Regression Estimator

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M. Revan Özkale - One of the best experts on this subject based on the ideXlab platform.

  • More on the restricted ridge Regression estimation
    Journal of Statistical Computation and Simulation, 2011
    Co-Authors: Selahattin Kaçıranlar, M. Revan Özkale, Sadullah Sakallıoğlu, Hüseyin Güler
    Abstract:

    Several alternative methods for derivation of the restricted ridge Regression Estimator (RRRE) are provided. Theoretical comparison and relationship of RRRE with related methods for Regression with the multicollinearity problem are described. We also find inter-connections among RRRE, ordinary ridge Regression Estimator (ORRE), restricted least squares Estimator (RLSE), modified ridge Regression Estimator (MRRE) and restricted modified generalized ridge Estimator (RMGRE). Finally, numerical comparison, in addition to theoretical derivation, is also conducted with a Monte Carlo simulation and a real data example.

  • A stochastic restricted ridge Regression Estimator
    Journal of Multivariate Analysis, 2009
    Co-Authors: M. Revan Özkale
    Abstract:

    Grosz [J. Grosz, Restricted ridge estimation, Statistics & Probability Letters 65 (2003) 57-64] proposed a restricted ridge Regression Estimator when exact restrictions are assumed to hold. When there are stochastic linear restrictions on the parameter vector, we introduce a new Estimator by combining ideas underlying the mixed and the ridge Regression Estimators under the assumption that the errors are not independent and identically distributed. Apart from [J. Grosz, Restricted ridge estimation, Statistics & Probability Letters 65 (2003) 57-64], we call this new Estimator as the stochastic restricted ridge Regression (SRRR) Estimator. The performance of the SRRR Estimator over the mixed Estimator in respect of the variance and the mean square error matrices is examined. We also illustrate our findings with a numerical example. The shrinkage generalized least squares (GLS) and the stochastic restricted shrinkage GLS Estimators are proposed.

  • Principal components Regression Estimator and a test for the restrictions
    Statistics, 2009
    Co-Authors: M. Revan Özkale
    Abstract:

    In this article, we introduce restricted principal components Regression (RPCR) Estimator by combining the approaches followed in obtaining the restricted least squares Estimator and the principal components Regression Estimator. The performance of the RPCR Estimator with respect to the matrix and the generalized mean square error are examined. We also suggest a testing procedure for linear restrictions in principal components Regression by using singly and doubly non-central F distribution.

Nico J Nieuwenbroek - One of the best experts on this subject based on the ideXlab platform.

  • aligning estimates for common variables in two or more sample surveys
    Journal of the American Statistical Association, 1997
    Co-Authors: Robbert H Renssen, Nico J Nieuwenbroek
    Abstract:

    Abstract In practice, for many sample surveys the estimates of several population totals are based on one set of weights, which reproduces the known population totals of auxiliary variables. Such a set can always be obtained by using the general Regression Estimator. If some variables, not necessarily with known population totals, are jointly collected in two sample surveys, then it may be desirable that the weights of both surveys produce the same estimates for the unknown population totals of the common variables. In this article we propose adjusting the general Regression Estimator to meet this consistency requirement by considering the common variables as additional auxiliary variables. It turns out that the adjusted general Regression Estimator generalizes Zieschang's method.

Nicolas Debarsy - One of the best experts on this subject based on the ideXlab platform.

R R Sitter - One of the best experts on this subject based on the ideXlab platform.

  • variance estimation for the Regression Estimator in two phase sampling
    Journal of the American Statistical Association, 1997
    Co-Authors: R R Sitter
    Abstract:

    Abstract Many techniques in survey sampling depend on the possession of information about an auxiliary variable x, or a vector of auxiliary variables, available for the entire population. Regression estimates require , the population mean. If such information is unavailable, then one can sometimes obtain a large preliminary sample of xi relatively cheaply and use this to obtain a good estimate, say , of A smaller subsample can then be taken and the characteristic of interest, yi , measured. A Regression Estimator can then be used treating as if it were This is termed double sampling, or two-phase sampling. This article focuses on variance Estimators for the Regression Estimator in the aforementioned context and their use in constructing confidence intervals. A design-based linearization variance Estimator that makes more complete use of the sample data than the standard one is considered for two-phase sampling. A jackknife variance Estimator and its linearized version are obtained and shown to be design c...

Dick J. Brus - One of the best experts on this subject based on the ideXlab platform.

  • Using Regression models in design-based estimation of spatial means of soil properties
    European Journal of Soil Science, 2000
    Co-Authors: Dick J. Brus
    Abstract:

    The precision of design-based sampling strategies can be increased by using Regression models at the estimation stage. A general Regression Estimator is given that can be used for a wide variety of models and any well-defined sampling design. It equals the Estimator plus an adjustment term that accounts for the differences between the Estimators for the spatial means of the auxiliary variables and the true spatial means of these variables. The Regression Estimator and ratio Estimator follow from certain assumptions on the model and the sampling design. These are compared with the Estimator in two case studies. In one study a bivariate field of linearly related variables was simulated and repeatedly sampled by Simple Random Sampling without replacement and sample sizes 10, 25, 50, 100 and 200. For all sample sizes the ratio of the standard error of the simple Regression Estimator to that of the Estimator was approximately 55ÐThe bias of the simple Regression Estimator was negligibly small. The confidence interval Estimators were valid for all sample sizes except for n = 10. Also the ratio Estimator was approximately unbiased, and the confidence interval Estimators were valid for all sample sizes, even for n = 10. This is remarkable because the ratio Estimator assumes that the intercept of the Regression line is 0 which was incorrect for the simulated field. On the other hand, only approximately 55␘f the potential gain was achieved because the model was inappropriate. In a second study the spatial means of the Mean Highest Watertable of map units were estimated by Stratified Simple Random Sampling and the combined (multiple) Regression Estimator. The NAP elevation, the local elevation, the Easting and the Northing were used as auxiliary variables. For all map units except one the combined (multiple) Regression Estimator was more precise than the Estimator. The ratio of the standard errors varied from 0.36 to 1.04. The domain for which the Regression Estimator was less precise than the Estimator showed strong variation between strata. For this domain it was more efficient to group the strata into two groups and to fit simple models for these groups separately.

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