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In this paper, the seven equivalent conditions of complete moment convergence and complete integral convergence for m -asymptotic negatively associated ( m -ANA, for short) random variables are established. The results obtained in the paper extend and improve some corresponding ones for negatively associated (NA, for short) random variables and negatively orthant dependent (NOD, for short) random variables. As an application of our main results, we present a result on complete consistency for the weighted estimator in a nonparametric regression model based on m-ANA errors. We perform a numerical simulation to verify the validity of the theoretical results. [ABSTRACT FROM AUTHOR]

In the standard secretary problem (SP), a decision-maker (DM) tries to choose the best applicant of a sequentially ordered set, and the goal is to maximize the probability of choosing the best applicant. In this paper, we extend the standard SP and present a satisficing policy. There are several satisfactory applicants for the DM to choose under the satisficing policy. The DM cannot rank all the applicants from best to worst due to the limits of the DM's incomplete preferences, and the goal is to maximize the probability of choosing one of satisfactory applicants. For the secretary problem with 2 and 3 satisfactory applicants respectively, on the one hand, the asymptotic results of the maximum probability of choosing a satisfactory applicant and the corresponding optimal cutoff value are computed respectively. On the other hand, a series of computer simulations are conducted to estimate the optimal cutoff value and the maximum probability of choosing a satisfactory applicant. The effects of incorporating endogenous search cost in the case of 50 and 100 applicants are investigated respectively under the satisficing policy. The satisficing policy of this paper can be regarded as an extension of the optimal policy of the standard SP. [ABSTRACT FROM AUTHOR]

In this paper, stochastic Gilpin-Ayala model driven by α-stable process under regime switching is presented. Firstly, we prove the existence and uniqueness of the solution for the stochastic model. Then, under certain conditions, the almost sure exponential stability and pth moment exponential stability of the trivial solution are obtained. The results indicated that the α-stable noises can make the trivial solution stable under some conditions. Computer simulations are presented to illustrate our theory. [ABSTRACT FROM AUTHOR]

In this paper, motivated by considerations of server utilization and energy consumption in cloud computing, we investigate a homogeneous queueing system with a threshold-based workload control scheme. In this system, a virtual machine will be turned off when there are no tasks in its buffer upon the completion of a service by the machine, and turned on when the number of tasks in its buffer reaches a pre-set threshold value. Due to complexity of this system, we propose approximations to system performance measures by mean field limits. An iterative algorithm is suggested for the solution to the mean field limit equations. In addition, numerical and simulation results are presented to justify the proposed approximation method and to provide a numerical analysis on the impact of the system performances by system parameters, which suggests that the proposed system saves about (1 − λ μ) × 100 % of the energy consumption compared to the ordinary supermarket models. [ABSTRACT FROM AUTHOR]

In this paper, we propose a MIXED penalty for the LAD regression model, which can estimate parameters and select important variables efficiently and stably. The proposed method has a good performance in the case of dependent variable with heavy tail and outliers, so this estimator is robust and efficient for tackling the problem of heterogeniety. We show that the proposed estimator possesses the good properties by applying certain assumptions. In the part of numerical simulation, we give several simulation studies to examine the asymptotic results, which shows that the method we proposed behaves better. [ABSTRACT FROM AUTHOR]

This paper investigates variable selection in semiparametric spatial autoregressive panel data model with random effects. A penalized profile maximum-likelihood method is proposed with adaptive lasso penalty which achieves parameter estimation and variable selection at the same time. Under some regular conditions, we prove the theoretical properties of the estimators, including consistency and oracle property. In addition, we develop a feasible logarithm and carry out numerical simulations to examine the finite sample performance of this method. At last, a real data study about the investment influencing factors of the "Belt and Road" initiative is presented for illustration purpose. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the mean exit time and the scale function for the geometric Brownian motion with Markovian switching, in which the drift coefficients and the diffusion coefficients are associated with regime changes. The explicit expressions of mean exit time and scale function are obtained by solving the corresponding Poisson problem. Furthermore, we estimate parameters for the geometric Brownian motion with Markovian switching by composite likelihood and explore some properties of the estimates. Computer simulations are performed to illustrate our proposed algorithm, showing high accuracy of the estimators. [ABSTRACT FROM AUTHOR]

In this paper we analyze the kth-to-default credit-linked notes (CLN) with counterparty risk by the reduced-form model. We study the structure of the kth-to-default CLN and present a general valuation framework for CLN values and counterparty valuation adjustments (CVA) under the conditional independence assumption. Explicit formulas of the kth-to-default CLN values and their CVAs are obtained by the PDE approach. Numerical simulations are conducted to show the effects of the correlated default risk on the kth-to-default CLN values and their CVAs. [ABSTRACT FROM AUTHOR]

In this paper, we mainly focus on the valuation for the risk-based premium of private pension plan with termination provided by the Pension Benefit Guaranty Corporation (PBGC). The dynamics for assets of both the pension fund and the sponsoring company are described by jump diffusion processes. We obtain the pricing formula for the risk-based premium with premature termination and analyze the impact of certain parameters on the premium through numerical simulations. Results indicate that the risk-based premium for PBGC increases with the increase of the risky asset investment proportion, the volatility of risky asset, and pension benefits. [ABSTRACT FROM AUTHOR]

Clustered ordinal data with high-dimensional covariates have become increasingly common in social and biomedical sciences. In this paper, we consider some asymptotic properties of generalized estimating equations (GEE) estimator in the case that the dimension of covariates goes to infinity as the sample size tends to infinity for such data. Under some regularity conditions, the existence, consistency and asymptotic normality of GEE estimator are proved. Besides, the effectiveness of asymptotic approximation is illustrated via numerical simulations. Our main result generalizes that of Wang [The Annals of Statistics, 39(1): 389–417, 2011] to the case of multinomial response variable. [ABSTRACT FROM AUTHOR]

An evaluation of FBST, Fully Bayesian Significance Test, restricted to survival models is the main objective of the present paper. A Survival distribution should be chosen among the tree celebrated ones, lognormal, gamma, and Weibull. For this discrimination, a linear mixture of the three distributions is an important tool: the FBST is used to test the hypotheses defined on the mixture weights space. Another feature of the paper is that all three distributions are reparametrized in that all the six parameters are written as functions of the mean and the variance of the population been studied. Some numerical results from simulations with some right-censored data are considered. [ABSTRACT FROM AUTHOR]

The paper considers the asymptotical expansion on the likelihood ratio (LR) statistic for testing the block circular symmetric (BCS) covariance structure of a multivariate Gaussian population. When the number of blocks u and the dimension of each block p satisfy p = p (n) → ∞ and p u / (n − 1) → c ∈ (0 , 1) as the sample size n → ∞ , the Edgeworth expansion of the null distribution of the LR test statistic and its uniform Berry-Esseen type bound are established. Some numerical simulations indicate that the proposed approximation is more accurate than the traditional Chi-square approximate method on dealing with the high-dimensional test. [ABSTRACT FROM AUTHOR]

Due to its flexibility, a partially linear single-index model arises in many contemporary scientific endeavors. In this paper, we set foot on its inference under settings of panel data and a serially correlated error component structure. By combining the local polynomial technique with the bias-corrected generalized estimating equations, we propose a feasible weighted generalized estimating equation estimation (GEE-FW) for unknown regression parameters. The GEE-FW is shown to be asymptotically normal and more efficient than the unweighted generalized estimating equation estimation based on working independence. Moreover, a two-stage local linear generalized estimating equation estimation (GEE-TS) of the unknown link function is also proposed, which takes the contemporaneous correlation into account and achieves an increase in its estimated efficiency. The asymptotic property of the GEE-TS is established as well and we show that it is asymptotically more efficient than the one which ignores the contemporaneous correlation. Conducted numerical simulation studies and actual data analysis show that the proposed estimation methods are effective and have good performance in both theory and application. [ABSTRACT FROM AUTHOR]

In this paper, we study the complete moment convergence for arrays of rowwise m-extended negatively dependent (m-END) random variables, which generalizes some corresponding ones for complete convergence. We also give an application to non-parametric regression model based on m-END errors by using the complete convergence that we establish. Finally, the choice of the fixed design points and the weight functions for the nearest neighbor estimator are proposed. We also provide a numerical simulation to verify the validity of our theoretical result. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to develop a detection algorithm for the first jump point in sampling trajectories of jump-diffusions which are described as solutions of stochastic differential equations driven by α-stable white noise. This is done by a multivariate Lagrange interpolation approach. To this end, we utilize computer simulation algorithm in MATLAB to visualize the sampling trajectories of the jump-diffusions for various combinations of parameters arising in the modeling structure of stochastic differential equations. [ABSTRACT FROM AUTHOR]

The observations of some samples are usually collected in an imprecise way. By employing uncertain variables to model these imprecise observations, this paper proposes uncertain statistical inferences for nonparametric regression model based on the least absolute deviations criterion. A numerical example and simulation comparison with least squares estimate are presented to illustrate the proposed method. [ABSTRACT FROM AUTHOR]

The most widely used approach for reliability estimation is the well-known stress-strength model, θ = P(X < Y), where X and Y are random variables. In this model, the reliability, θ, of the system is the probability that the system is strong enough to overcome the stress imposed on it. In most cases, X and Y are assumed to be independent. Nevertheless, in reality, the strength variable Y could be highly dependent on the stress variable X. In this paper, we discuss the kernel-based estimation of θ when X and Y are dependent random variables under progressive type II censored sample. The asymptotic properties of the kernel-based estimators of θ based on progressive type II censoring are proposed. An extensive computer simulation is conducted to gain insight into the performance of the proposed estimators. A real data example is provided to illustrate the process. [ABSTRACT FROM AUTHOR]

The present paper deals with the performance evaluation of an M / M / 1 retrial queue with collisions, transmission errors and unreliable server. To the best of our knowledge, there are no works that have dealt with retrial queues by considering all the above-mentioned aspects (collisions, transmission errors and unreliable server). This queue can be used as a mathematical model of several computer systems and telecommunication networks. We apply the generating function method to derive the joint distribution of the server state and the orbit length in the steady state, and we obtain some performance measures. Finally, we provide numerical illustrations to show the effectiveness and the applicability of the model. [ABSTRACT FROM AUTHOR]

In this paper, we consider a semiparametric model to find the optimal treatment regimes. A-learning type equation method is proposed to construct a doubly robust estimating equation for the parameters of interest in the optimal treatment. To overcome bias from the censoring time, we consider the inverse probability censoring weighting method in estimating equation. The resulting estimator is shown to be consistent and asymptotic normal when either the baseline effect model for covariates or the propensity score is correctly specified. Also, numerical simulations and an application with real data illustrate the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we propose an empirical likelihood based diagnostic technique for heteroscedasticity in the semiparametric varying-coefficient partially linear errors-in-variables models. Under mild conditions, a nonparametric version of Wilk’s theorem is derived. Simulation results reveal that our test performs well in both size and power. [ABSTRACT FROM AUTHOR]

Quantile regression has great flexibility in describing the effect of covariate on response. In this paper, based on the censored median regression proposed by Zhou, we develop a new weighted quantile regression of nonlinear models when the response is randomly censored. Our method can be applied to more complicated quantile regression models at any quantile within (0, 1), which contains censored median regression. Furthermore, the consistency and asymptotic normality of the proposed estimator are derived under appropriate assumptions. Finally, the finite sample performance of the proposed estimator is examined by numerical simulation. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the median-of-means approach for estimating unknown parameters in multiple linear regression model and the regression model with autocorrelated error. The proposed estimators are not only robust against the outliers of data but also proved to be consistent. Extensive numerical simulations and one real dataset are presented to show the performances of new estimators. [ABSTRACT FROM AUTHOR]

This paper is concerned with the interval estimation for the log odds of the posterior probability that the observation vector belongs to one of two homoscedastic multivariate normal distributions (Π1and Π2). We give the limiting distribution of the unbiased estimator for the log odds as the sample sizes and the dimension jointly tend to infinity, and approximate the confidence interval based on the asymptotic distribution. Small-scale simulations are performed to check the precision of the approximation. [ABSTRACT FROM AUTHOR]

This paper considers likelihood-based estimation under the Cox proportional hazards model in the situations where some covariate entries are missing not at random. Assuming the conditional distribution of the missing entries is known, we demonstrate the existence of the semiparametric maximum likelihood estimator of the model parameters, establish the consistency and weak convergence. By simulation, we examine the finite-sample performance of the estimation procedure, and compare the SPMLE with the one resulted from using an estimated conditional distribution of the missing entries. We analyze the data from a tuberculosis (TB) study applying the proposed approach for illustration. [ABSTRACT FROM AUTHOR]

In this paper, we consider sufficient conditions for the stationary distribution of generalized Ait-Sahalia-type interest rate model. We show that ifr⩾ 2ρ − 1, then the generalized Ait-Sahalia interest rate model has a unique stationary distribution and ifr< 2ρ − 1, then the generalized Ait-Sahalia interest rate model is recurrent relative to the domain (0, ϵ), for any ϵ > 0. Besides, some recursion formulas for the stationary distribution are presented. Finally, some numerical simulations are used to illustrate our results. [ABSTRACT FROM AUTHOR]

Selection of appropriate predictors for right censored time to event data is very often encountered by the practitioners. We consider the ℓ1penalized regression or “least absolute shrinkage and selection operator” as a tool for predictor selection in association with accelerated failure time model. The choice of the penalizing parameter λ is crucial to identify the correct set of covariates. In this paper, we propose an information theory-based method to choose λ under log-normal distribution. Furthermore, an efficient algorithm is discussed in the same context. The performance of the proposed λ and the algorithm is illustrated through simulation studies and a real data analysis. The convergence of the algorithm is also discussed. [ABSTRACT FROM AUTHOR]

As direct generalization of the quantile regression for complete observed data, an estimation method for quantile regression models with interval censored data is proposed, and the property of consistency is obtained. The property of asymptotic normality is also established with a bias converging to zero, and to reduce the bias, two bias correction methods are proposed. Methods proposed in this paper do not require the censoring vectors to be identically distributed, and can be applied to models with various covariates. Simulation results show that the proposed methods work well. [ABSTRACT FROM AUTHOR]

In Bayesian theory, calculating a posterior probability distribution is highly important but typically difficult. Therefore, some methods have been proposed to deal with such problem, among which, the most popular one is the asymptotic expansions of posterior distributions. In this paper, we propose an alternative approach, named a random weighting method, for scaled posterior distributions, and give an ideal convergence rate,o(n( − 1/2)), which serves as the theoretical guarantee for methods of numerical simulations. [ABSTRACT FROM AUTHOR]

In computer experiments, space-filling designs with a sliced structure or nested structure have received much recent interest and been studied separately. However, it is likely that designs with both structures are needed in some situations, but there are no suitable designs so far. In this paper, we construct a special class of nested Latin hypercube designs with sliced structures, in such a design, a small sliced Latin hypercube design is nested within a large one. The construction method is easy to implement and the number of factors is flexible. Numerical simulations show the usefulness of the newly proposed designs. [ABSTRACT FROM PUBLISHER]

In this paper a new distribution is proposed. This new model provides more flexibility to modeling data with upside-down bathtub hazard rate function. A significant account of mathematical properties of the new distribution is presented. The maximum likelihood estimators for the parameters in the presence of complete and censored data are presented. Two corrective approaches are considered to derive modified estimators that are bias-free to second order. A numerical simulation is carried out to examine the efficiency of the bias correction. Finally, an application using a real data set is presented in order to illustrate our proposed distribution. [ABSTRACT FROM AUTHOR]

This paper addresses the optimal design problems for constant-stress accelerated degradation test (CSADT) based on gamma processes with fixed effect and random effect. For three optimization criteria, we prove that optimal CSADT plans with multiple stress levels degenerate to two-stress-level test plans only using the minimum and maximum stress levels under model assumptions. Under each optimization criterion, the optimal sample size allocation proportions for the minimum and maximum stress levels are determined theoretically. The effect of the stress level on the objective functions is also discussed. A numerical example and a simulation study are provided to illustrate the obtained results. [ABSTRACT FROM AUTHOR]

Affiliation network is one kind of two-mode social network with two different sets of nodes (namely, a set of actors and a set of social events) and edges representing the affiliation of the actors with the social events. The connections in many affiliation networks are only binary weighted between actors and social events that can not reveal the affiliation strength relationship. Although a number of statistical models are proposed to analyze affiliation binary weighted networks, the asymptotic behaviors of the maximum likelihood estimator (MLE) are still unknown or have not been properly explored in affiliation weighted networks. In this paper, we study an affiliation model with the degree sequence as the exclusively natural sufficient statistic in the exponential family distributions. We derive the consistency and asymptotic normality of the maximum likelihood estimator in affiliation finite discrete weighted networks when the numbers of actors and events both go to infinity. Simulation studies and a real data example demonstrate our theoretical results. [ABSTRACT FROM AUTHOR]

Non parametric approaches to classification have gained significant attention in the last two decades. In this paper, we propose a classification methodology based on the multivariate rank functions and show that it is a Bayes rule for spherically symmetric distributions with a location shift. We show that a rank-based classifier is equivalent to optimal Bayes rule under suitable conditions. We also present an affine invariant version of the classifier. To accommodate different covariance structures, we construct a classifier based on the central rank region. Asymptotic properties of these classification methods are studied. We illustrate the performance of our proposed methods in comparison to some other depth-based classifiers using simulated and real data sets. [ABSTRACT FROM AUTHOR]

This paper is an attempt to analyze the effect of scrambled response techniques to estimate the current population mean in two-occasion successive sampling when study and auxiliary variables are sensitive in nature. Using additive and multiplicative scrambled response models on both occasions, some generalized estimation strategies of current population mean have been proposed and their properties are examined. Empirical studies are performed on real data (abortion rate in the states of United States) and simulation studies are also carried out to evaluate the performances of the proposed estimators over other estimators. Results have proved the worthiness of the scrambled response techniques in real-life situations. [ABSTRACT FROM PUBLISHER]

In this paper, we introduce a generalization of the Bilal distribution, where a new two-parameter distribution is presented. We show that its failure rate function can be upside-down bathtub shaped. The failure rate can also be decreasing or increasing. A comprehensive mathematical treatment of the new distribution is provided. The estimation by maximum likelihood is discussed, and a closed-form expression for Fisher’s information matrix is obtained. Asymptotic interval estimators for both of the two unknown parameters are also given. A simulation study is conducted and applications to real data sets are presented. [ABSTRACT FROM AUTHOR]

In this paper, we apply empirical likelihood for two-sample problems with growing high dimensionality. Our results are demonstrated for constructing confidence regions for the difference of the means of twop-dimensional samples and the difference in value between coefficients of twop-dimensional sample linear model. We show that empirical likelihood based estimator has the efficient property. That is, asp→ ∞ for high-dimensional data, the limit distribution of the EL ratio statistic for the difference of the means of two samples and the difference in value between coefficients of two-sample linear model is asymptotic normal distribution. Furthermore, empirical likelihood (EL) gives efficient estimator for regression coefficients in linear models, and can be as efficient as a parametric approach. The performance of the proposed method is illustrated via numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the consistency of the Expectation Maximization (EM) algorithm-based information criteria for model selection with missing data. The criteria correspond to a penalization of the conditional expectation of the complete data log-likelihood given the observed data and with respect to the missing data conditional density. We present asymptotic properties related to maximum likelihood estimation in the presence of incomplete data and we provide sufficient conditions for the consistency of model selection by minimizing the information criteria. Their finite sample performance is illustrated through simulation and real data studies. [ABSTRACT FROM AUTHOR]

The present paper considers the Bayesian analysis of a linear regression model involving structural change, which may occur either due to shift in disturbances precision or due to shift in regression parameters. The posterior density for the regression parameter has been derived and posterior odds ratio for testing the hypothesis that structural change is due to shift in disturbances precision against the alternative that the change is due to shift in regression parameters has been obtained. The findings of a numerical simulation have been presented. The proposed model has been applied to RBI data set on corporate sector. [ABSTRACT FROM AUTHOR]

Tabakan and Akdeniz introduced a difference-based ridge estimator in partially linear model. In this article a generalized difference-based weighted mixed ridge estimator in partially linear model is presented by combining the ideas underlying the generalized difference-based weighted mixed estimator and the generalized difference-based ridge estimator, when stochastic linear restrictions are assumed to hold. We also discussed the properties of the new estimator and compared the new estimator to the difference-based ridge estimator and difference-based weighted mixed estimator in the mean squared error matrix. A method to select the biasing parameters is also discussed. Finally, a numerical example and a simulation study are given to show the performances of the estimators. [ABSTRACT FROM AUTHOR]

We discover three interesting strings of inequalities among six Bayes estimators, where for the parameter space (0, 1), (0, ∞), and ( − ∞, ∞), each case has a string of inequalities. The three strings of inequalities only depend on the loss functions, and the inequalities are independent of the chosen models and the used priors provided the Bayes estimators exist. Therefore, they exist in a general setting which makes them quite interesting. Finally, the numerical simulations exemplify the two strings of inequalities defined on (0, 1) and (0, ∞), and that there does not exist a string of inequalities among the six smallest posterior expected losses. [ABSTRACT FROM PUBLISHER]

The original or generalized Lindley distribution has been proposed in order to fit a stochastic model to real data, that is, it establishes the distribution of the sum of independent variables. The distribution of the sum of independent and non identically generalized Lindley random variables is obtained by using inverse transformation of the moment generating function. A saddlepoint and a normal approximations are used to approximate the derived distribution. The accuracy of the approximations is shown by numerical simulations. [ABSTRACT FROM AUTHOR]

The problem of constructing the equal-tailed and shortest Bayesian tolerance intervals that control percentages in both tails of the exponential distribution based onk-record values is considered. Equal-tailed and shortest Bayesian tolerance factors are derived. Practical examples using real and simulatedk-record values are given to illustrate the proposed results. [ABSTRACT FROM AUTHOR]

We address statistical issues involved in the partially clustered design where clusters are only employed in the intervention arm, but not in the control arm. We develop a cluster adjustedt-test to compare group treatment effects with individual treatment effects for continuous outcomes in which the individual level data are used as the unit of the analysis in both arms, we develop an approach for determining sample sizes using this cluster adjustedt-test, and use simulation to demonstrate the consistent accuracy of the proposed cluster adjustedt-test and power estimation procedures. Two real examples illustrate how to use the proposed methods. [ABSTRACT FROM AUTHOR]

In this article, we focus on the variable selection for partially varying coefficient model under high dimensional data. Variable selection is proposed based on modal regression estimation with bridge method. Using the B-spline basic function to approximate the non parametric function, a penalty estimation objective equation is constructed. It establishes and proves that the variable selection methods have oracle property. Numerical simulations tested the performance of the proposed methods in a finite sample and verified the significance of the proposed estimation and the variable selection methods. [ABSTRACT FROM AUTHOR]

We proposed a generalized two stage optional randomized response model by single sample approach and developed a generalized exponential type estimator for the mean of sensitive variable using information from a non-sensitive auxiliary variable. Privacy protection and some special cases for the suggested model has also been discussed. Simulation and numerical study are carried out to assess the performance of the suggested estimator. We compare the proposed model with some existing estimators and conclude that our proposed model is more efficient under certain conditions. [ABSTRACT FROM AUTHOR]

Under the framework of multivariate regular variation, we obtain the asymptotic ratio between the tail distortion risk measure for portfolio loss and the sum of value-at-risk for single loss by a different method from the one in Zhu and Li when the confidence level tends to one. In order to illustrate the derived result, a relevant example is given and the corresponding numerical simulation is also carried out. [ABSTRACT FROM AUTHOR]

In this article, Bahadur type expansions of a nonparametric kernel estimator for ES under NA sequences are given. The strong consistency and the uniformly asymptotic normality of the estimator are yielded from the Bahadur type expansions, while the convergence rates of the above asymptotic properties are also obtained. Moreover, the expectation, the variance and the mean squared error (MSE) of the estimator are given. Besides, the optimal bandwidth selection of this estimator is discussed. We point out that all above results are based on the NA sequences. Finally, we conduct numerical simulations and compare performances of some ES estimators. [ABSTRACT FROM AUTHOR]

The asymptotic cumulants of the minimum phi-divergence estimators of the parameters in a model for categorical data are obtained up to the fourth order with the higher-order asymptotic variance under possible model misspecification. The corresponding asymptotic cumulants up to the third order for the studentized minimum phi-divergence estimator are also derived. These asymptotic cumulants, when a model is misspecified, depend on the form of the phi-divergence. Numerical illustrations with simulations are given for typical cases of the phi-divergence, where the maximum likelihood estimator does not necessarily give best results. Real data examples are shown using log-linear models for contingency tables. [ABSTRACT FROM AUTHOR]

To overcome multicollinearity, a new stochastic mixed Liu estimator is presented and its efficiency is considered. We also compare the proposed estimators in the sense of matrix mean squared error criteria. Finally a numerical example and a simulation study are given to show the performance of the estimators. [ABSTRACT FROM AUTHOR]

When there is an outlier in the data set, the efficiency of traditional methods decreases. In order to solve this problem, Kadilar et al. (2007) adapted Huber-M method which is only one of robust regression methods to ratio-type estimators and decreased the effect of outlier problem. In this study, new ratio-type estimators are proposed by considering Tukey-M, Hampel M, Huber MM, LTS, LMS and LAD robust methods based on the Kadilar et al. (2007). Theoretically, we obtain the mean square error (MSE) for these estimators. We compared with MSE values of proposed estimators and MSE values of estimators based on Huber-M and OLS methods. As a result of these comparisons, we observed that our proposed estimators give more efficient results than both Huber M approach which was proposed by Kadilar et al. (2007) and OLS approach. Also, under all conditions, all of the other proposed estimators except Lad method are more efficient than robust estimators proposed by Kadilar et al. (2007). And, these theoretical results are supported with the aid of a numerical example and simulation by basing on data that includes an outlier. [ABSTRACT FROM AUTHOR]