Modified spline regression based on randomly right-censored data: A comparative study

ABSTRACT

In this paper, we propose modified spline estimators for nonparametric regression models with right-censored data, especially when the censored response observations are converted to synthetic data. Efficient implementation of these estimators depends on the set of knot points and an appropriate smoothing parameter. We use three algorithms, the default selection method (DSM), myopic algorithm (MA), and full search algorithm (FSA), to select the optimum set of knots in a penalized spline method based on a smoothing parameter, which is chosen based on different criteria, including the improved version of the Akaike information criterion (AICc), generalized cross validation (GCV), restricted maximum likelihood (REML), and Bayesian information criterion (BIC). We also consider the smoothing spline (SS), which uses all the data points as knots. The main goal of this study is to compare the performance of the algorithm and criteria combinations in the suggested penalized spline fits under censored data. A Monte Carlo simulation study is performed and a real data example is presented to illustrate the ideas in the paper. The results confirm that the FSA slightly outperforms the other methods, especially for high censoring levels.     

On Optimum Regression Estimator for Population Mean Using Two Auxiliary Variables in Simple Random Sampling

In this paper, a difference-in-regression estimator is proposed by using two auxiliary variables in simple random sampling. Variance of proposed estimator up to the first order of approximation is compared with other competing estimators. Additionally, by taking the known value of one of the population regression coefficients, another version of the proposed estimator is also obtained. The proposed estimator is found optimum in the class of estimators based on two auxiliary variables. A simulation study is carried out in support with theoretical results. If only the means of auxiliary variables are available, another estimator can be obtained for large trivariate normal population.     

A Class of s–K Type Principal Components Estimators in the Linear Model

In this article, we introduce a new class of estimators called the s–K type principal components estimators to combat multicollinearity, which include the principal components regression (PCR) estimator, the r–k estimator and the s–K estimator as special cases. Necessary and sufficient conditions for the superiority of the new estimator over the PCR estimator, the r–k estimator and the s–K estimator are derived in the sense of the mean squared error matrix criterion. A Monte Carlo simulation study and a numerical example are given to illustrate the performance of the proposed estimator.     

Objective Bayesian Analysis for Log-logistic Distribution

In this article, Bayesian approach is applied to estimate the parameters of Log-logistic distribution under reference prior and Jeffreys’ prior. The reference prior is derived and it is found that the reference prior is also a second-order matching priors as for the case of any parameter of interest. The Bayesian estimators cannot be obtained in explicit forms. Metropolis within Gibbs sampling algorithm is used to obtain the Bayesian estimators. The Bayesian estimates are compared with the maximum likelihood estimates via simulation study. A real dataset is considered for illustrative purposes.     

The exact distribution and density functions of the stein-type estimator for normal variance

In this paper, we derive the exact distribution and density functions of the Stein-type estimator for the normal variance. It is shown by numerical evaluation that the density function of the Stein-type estimator is unimodal and concentrates around the mode more than that of the usual estimator.     

Unbiasedness of fourier integral estimator under weaker assumptions

The Fourier integral estimator (FIE) of the hazard rate function have been introduced by Singpurwalla and Wong (1983) in order to improve the rate of convergence of mean square error. However, the asymptotic properties are derived under several assumptions. These assumptions are too strong to be satisfied in most applications. The situation becomes worse when some of these assumptions appear contradictory to each other. This greatly limits the usage of FIE. This paper endeavors to release or weaken some of these assumptions and therefore expand the applicable coverage of FIE.     

The general expressions for the moments of lawless and wang's ordinary ridge regression estimator

In this paper, we derive the exact general expressions for the moments of an ordinary ridge regression (ORR) estimator for individual regression coefficients in a different way from Firinguetti (1987). Using the derived expressions, we evaluate numerically the first four moments of the ORR estimator, and examine its bias, mean square error, skewness and kurtosis. Further, Monte Carlo experiments are carried out in order to examine the shape of the density function of the ORR estimator.     

A functional approach to estimating finite population distribution functions

Existing estimators of a finite population distribution function that utilize auxiliary information are often constructed by a point wise argument. As a result, these estimators are not always monotone. We adopt a functional approach to the problem and propose two estimators based on compositions of functions. Asymptotic variance formulae are derived for the proposed es-timators. Comparisons are made with existing estimators in a simulation study using three natural populations.     

Estimation of non-occurrence probability in periodic model

Dimitrov and Khalil (1992) introduced a class of new probability distributions for modeling environmental evolution with periodic behavior. One of the key parameters in these distributions is α, the probability that the event being studied does not occur. In that article the authors derive an estimator for this parameter assuming a series of conditions. In this article it is shown that the estimator is valid under more general conditions, i.e. same of the assumptions are not necessary. It is shown that under the assumption that the elapsed time measured from the starting point of a period until the first occurrence time of the event given that the event occurred in this cycle is related to α, an approximate maximum likelihood estimator of a is proposed. The large sample properties of the estimator are discussed. Monte Carlo study is done for supporting the theoretical results.     

Estimation of reliability under ordered restriction on the parameters

This paper deals with the estimation of reliability for a strength-stress model under ordered restriction on the parameters. It is assumed that components have exponential distributions and are arranged in a parallel system and the failure of one component, results in increasing the failure rate of the remaining components. Results are derived when (i) the ordering of the means is taken into account and when (ii) the ordering of the means is ignored. Simulation studies are carried out to compare the results. It is noticed that, in almost all cases, in case (i) the estimates are closer to the true value with smaller mean squared error (MSE) and smaller’ standard deviation than in case (ii). Thus when the ordering of the means is present in the model, such information should be incorporated in the estimation of reliability.