Shrinkage ridge regression in partial linear models

ABSTRACT

In this paper, shrinkage ridge estimator and its positive part are defined for the regression coefficient vector in a partial linear model. The differencing approach is used to enjoy the ease of parameter estimation after removing the non parametric part of the model. The exact risk expressions in addition to biases are derived for the estimators under study and the region of optimality of each estimator is exactly determined. The performance of the estimators is evaluated by simulated as well as real data sets.     

A variance shift model for detection of outliers in the linear mixed measurement error models

ABSTRACT

In this paper, we extend a variance shift model, previously considered in the linear mixed models, to the linear mixed measurement error models using the corrected likelihood of Nakamura (1990 Nakamura, T. (1990). Corrected score function for errors in variables models: methodology and application to generalized linear models. Biometrika 77:127–137.[Crossref], [Web of Science ®] , [Google Scholar]). This model assumes that a single outlier arises from an observation with inflated variance. We derive the score test and the analogue of the likelihood ratio test, to assess whether the ith observation has inflated variance. A parametric bootstrap procedure is implemented to obtain empirical distributions of the test statistics. Finally, results of a simulation study and an example of real data are presented to illustrate the performance of proposed tests.     

Mixture of the Riesz distribution with respect to the generalized multivariate gamma distribution

Wishart natural exponential families (NEFs) characterized by Letac (1989) are extended to the Riesz NEFs on symmetric matrices. These families are characterized by their variance functions defined in Hassairi and Lajmi (2001). This work uses a particular basis of these NEFs to describe the class of the generalized multivariate gamma distributions and then to study the statistical model obtained by the mixture of this distribution with the Riesz one on the space of symmetric matrices.     

Bayes Estimation Based on Joint Progressive Type II Censored Data Under LINEX Loss Function

In the lifetime experiments, the joint censoring scheme is useful for planning comparative purposes of two identical products manufactured coming from different lines. In this article, we will confine ourselves to the data obtained by conducting a joint progressive Type II censoring scheme on the basis of the two combined samples selected from the two lines. Moreover, it is supposed that the distributions of lifetimes of the two products satisfy in a proportional hazard model. A general form for the distributions is considered, and we tackle the problem of obtaining Bayes estimates under the squared error and linear-exponential (LINEX) loss functions. As a special case, the Weibull distribution is discussed in more detail. Finally, the estimated risks of the various estimators obtained are compared using the Monte Carlo method.     

Some Modifications for Choosing Ridge Parameters

Standard least square regression can produce estimates having a large mean squares error (MSE) when predictor variables are highly correlated or multicollinear. In this article, we propose four modifications to choose the ridge parameter (K) when multicollinearity exists among the columns of the design matrix. The proposed new estimators are extended versions of that suggested by Khalaf and Shukur (2005 Khalaf , G. , Shukur , G. ( 2005 ). Choosing ridge parameter for regression problems . Commun. Statist. A 34 : 1177 – 1182 . [CSA] [Taylor & Francis Online] , [Google Scholar]). The properties of these estimators are compared with those of Hoerl and Kennard (1970a Hoerl , A. E. , Kennard , R. W. ( 1970a ). Ridge regression: biased estimation for non-orthogonal problems . Tech. . 12 : 55 – 67 . [CSA] [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) and the OLS using the MSE criterion. All estimators under consideration are evaluated using simulation techniques under certain conditions where a number of factors that may affect their properties have been varied. In addition, it is shown that at least one of the proposed estimators either has a smaller MSE than the others or is the next best otherwise.     

Evidential inference and optimal sample size determination on the basis of record values and record times under random sampling scheme

In this paper, the likelihood ratio approach is applied for measuring evidence provided by record data in favor of a hypothesis against an alternative under a random sampling scheme. Explicit expressions for probabilities of observing strong and weak evidences are derived. Asymptotic behaviors of these probabilities are investigated in a greater detail. Optimal sample size in which the substantial evidence reaches a desired level is determined. An illustrative example concerning records of times between consecutive telephone calls to a company’s switchboard is also analyzed.     

An inventory model with random discount offerings

We consider an inventory model in which a supplier makes deal offers with random discount prices at random points in time. Assuming that discount offerings follow a Poisson process and discount price is a discrete random variable with a known distribution, we propose a continuous-review control policy for the model and derive optimality conditions for the policy parameters. The model is then extended to the case of multiple suppliers that offer discount deals with supplier-specific Poisson processes and discount prices. Numerical examples are presented to demonstrate cost savings due to discount offers.     

A note on the most powerful invariant test of Rayleigh against exponential distribution

Abstract

The problem of testing Rayleigh distribution against exponentiality, based on a random sample of observations is considered. This problem arises in survival analysis, when testing a linearly increasing hazard function against a constant hazard function. It is shown that for this problem the most powerful invariant test is equivalent to the “ratio of maximized likelihoods” (RML) test. However, since the two families are separate, the RML test statistic does not have the usual asymptotic chi-square distribution. Normal and saddlepoint approximations to the distribution of the RML test statistic are derived. Simulations show that saddlepoint approximation is more accurate than the normal approximation, especially for tail probabilities that are the main values of interest in hypothesis testing.     

On a Characterization of Generalized Pareto Distribution Based on Generalized Order Statistics

In recent years, several attempts have been made to characterize the generalized Pareto distribution (GPD) based on the properties of order statistics and record values. In the present article, we give a characterization result on GPD based on the spacing of generalized order statistics.     

Comparison of estimation methods for the Weibull distribution

Weibull distributions have received wide ranging applications in many areas including reliability, hydrology and communication systems. Many estimation methods have been proposed for Weibull distributions. But there has not been a comprehensive comparison of these estimation methods. Most studies have focused on comparing the maximum likelihood estimation (MLE) with one of the other approaches. In this paper, we first propose an L-moment estimator for the Weibull distribution. Then, a comprehensive comparison is made of the following methods: the method of maximum likelihood estimation (MLE), the method of logarithmic moments, the percentile method, the method of moments and the method of L-moments.