Fikri Akdeniz

On the almost unbiased generalized liu estimator and unbiased estimation of the bias and mse

In this paper, we derive the almost unbiased generalized Liu estimator and examine an exact unbiased estimator of the bias and mean squared error of the feasible generalized Liu estimator . We compare the almost unbiased generalized Liu estimator (AUGLE) with the generalized Liu estimator (GLE) and with the ordinary least squares estimator (OLSE).

Mean Squared Error Matrix Comparisons of Some Biased Estimators in Linear Regression

Abstract Consider the linear regression model in the usual notation. In the presence of multicollinearity certain biased estimators like the ordinary ridge regression estimator and the Liu estimator introduced by Liu (Liu, Ke Jian. (1993). A new class of biased estimate in linear regression. Communications in Statistics-Theory and Methods 22(2):393–402) or improved ridge and Liu estimators are used to outperform the ordinary least squares estimates in the linear regression model. In this article we compare the (almost unbiased) generalized ridge regression estimator with the (almost unbiased) generalized Liu estimator in the matrix mean square error sense.

A theorem on the difference of the generalized inverses of two nonnegative matrices

A necessary and sufficient condition for to be a non-negative matrix is presented when are assumed to be nonnegative matrices. To demonstrate the applicability of the theorem, the intra-block and combined intra-inter-block estimators of the treatment effects for an incomplete block model are compared.

MEAN SQUARED ERROR COMPARISONS OF SOME BIASED REGRESSION ESTIMATORS

Gunst and Mason (1976) and Trenkler (1980) have compared several regression estimators with respect to the generalized mean squared error criterion. The purpose of this paper is to deal with the comparisons among the some other biased estimators constructed as alternatives to the least squares estimator when multicollinearity is present.

Mean squared error comparisons of the modified ridge regression estimator and iiie restricted ridge regression estimator

Swindel (1976) introduced a modified ridge regression estimator based on prior information. Sarkar (1992) suggested a new estimator by combining in a particular way the two approaches followed in obtaining the restricted ieast squares and ordinary ndge regression estimators. In this paper we compare the mean square error matrices of the modified ridge regression estimator based on prior information and die restricted ridge regression estimator introduced by Sarkar (1992). We stated a sufficient condition for the mean square error matrix of the modified ndge regression estimator to exceed the mean square enor matrix of the restricted ridge regression estimator.

A per‐field classification method based on mixture distribution models and an application to Landsat Thematic Mapper data

This study has three aims: firstly, to define an efficient and accurate supervised classification method to classify land use/land cover on per‐field basis using mixture distribution models. The second aim was to demonstrate the working principle of the per‐field classification method based on mixture distribution models by classifying a Landsat Thematic Mapper selected test image of an agricultural area. The third aim was to compare the overall classification accuracy and performance of the per‐field classification method based on mixture distribution models with those of three per‐pixel classification methods: minimum distance, nearest neighbour and maximum likelihood.

Efficiency of a Liu-type estimator in semiparametric regression models

In this paper we consider the semiparametric regression model, y=X@b+f+@e. Recently, Hu [11] proposed ridge regression estimator in a semiparametric regression model. We introduce a Liu-type (combined ridge-Stein) estimator (LTE) in a semiparametric regression model. Firstly, Liu-type estimators of both @b and f are attained without a restrained design matrix. Secondly, the LTE estimator of @b is compared with the two-step estimator in terms of the mean square error. We describe the almost unbiased Liu-type estimator in semiparametric regression models. The almost unbiased Liu-type estimator is compared with the Liu-type estimator in terms of the mean squared error matrix. A numerical example is provided to show the performance of the estimators.

Liu-type estimator in semiparametric regression models

In this paper, we introduced a Liu-type estimator for the vector of parameters β in a semiparametric regression model. We also obtained the semiparametric restricted Liu-type estimator for the parametric component in a semiparametric regression model. The ideas in the paper are illustrated in a real data example and in a Monte Carlo simulation study.

Ill-conditioning and multicollinearity

Abstract It is well known that unstability of solutions to small changes in inputs causes many problems in numerical computations. Existence, uniqueness and stability of solutions are important features of mathematical problems. Problems that fail to satisfy these conditions are called ill-posed. The purpose of this study is to remind briefly some methods of solution to ill-posed problems and to see the impacts or connections of these techniques to some statistical methods.

A multispectral classification algorithm for classifying parcels in an agricultural region

Abstract A multispectral classification algorithm is developed for classifying remotely-sensed data extracted from parcels in an agricultural region. The developed multispectral classification algorithm is based on the comparison of the probability density function of the mixture of three normal distributions constructed for a test parcel (test class) with the probability density functions of the mixture of three normal distributions constructed for control parcels (control or information classes) one by one according to the distances between them. A discriminant function is defined and a decision rule is established for the developed multispectral classification algorithm. The discriminant functions for the developed multispectral classification algorithm take values between 0 and 2, end points are included. The discriminant function values give extra information which can be used in decisions about the comparisons in the developed multispectral classification algorithm. The extra information includes si...