incorrect. Some versions of these tests, which are developed for situations with moderately many instruments, are also shown to be asymptotically invalid in this framework. We propose modifications of the AR and J tests that deliver asymptotically correct sizes. Importantly, the corrected tests are robust to the numerosity of the moment conditions in the sense that they are valid for both few and many instruments. The simulation results illustrate the excellent properties of the proposed tests.

Height measurements in images: how to deal with measurement uncertainty correlated to actual height

The accuracy of body height estimations in images may be validated by performing height measurements on test persons of known height on images taken under similar conditions. The observed differences between actual and measured heights of test persons are then used to adjust the measurement on the perpetrator, leading to a confidence interval for his actual height. The statistical model used in casework assumes that the actual heights of test persons and the differences of measured and actual heights are uncorrelated. In an experimental set-up, it is investigated whether there is a linear dependence between actual heights and differences between actual and measured heights. The assumption of independence of differences to actual heights is violated in one out of four experimental cases. For cases in which a linear dependence is present, an alternative statistical model is described for determining confidence intervals. A step-by-step illustration is given of implementation of the data analysis proposed both for a linear and for a restricted linear model.

LIU-TYPE ESTIMATION FOR THE LINEAR MODEL WITH LINEAR RESTRICTIONS

For the multicollinearity in restricted linear regression,there are some problems still left open in current popular ordinary restricted least square estimation.By introducing stochastic linear restrictions,a restricted Liu-type estimation is proposed,which generalizes the ordinary restricted least square estimation and restricted ridge estimation.Then the selection method of the scalars k and d is disscussed and is generalized to the estimation of restricted linear model and canonical form.

Comment on Ridge Estimation to the Restricted Linear Model

In this note, we show that the estimator and the following results given by Zhong and Yang (2007) are the same with that of Groß (2003).

Ridge Estimation to the Restricted Linear Model

This article is concerned with the problem of multicollinearity in a linear model with linear restrictions. After introducing a spheral restricted condition, a new restricted ridge estimation method is proposed by minimizing the sum of squared residuals. The property of the new estimator in its superiority over the ordinary restricted least squares estimation is then theoretically analyzed. Furthermore, a sufficient and necessary condition for selecting the ridge parameter k is obtained. To simplify the selection of the ridge parameter, a sufficient condition is also given. Finally, a numerical example demonstrates the merit of the new method in the aspect of solving the multicollinearity over the ordinary restricted least squares estimation.

Testing linear restrictions in linear models with empirical likelihood

In this paper we analyse the higher order asymptotic behaviour of a profiled empirical likelihood ratio which can be used to test a set of linear restrictions in linear regression models. We show that the resulting profiled empirical likelihood ratio admits a Bartlett correction which can be used to improve to third order the accuracy of commonly used tests in applied research without any distributional assumptions about the error process.

Some further remarks on a superiority problem in misspecified restricted singular linear models

Razzaghi (1987) examined the difference of covariance matrices of competing estimators in misspecified restricted linear models. Further, Gross, Trenkler and Liski (1998) extended Razzaghi's result by asserting his sufficient condition for nonnegative definiteness of the covariance matrix difference to be also necessary. In this paper, when the covariance matrix of the disturbance vector is nonnegative definite, the necessary and sufficient conditions for nonnegative definiteness of the covariance matrix difference are derived. So above results are strengthened.

Comparison of linear restricted models with respect to the validity of admissible and linearly sufficient estimators

Two restricted linear models M 0 and M are considered. The models can differ in model matrices, dispersion matrices, and possibly in parameter restrictions. The validity under M of estimators that are admissible and linearly sufficient under M 0 is studied. Criteria are derived for strong and week validity, i.e. when all estimators and at least one, respectively, preserve their properties. Some supplementary results for unrestricted model are also given.

Testing in the restricted linear model using canonical partitions

This paper treats the normal linear model y ∼ N n ( Xβ, σ 2 I n ) under the restriction Cβ = 0 for arbitrary C. Considered is the identifiable testing problem H 0 : Dβ = 0 against H 1 : Dβ ≠ 0. A canonical partition of the rows of C admits a simple form of involved linear subspaces. This leads to a numerically tractable form of the usual F-statistic for this testing problem.

Some results for a superiority problem in misspecified restricted linear models

Razzaghi (1987) conjectured that a wrong choice of covariance matrix in a restricted linear model results in loss of efficiency. This conjecture was proved correct by Kabe and Gupta for a wrong choice of constant covariance matrix. The present paper demonstrates that this loss of efficiency persists even with an estimated covariance matrix, thereby resulting in inefficient estimation, prediction, and confidence intervals.

Linear hypotheses made explicit

In testing a linear hypothesis under a general linear model, a simplest and most natural equivalent hypothesis involving only estimable parametric functions is provided, yieIding a test statistic that, is explicitly expressible in terms of the model matrices. A neat and unified treatment for the inference under a restricted linear model is then achieved

Linear sufficiency and admissibility in restricted linear models

The linearly sufficient and admissible linear estimators with bounded mean squared error in linear models with parameter restrictions are identified as special general ridge estimators. This is based on a decomposition result for admissible estimators and on the characterization of linearly sufficient and admissible estimators in unrestricted models given in Markiewicz (1996).

Four equivalent definitions of reparametrizations and restrictions in linear models

Reparametrizations and restrictions are transformations of linear models. Four equivalent definitions of these transformations are proposed in this article. Each of these definitions is based on one of the following concepts: (1) estimation sets, (2) column spaces, (3) residual vectors, and (4) degrees of freedom. These four definitions include as special cases all other definitions of reparametrizations and restrictions found in the literature. Unlike those used by other authors, the definitions in this article allow the original and transformed models to have different response vectors. This approach is useful in tests of nonhomogeneous hypotheses and other applications. However, a transformation of the original model into a reparametrized or restricted model with different response may produce counterintuitive effects on the coefficient of determination and other statistics.

Toepassing van 'n lineêre regressiemodel op verskillende inligtingstelselfasette

Application of a linear regression model to different information system facets Evaluation techniques with regard to the information system function in organizations could well be used to serve as a tool to identify problem areas and the corresponding corrective actions to be taken. In the past quite a number of computer-based application systems have failed in large as well as small organizations not because of inadequate technical quality but because some important non-technical factors of critical importance for the success of the system have not been diagnosed timely. In a previous research project (Bruwer: 1983) a restricted linear regression model method has been used to evaluate the success of the information system function in organizations. In this article the same model is applied on three different areas of the information system function. These areas are: Aspects of strategic planning of information systems; evaluation of the use of micro-computer systems and the evaluation of computer facilities in organizations.

Pressure-density-temperature ( p-p-T) relations of CHF 3, N 2O, and C 3H 6 in the critical region

The pressure-density-temperature ( p-ϱ-T) relations in the critical region (0.996 < T r< 1.004 and 0.6 < ϱ r < 1.4) are determined for CHF 3, N 2O, and C 3H 6 by means of a direct method. The critical properties are determined from a logarithmic plot based on the power law for the vapor-liquid coexistence curve and the p-ϱ relation on the critical isotherm for each system. The restricted linear model, one of the simplest scaled equations-of-state, is applied to describe the p-p-T relations in the critical region.

Nonequilibrium States of a Binary Mixture with Miscibility Gap in the Homogeneous One‐Fluid‐Phase Region: Study of the System 2,6‐Dimethylpyridine/Water with Off‐Critical Compositions Near its Lower Critical Point

AbstractThe temperature of homogeneous 2,6‐dimethylpyridine/water mixtures of off‐critical composition near the lower critical point of the system (|x1 — x1,c| &lt; 0.01; x1, mole fraction of 2,6‐dimethylpyridine) is raised by a fast temperature jump (Joule heating pulse) bringing the system closer to its temperature of phase separation. The delayed increase of intensity of scattered light is measured as function of time at different scattering angles (ϑ = 20°, 30°, 40°) and different temperature differences (Tp — Tf) (TP and Tf, temperature of phase separation and final temperature of the sample after the temperature jump). The measured relaxation curves are single exponentials. The relaxation times decrease with increasing values of |x1 — x1,c|. It is found that for kζr &lt; 0.4 (ζr, correlation length of local concentration fluctuations at Tf; k, absolute value of scattering vector) the structure factor of mixtures of off‐critical composition relaxes as expected on the basis of linear response within the accuracy of the measurements (τhyd/τexp = 1;τhyd, hydrodynamic relaxation time; τexp, experimental relaxation time). For the calculation of τhyd it is assumed that the change of τhyd with composition and temperature is caused only by changes of τf with composition and temperature. The restricted linear model of the critical equation of state is used to obtain τf as function of these variables. The data are used to calculate τhyd.

On a superiority problem in misspecified restricted linear models

Razzaghi (1987) conjectures that a wrong choice of covariance matrix in a restricted linear model results in loss of efficiency, This conjecture is proved to be correct.

Theory and computation of restricted linear models

Least squares inverses and complementary matrices are used to develop a comprehensive theory of estimation for a restricted linear model. Testable hypotheses as defined in Searle [8] are extended to involve nonestimable functions. An explicit expression for the sum of squares of deviation from the null hypothesis under the general setup with restrictions (Rao [7, p. 242]) and the corresponding number of degrees of freedom are obtained for implementation on computers.