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The study attempts to investigate the dynamic relationship between acreage allocation of oilseeds and price (own price and prices of competitive crops) and also search for the link between area allocation and other non-price factors including productivity, irrigation, rainfall, technology and a policy-making variable (economic liberalization). The dynamic panel data for the year 1976-77 to 2017-18 have been used in the analysis. The study has used the autoregressive distributive lag (ARDL) model to understand the relationship between the dependent and the independent variables and to investigate the long-run equilibrium relationship between them. To estimate the model, both PMG (Pooled Mean Group) and MG (Mean group) estimation methods have been used. The Hausman test has been conducted to see the difference between the PMG and the MG results. The outcomes show that PMG serves as an efficient estimator here. The error correction terms are negative and significant. The results show strong evidence of area allocation towards oilseed crops, indicate a strong co-integration among their determinants in the long run. The ARDL results indicate that the speed of adjustment towards long-run equilibrium varies from 14.8 to 40.6 percent.

To deal with multicollinearity problem, the biased estimators with two biasing parameters have recently attracted much research interest. The aim of this article is to compare one of the last proposals given by Yang and Chang (2010) with Liu-type estimator (Liu 2003) and k − d class estimator (Sakallioglu and Kaciranlar 2008) under the matrix mean squared error criterion. As well as giving these comparisons theoretically, we support the results with the extended simulation studies and real data example, which show the advantages of the proposal given by Yang and Chang (2010) over the other proposals with increasing multicollinearity level.

We introduce a robust estimator of the location parameter for the change-point in the mean based on Wilcoxon statistic and establish its consistency for L1 near-epoch dependent processes. It is shown that the consistency rate depends on the magnitude of the change. A simulation study is performed to evaluate the finite sample properties of the Wilcoxon-type estimator under Gaussianity as well as under heavy-tailed distributions and disturbances by outliers, and to compare it with a CUSUM-type estimator. It shows that the Wilcoxon-type estimator is equivalent to the CUSUM-type estimator under Gaussianity but outperforms it in the presence of heavy tails or outliers in the data.

In this paper, we proposed an alternative stochastic restricted Liu-type estimator β^SRLTE for the vector of parameters in a linear regression model. The new estimator is a combination of ordinary mixed estimator β^OME and Liu-Type estimator β^LTE, which was proposed by Liu. Necessary and sufficient conditions for the superiority of new stochastic restricted Liu-type estimator β^SRLTE over the ordinary mixed estimator β^OME and the Liu-type estimator β^LTE in the mean squared error matrix sense are derived for the two cases in which the parametric restrictions are correct and are not correct. In particular, we showed that β^SRLTE was superior in the mean squared error matrix sense over both β^OME and to the Liu-type estimator introduced by Liu (2003).

Survival functions are often estimated by nonparametric estimators such as the Kaplan-Meier estimator. For valid estimation, proper adjustment for confounding factors is needed when treatment assignment may depend on confounding factors. Inverse probability weighting is a commonly used approach, especially when there is a large number of potential confounders to adjust for. Direct adjustment may also be used if the relationship between the time-to-event and all confounders can be modeled. However, either approach requires a correctly specified model for the relationship between confounders and treatment allocation or between confounders and the time-to-event. We propose a pseudo-observation-based doubly robust estimator, which is valid when either the treatment allocation model or the time-to-event model is correctly specified and is generally more efficient than the inverse probability weighting approach. The approach can be easily implemented using standard software. A simulation study was conducted to evaluate this approach under a number of scenarios, and the results are presented and discussed. The results confirm robustness and efficiency of the proposed approach. A real data example is also provided for illustration.

In this paper, we provide the proof of nonexistence of the James–Stein estimator in the whole parameter space for normal random matrices, equivalently, for multivariate linear regression models, which solves the open problem raised by S.F. Arnold [1] . By introducing the concepts of left and right James–Stein estimators, we obtain the left James–Stein estimator of mean matrix and show that the left James–Stein estimator has minimaxity and optimality in terms of the Efron–Morris type modification. We construct a new minimax combination estimator with lower risk by absorbing the advantages of the left James–Stein estimator and the existing modified Stein estimator. Risk comparisons through finite sample simulation studies illustrate that the proposed combination estimator has a better performance, under the mean-squared error or l 2 risk, compared with all existing estimators.

We study the efficient estimation procedure of a new single-index model which can reflect the time-dynamic effects for longitudinal covariates. We propose a efficient estimator of the single-index parameter by using a feasible bias-corrected generalized estimating equation. In order to achieve this goal, we use the working independence estimator as an initial estimation, and then a non parametric smoothing technique is used to model the covariance matrix. With appropriate initial estimates of the parametric index, the proposed estimators are shown to be -consistent and asymptotically normally distributed, and the two-stage estimator is shown to be more efficient than the first-stage estimator. We also address the non parametric estimation of regression functions and provide estimates with optimal convergence rates. The finite-sample properties of the estimator are illustrated by some simulation examples, as well as a real data application.

This paper discusses the parameter estimation in a partially linear model. We proposed a difference-based Liu-type estimator of the unknown parameters in the partially linear model. The asymptotically properties of the proposed estimator are discussed. We propose a iterative method to choose the biasing parameters. Finally, a simulation study and a numerical example are presented to explain the performance of the estimators.

A new estimator for estimating the proportion of a potentially sensitive attribute in survey sampling has been introduced by solving a linear equation. The proposed estimator has been compared with the estimator proposed by Odumade and Singh (2009) with equal protection to all of the respondents. The asymptotic properties of the proposed estimator are investigated through exact numerical illustrations for different choices of parameters. A non randomized response approach has been suggested. A scope for further research has also been pointed out.

A preliminary test double sampling regression estimator (PTDSRE) in finite survey sampling has been developed when the prior value of the correlation coefficient between a study variable and an auxiliary variable is available. The PTDSRE has been found to be the unbiased estimator of population mean. Its variance has been derived. Numerical findings showed that PTDSRE has outperformed the usual double sampling difference and regression estimators.

This study proposes a more efficient calibration estimator for estimating population mean in stratified double sampling using new calibration weights. The variance of the proposed calibration estimator has been derived under large sample approximation. Calibration asymptotic optimum estimator (CAOE) and its approximate variance estimator are derived for the proposed calibration estimator and existing calibration estimators in stratified double sampling. Analytical results showed that the proposed calibration estimator is more efficient than existing members of its class in stratified double sampling. Analysis and evaluation are presented.

In this paper, we are proposing a modified jackknife Liu-type estimator (MJLTE) that was created by combining the ideas underlying both the Liu-type estimator (LTE) and the jackknifed Liu-t...

We explore the standard life table (actuarial) estimator for grouped right-censored survival data and its extensions in order to consider its relationship with the Kaplan–Meier estimator, and to investigate the critical properties of the extended life table estimators (ELTEs). We discuss certain conditions for the ELTE to be consistent and develop a characterization of the standard life table estimator using the consistency property under any choice of at least two observation times of a finite interval. We also perform a comparative analysis of the ELTEs with the corresponding maximum likelihood estimators for grouped right-censored survival data.

This article proposes an alternative to usual ratio estimator of population mean in post-stratified sampling procedure and its properties are analyzed. Both theoretical and empirical findings are encouraging and support the soundness of the proposed procedure for mean estimation over an alternative to ratio estimator in simple random sampling without replacement suggested by Srivenkataramana and Tracy (1980), usual combined ratio estimators suggested by Ige and Tripathi (1989), and usual unbiased estimator in post-stratified sampling scheme. Both theoretical and empirical findings are encouraging and support the soundness of the present study. At the end, a simulation study has been carried out to verify the superiority of the proposed estimator.

SYNOPTIC ABSTRACTThe problem of estimating the common scale parameter of two gamma populations has been considered when the shape parameters are unknown and possibly different. The performance of an estimator is evaluated using both bias and mean squared error. The maximum likelihood estimator (MLE) has been obtained numerically using the Monte-Carlo simulation, as the closed form does not exist. The Fisher information matrix has been obtained for our model and, consequently, asymptotic confidence intervals have been constructed. Certain Bayes estimators, using various priors, have been obtained. Like the MLE, the closed form of these Bayes estimators does not exist. An approximation due to Lindley (1980) has been used to obtain these Bayes estimators approximately. Finally, the bias and the mean squared error of all these estimators have been numerically compared through the Monte-Carlo simulation method.

This paper gives simple and intuitive derivations of three equivalent forms of a distribution-free and unbiased estimator of the squared covariance matrix Σ 2 . Particularly, computationally efficient forms of the unbiased estimators of Σ 2 and its trace are derived from the computationally intensive U-statistic forms.

The analysis of (approximately) periodic signals is an importantelement in numerous applications. One generalization of standardperiodic signals often occurring in practice are harmonic chirpsignals where the instantaneous frequency increases/decreases linearlyas a function of time. A statistically efficient estimator forextracting the parameters of the harmonic chirp model in additivewhite Gaussian noise is the maximum likelihood (ML) estimator whichrecently has been demonstrated to be robust to noise and accurate ---even when the model order is unknown. The main drawback of the MLestimator is that only very computationally demanding algorithms forcomputing an estimate are known. In this paper, we give an algorithmfor computing an estimate to the ML estimator for a number ofcandidate model orders with a much lower computational complexity thanpreviously reported in the literature. The lower computationalcomplexity is achieved by exploiting recursive matrix structures,including a block Toeplitz-plus-Hankel structure, the fast Fouriertransform, and using a two-step approach composed of a grid andrefinement step to reduce the number of required functionevaluations. The proposed algorithms are assessed via Monte Carlo andtiming studies. The timing studies show that the proposed algorithm isorders of magnitude faster than a recently proposed algorithm forpractical sizes of the number of harmonics and the length of thesignal.

We propose a new estimator for the population proportion using a concomitant-based ranked set sampling (RSS) scheme. Simulation results show that the new estimator beats the standard estimator in the RSS as long as the ranking quality is fairly good.

Summary Retrospectively measuring markers on stored baseline samples from participants in a randomized controlled trial (RCT) may provide high quality evidence as to the value of the markers for treatment selection. Originally developed for approximating gene-environment interactions in the odds ratio scale, the case-only method has recently been advocated for assessing gene-treatment interactions on rare disease endpoints in randomized clinical trials. In this article, the case-only approach is shown to provide a consistent and efficient estimator of marker by treatment interactions and marker-specific treatment effects on the relative risk scale. The prohibitive rare-disease assumption is no longer needed, broadening the utility of the case-only approach. The case-only method is resource-efficient as markers only need to be measured in cases only. It eliminates the need to model the marker's main effect, and can be used with any parametric or nonparametric learning method. The utility of this approach is illustrated by an application to genetic data in the Women's Health Initiative (WHI) hormone therapy trial.

This paper considers the problem of estimating the population variance S2y of the study variable y using the auxiliary information in sample surveys. We have suggested the (i) chain ratio-type estimator (on the lines of Kadilar and Cingi (2003)), (ii) chain ratio-ratio-type exponential estimator and their generalized version [on the lines of Singh and Pal (2015)] and studied their properties under large sample approximation. Conditions are obtained under which the proposed estimators are more efficient than usual unbiased estimator s2y and Isaki (1893) ratio estimator. Improved version of the suggested class of estimators is also given along with its properties. An empirical study is carried out in support of the present study.

In this paper, we introduce mixed Liu estimator (MLE) for the vector of parameters in linear measurement error models by unifying the sample and the prior information. The MLE is a generalization o...

Let π1, …, πk be k (⩾ 2) independent populations, where πi denotes the uniform distribution over the interval (0, θi) and θi > 0 (i = 1, …, k) is an unknown scale parameter. The population associat...

In this paper, the preliminary test approach to the estimation of the linear regression model with student's t errors is considered. The preliminary test almost unbiased two-parameter estimator is proposed, when it is suspected that the regression parameter may be restricted to a constraint. The quadratic biases and quadratic risks of the proposed estimators are derived and compared under both null and alternative hypotheses. The conditions of superiority of the proposed estimators for departure parameter and biasing parameters k and d are derived, respectively. Furthermore, a real data example and a Monte Carlo simulation study are provided to illustrate some of the theoretical results.

In this paper, we have considered an estimation of the population total Y of the study variable y, making use of information on an auxiliary variable x. A class of estimators for the population total Y using transformation on both the variables study as well as auxiliary has been suggested based on the probability proportional to size with replacement (PPSWR). In addition to many the usual PPS estimator, Reddy and Rao's (1977) estimator and Srivenkataramana and Tracy's (1979, 1984, 1986) estimators are shown to be members of the proposed class of estimators. The variance of the proposed class of estimators has been obtained. In particular, the properties of 75 estimators based on different known population parameters of the study as well as auxiliary variables have been derived from the proposed class of estimators. In support of the present study, numerical illustrations are given.

A generalized estimator is introduced for finite population mean in stratified random sampling when observations are contaminated with measurement errors. Many special cases of the proposed estimator are possible. The bias and mean square error of the proposed family of estimators are derived. The performance of the proposed estimator is evaluated both theoretically and empirically in the presence and absence of measurement error.

In this paper, we propose a new efficient estimator namely Optimal Generalized Logistic Estimator (OGLE) for estimating the parameter in a logistic regression model when there exists multicollinearity among explanatory variables. Asymptotic properties of the proposed estimator are also derived. The performance of the proposed estimator over the other existing estimators in respect of Scalar Mean Square Error criterion is examined by conducting a Monte Carlo simulation.

In this paper we propose a new difference-type estimator in estimating the finite population mean in stratified double sampling by using the ranks of two auxiliary variables as an additional information. The proposed estimator performs better than the usual sample mean estimator, ratio estimator, exponential estimator, Choudhury and Singh (2012) estimator, Vishwakarma and Gangele (2014) estimator, Singh and Khalid (2015) estimator, Khan and Al-Hossain (2016) estimator, Khan (2016) estimator and usual difference estimator. Two real data sets are used to observe the performances of estimators.

The principal objective of this paper is to estimate a nonlinear functional of state vector (NFS) in dynamical system. The NFS represents a multivariate functional of state variables which carries useful information of a target system for control. The paper focuses on estimation of the NFS in linear continuous-discrete systems. The optimal nonlinear estimator based on the minimum mean square error approach is derived. The estimator depends on the Kalman estimate of a state vector and its error covariance. Some challenging computational aspects of the optimal nonlinear estimator are solved by usage of the unscented transformation for implementation of the nonlinear estimator. The special quadratic functional of state vector (QFS) is studied in detail. We derive effective matrix formulas for the optimal quadratic estimator and mean square error. The quadratic estimator has a simple closed-form calculation procedure and it is easy to implement in practice. The obtained results we demonstrate on theoretical and practical examples with different types of an nonlinear functionals. Comparison analysis of the optimal and suboptimal estimators is presented. The subsequent application of the proposed optimal nonlinear and quadratic estimators demonstrates their effectiveness.

This article considers some different parameter estimation methods in logistic regression model. In order to overcome multicollinearity, the almost unbiased ridge-type principal component estimator...

The multivariate Bayesian hierarchical model with independent means has been studied extensively and is widely used in practice. In contrast, the case of dependent means has received scant attention, even though multivariate observations are often correlated. In this paper, we investigate a multivariate heteroscedastic Bayesian hierarchical model in which an informative prior with equicorrelated means is assumed. We estimate the mean vector by the shrinkage estimator based on Stein’s unbiased risk estimation (SURE). It is shown that the squared error loss of the SURE estimator is close to that of an oracle estimator as the number of means grows. Our SURE estimator includes the SURE estimator under independence considered by Xie et al. (2012) as a special case. The finite-sample performance of our estimator is explored via simulations and two real data sets are used for illustration purposes.

In estimating the parameters of the two-parameter Pareto distribution it is well known that the performance of the maximum likelihood estimator deteriorates when sample sizes are small or the underlying model is contaminated. In this paper we propose a new parameter estimator that utilizes a pivotal quantity based on the regression framework, allowing separate estimation of the two parameters in a straightforward manner. The consistency of the estimator is also established. Simulation studies show that the proposed estimator is a competitive, well-rounded robust estimator for both Pareto and contaminated Pareto datasets when the sample sizes are small.

We derive the asymptotic efficiency bound for regular estimates of the slope coefficient in a linear continuous-time regression model for the continuous martingale parts of two Ito semimartingales observed on a fixed time interval with asymptotically shrinking mesh of the observation grid. We further construct an estimator from high-frequency data that achieves this efficiency bound and, indeed, is adaptive to the presence of infinite-dimensional nuisance components. The estimator is formed by taking optimal weighted average of local nonparametric volatility estimates that are constructed over blocks of high-frequency observations. The asymptotic efficiency bound is derived under a Markov assumption for the bivariate process while the high-frequency estimator and its asymptotic properties are derived in a general Ito semimartingale setting. To study the asymptotic behavior of the proposed estimator, we introduce a general spatial localization procedure which extends known results on the estimation of integrated volatility functionals to more general classes of functions of volatility. Empirically relevant numerical examples illustrate that the proposed efficient estimator provides nontrivial improvement over alternatives in the extant literature.

For GSTAR models, the least squares estimation method is commonly used since errors are assumed be uncorrelated. However, this method is not appropriate when errors are correlated, either in time or spatially. For these cases, the generalized least squares (GLS) method can be applied. GLS is more powerful since it has an error parameter that can act as a controller of the model to produce an efficient estimator. In this study, R Software was used to estimate GSTAR parameters. The resulted model was applied to real data, i.e. the monthly tea production of five plantations in West Java, Indonesia. The best model for forecasting was the GSTAR(1;1) model with temporally correlated error assumption.

In this article, we present the wald_mse command, which computes the maximum mean squared error of a user-specified point estimator of the mean for a population of interest in the presence of missing data. As pointed out by Manski (1989, Journal of Human Resources 24: 343–360; 2007, Journal of Econometrics 139: 105–115), the presence of missing data results in the loss of point identification of the mean unless one is willing to make strong assumptions about the nature of the missing data. Despite this, decision makers may be interested in reporting a single number as their estimate of the mean as opposed to an estimate of the identified set. It is not obvious which estimator of the mean is best suited to this task, and there may not exist a universally best choice in all settings. To evaluate the performance of a given point estimator of the mean, wald_mse allows the decision maker to compute the maximum mean squared error of an arbitrary estimator under a flexible specification of the missing-data process.

We consider efficient estimation of panel data models with interactive effects, which relies on a high-dimensional inverse covariance matrix estimator. By using a consistent estimator of the error covariance matrix, we can take into account both cross-sectional correlations and heteroskedasticity. In the presence of cross-sectional correlations, the proposed estimator eliminates the cross-sectional correlation bias, and is more efficient than the existing methods. The rate of convergence is also improved. In addition, we find that when the statistical inference involves estimating a high-dimensional inverse covariance matrix, the minimax convergence rate on large covariance estimations is not sufficient for inferences. To address this issue, a new “doubly weighted convergence” result is developed. The proposed method is applied to the US divorce rate data. We find that our more efficient estimator identifies the significant effects of divorce-law reforms on the divorce rate, and provides tighter confidence intervals than existing methods. This provides a confirmation for the empirical findings of Wolfers (2006) under more general unobserved heterogeneity.

In this study an improved version of ratio type exponential estimator is been proposed for estimating average of study variable when the population parameter(s) information of second auxiliary variable is available. The proposed estimator compared with usual unbiased estimator and conventional ratio estimators numerically and hypothetically. The mean square error is also obtained and checked the efficiency of the proposed estimator with usual ratio, Singh and Vishwakarma (2007), Singh et al. (2008), Noor-ul-Amin and Hanif (2012), Yadav et al. (2013) and Sanaullah et al. (2015) estimators.

We treat a non parametric estimator for joint probability mass function, based on multivariate discrete associated kernels which are appropriated for multivariate count data of small and moderate s...

Survival data collected from a prevalent cohort are subject to left truncation and the analysis is challenging. Conditional approaches for left-truncated data could be inefficient as they ignore the information in the marginal likelihood of the truncation times. Length-biased sampling methods may improve the estimation efficiency but only when the underlying truncation time is uniform; otherwise, they may generate biased estimates. We propose a semiparametric method for left-truncated data under the Cox model with no parametric distributional assumption about the truncation times. Our approach is to make inference based on the conditional likelihood augmented with a pairwise likelihood, which eliminates the truncation distribution, yet retains the information about the regression coefficients and the baseline hazard function in the marginal likelihood. An iterative algorithm is provided to solve for the regression coefficients and the baseline hazard function simultaneously. By empirical process and U-process theories, it has been shown that the proposed estimator is consistent and asymptotically normal with a closed-form consistent variance estimator. Simulation studies show substantial efficiency gain of our estimator in both the regression coefficients and the cumulative baseline hazard function over the conditional approach estimator. When the uniform truncation assumption holds, our estimator enjoys smaller biases and efficiency comparable to that of the full maximum likelihood estimator. An application to the analysis of a chronic kidney disease cohort study illustrates the utility of the method.

In the linear regression model with elliptical errors, a shrinkage ridge estimator is proposed. In this regard, the restricted ridge regression estimator under sub-space restriction is improved by incorporating a general function which satisfies Taylor’s series expansion. Approximate quadratic risk function of the proposed shrinkage ridge estimator is evaluated in the elliptical regression model. A Monte Carlo simulation study and analysis based on a real data example are considered for performance analysis. It is evident from the numerical results that the shrinkage ridge estimator performs better than both unrestricted and restricted estimators in the multivariate t-regression model, for some specific cases.

This paper discusses the problem of estimation of population mean in case of post-stratification. Improved ratio- and product-type exponential estimators of finite population mean are suggested with their case of post-stratification. Bias and mean-squared error of the suggested estimators are obtained up to the first degree of approximation. Suggested estimators have been compared with unbiased estimator, ratio estimator, and product estimator in case of post-stratification. An empirical study has been carried out to demonstrate the performance of the suggested estimator.

The focused information criterion for model selection is constructed to select the model that best estimates a particular quantity of interest, the focus, in terms of mean squared error. We extend this focused selection process to the high-dimensional regression setting with potentially a larger number of parameters than the size of the sample. We distinguish two cases: (i) the case where the considered submodel is of low dimension and (ii) the case where it is of high dimension. In the former case, we obtain an alternative expression of the low-dimensional focused information criterion that can directly be applied. In the latter case, we use a desparsified estimator that allows us to derive the mean squared error of the focus estimator. We illustrate the performance of the high-dimensional focused information criterion with a numerical study and a real dataset.

Purpose The purpose of this paper is to compare various methods of estimation of P(X