Preliminary Estimator Research Articles

A new approach for estimating variance of a population employing information obtained from a stratified random sampling

In this article, we suggest an enhanced estimator for the estimation of finite population variance using twofold auxiliary variable under stratified random sampling. The numerical expressions for the bias and MSE are determined up to the first order of approximation. In order to effectively validate the theoretical findings, three actual data sets are included. Additionally, the application of the suggested estimators is demonstrated using a simulation study. Results of an empirical comparison among the suggested and existing estimators were investigated. To determine how good the suggested estimator, in comparison to the preliminary estimators, the MSE criterion is used. The suggested estimator has a smaller MSE and better PRE than existing estimators, according to numerical results utilizing actual data sets and a simulation analysis.

James-Stein type estimators in beta regression model: simulation and application

Recently, the beta regression model has been used in several fields of science to model data in the form of rate or proportion. In this paper, some novel and improved methods to estimate parameters in the beta regression model are proposed. We consider a sub-space on the regression coefficients of the beta regression model and combine the unrestricted and restricted estimators then we present Stein-type and preliminary estimators. We develop the expressions for the proposed estimators' asymptotic biases and their quadratic risks. Numerical studies through Monte Carlo simulations are used to evaluate the performance of the proposed estimators in terms of their simulated relative efficiency. The results show that the proposed estimators outperform the unrestricted estimator when the restrictions hold. Finally, an empirical application is given to show how useful the proposed estimators are in the practical area.

Robust estimation for functional quadratic regression models

Functional quadratic regression models postulate a polynomial relationship rather than a linear one between a scalar response and a functional covariate. As in functional linear regression, vertical and especially high–leverage outliers may affect the classical estimators. For that reason, providing reliable estimators in such situations is an important issue. Taking into account that the functional polynomial model is equivalent to a regression model that is a polynomial of the same order in the functional principal component scores of the predictor processes, our proposal combines robust estimators of the principal directions with robust regression estimators based on a bounded loss function and a preliminary residual scale estimator. Fisher–consistency of the proposed method is derived under mild assumptions. Consistency, asymptotic robustness as well as an expression for the influence function of the related functionals are derived when the covariates have a finite–dimensional expansion. The results of a numerical study show the benefits of the robust proposal over the one based on sample principal directions and least squares for the considered contaminating scenarios. The usefulness of the proposed approach is also illustrated through the analysis of a real data set which reveals that when the potential outliers are removed the classical method behaves very similarly to the robust one computed with all the data.

A simulation study: An enhanced generalized class of estimators for estimation of population proportion using twofold auxiliary attribute

The article introduces a novel class of estimators designed for estimating finite population proportions. These estimators utilize dual auxiliary attributes and are applicable under simple random sampling. The proposed class of estimators includes various members with distinct characteristics. The article provides numerical terminologies for the bias and MSE of the estimators, acquire up to first order of approximation. Four actual data sets are used. Additionally, a simulation study is accompanied to perceive the presentations of estimators. The MSE criterion is used to assess how well the proposed estimator performed as likened to the preliminary estimators. The simulation analysis revealed that, in contrast to other examined estimators, the suggested class of estimators provided better results. The empirical investigation offers evidence to substantiate the findings of the argument. Theoretical research also displays that the suggested class of estimators outperforms its competitors.

Optimal stable Ornstein–Uhlenbeck regression

We prove asymptotically efficient inference results concerning an Ornstein–Uhlenbeck regression model driven by a non-Gaussian stable Lévy process, where the output process is observed at high frequency over a fixed period. The local asymptotics of non-ergodic type for the likelihood function is presented, followed by a way to construct an asymptotically efficient estimator through a suboptimal, yet very simple preliminary estimator.

A Generalized Approach for Estimation of a Finite Population Mean in Two-Phase Sampling

The present paper deals with the formulation of a generalized class of ratio-cum-product estimators for the estimation of a finite population mean in two-phase sampling. The mathematical expressions for the mean square errors (MSEs) of the preliminary and proposed estimators are derived. It has been established that the proposed class encompasses a wide range of estimators for specific choices of the scalars. The relative performance of the proposed class, as compared to the preliminary estimators, is evaluated using the MSE criterion. In addition, optimum sample sizes of the first-phase and second-phase samples are obtained using a specified cost function. The theoretical findings are empirically assessed by computing MSEs and percent relative efficiencies (PREs) of various estimators based on real population datasets. The findings of the study reveal that the proposed class of estimators are superior as compared to the preliminary estimators for the estimation of mean.

Adaptive Kalman filtration for low noise systems

Kalman filter identification problem is considered in the situation of low noise in observations. This model of observations is widely used in trafic management Antoniou et al. (2010). The proposed procedure consists of several steps. First a preliminary consistent estimator is constructed on the vanishing learning interval. Then this estimator is used to define One-step MLE-process and finally this estimator-process is used for approximation of the unobserved state. It is shown that the estimate thus obtained is consistent, asymptotically Gaussian, and asymptotically efficient. As a result, it is possible to implement a high-speed algorithm for filtering an information process with unknown parameters, which provides good accuracy characteristics.

Approximation of BSDE with hidden forward equation and unknown volatility

The focus is on the approximation of the solution of BSDE in the case where the solution of forward equation is observed in the presence of small Gaussian noise. The volatility of the forward equation is considered to depend on some unknown parameter. This approximation is made in several steps. First a preliminary estimator of the unknown volatility is obtained, then using Kalman-Bucy filtration equations and Fisher-score device one-step MLE-process of this parameter is constructed. The solution of BSDE is approximated by means of the solution of PDE and the One-step MLE-process. The error of approximation is described in different metrics.

Preliminary Test Regression Estimator in Double Sampling Based on Two-Stage and Ranked Set Sampling with Two Auxiliary Variables

Preliminary Test Regression Estimator in Double Sampling Based on Two-Stage and Ranked Set Sampling with Two Auxiliary Variables

A presmoothing approach for estimation in the semiparametric Cox mixture cure model

A challenge when dealing with survival analysis data is accounting for a cure fraction, meaning that some subjects will never experience the event of interest. Mixture cure models have been frequently used to estimate both the probability of being cured and the time to event for the susceptible subjects, by usually assuming a parametric (logistic) form of the incidence. We propose a new estimation procedure for a parametric cure rate that relies on a preliminary smooth estimator and is independent of the model assumed for the latency. On a second stage one can assume a semiparametric model for the latency and estimate also the survival distribution of the uncured subject. For the particular case of the logistic/Cox model, we investigate the theoretical properties of the estimators and show through simulations that presmoothing leads to more accurate results compared to the maximum likelihood estimator. To illustrate the practical use, we apply the new estimation procedure to two studies of melanoma survival data.

Liu-type shrinkage strategies in zero-inflated negative binomial models with application to Expenditure and Default Data

In modeling count data with overdispersion and extra zeros, zero-inflated negative binomial (ZINB) regression model is useful. In a regression model, the multicollinearity problem arises when there are some high correlations between predictor variables. This problem leads to the maximum likelihood method will not be an efficient estimator. The ridge and Liu-type estimators have been proposed to combat the multicollinearity problem so that the Liu-type estimator is better. In this paper, we proposed the Liu-type shrinkage estimators, namely linear shrinkage, preliminary test, shrinkage preliminary test, Stein-type, and positive Stein-type Liu estimators to estimate the count parameters in the ZINB model, when some of the predictor variables have not a significant effect to predict the response variable so that a sub-model may be sufficient. The asymptotic distributional biases and variances of the proposed estimators are nicely demonstrated. We also compared the performance of the Liu-type shrinkage estimators along with the Liu-type unrestricted estimator by using an extensive Monte Carlo simulation study. The results show that the performances of the proposed estimators are superior to those based on Liu-type unrestricted estimators. We also applied the proposed estimation methods to Expenditure and Default Data.

Hazard Ratio and Hazard Index as Preliminary Estimators Associated to the Presence of Furans and Alkylfurans in Belgian Foodstuffs.

This paper provides an estimation of the hazard related to the presence of furan and five alkyl furans (2- and 3-methylfuran, 2-ethylfuran, 2,5- and 2,3-dimethylfuran) in foodstuffs available in the Belgian market. To achieve this objective, a specific sampling plan was designed to ensure that the samples collected (n = 1003) represent the diversity of the Belgian food chain. Herein, the concepts of the Hazard Ratio of a sample (HRs) and the Hazard Index of a sample (HIs) were introduced to primarily characterize the hazard related to the co-occurrence of these compounds. The HRs was measured as the ratio of the potential daily exposure to a substance (expressed in mg/Kg of food) to both the 10% reference dose level for chronic effects (expressed in mg/(kg b.w*day)) and the human standard weight (expressed in kg). Whereas the HIs is the sum of the HRs of compounds that affect the same target organ/system, a hazard index greater than one indicates a highly contaminated matrix that could induce a hazard. It is an alarm indicating that additional attention should be given to this matrix. This may involve additional analyses to confirm the high level, to identify sources, etc. It is also an alarm for the risk assessor to be very careful with flagged matrices and to avoid combination with other matrices. The HIs highlight a relatively low concern for all foods analyzed (HI median < 1.0) with a relatively higher suspected hazard for coffee drinks (HI median = 0.068, HI max = 0.57). This preliminary estimation of the potential hazard suggests that coffee beverages should be examined in more detail in a full risk assessment and that coffee consumption should be taken with caution given the levels of furan and alkylfurans reported in this study.

Mendelian randomization mixed-scale treatment effect robust identification and estimation for causal inference.

Standard Mendelian randomization (MR) analysis can produce biased results if the genetic variant defining an instrumental variable (IV) is confounded and/or has a horizontal pleiotropic effect on the outcome of interest not mediated by the treatment variable. We provide novel identification conditions for the causal effect of a treatment in the presence of unmeasured confounding by leveraging a possibly invalid IV for which both the IV independence and exclusion restriction assumptions may be violated. The proposed Mendelian randomization mixed-scale treatment effect robust identification (MR MiSTERI) approach relies on (i) an assumption that the treatment effect does not vary with the possibly invalid IV on the additive scale; (ii) that the confounding bias does not vary with the possibly invalid IV on the odds ratio scale; and (iii) that the residual variance for the outcome is heteroskedastic with respect to the possibly invalid IV. Although assumptions (i) and (ii) have, respectively, appeared in the IV literature, assumption (iii) has not; we formally establish that their conjunction can identify a causal effect even with an invalid IV. MR MiSTERI is shown to be particularly advantageous in the presence of pervasive heterogeneity of pleiotropic effects on the additive scale. We propose a simple and consistent three-stage estimator that can be used as a preliminary estimator to a carefully constructed efficient one-step-update estimator. In order to incorporate multiple, possibly correlated, and weak invalid IVs, a common challenge in MR studies, we develop a MAny Weak Invalid Instruments (MR MaWII MiSTERI) approach for strengthened identification and improved estimation accuracy. Both simulation studies and UK Biobank data analysis results demonstrate the robustness of the proposed methods.

A robust deterministic affine-equivariant algorithm for multivariate location and scatter

A new computationally feasible algorithm for the Minimum Covariance Determinant (MCD) estimator is proposed. The resulting estimator is deterministic, affine equivariant and permutation invariant unlike prominent alternatives. The new procedure, referred to as Projection Pursuit MCD, combines a single preliminary estimator obtained with a type of non-linear principal component analysis and the so-called concentration step (C-step). Fixed points of the C-step are proved to be local minimizers of the covariance determinant objective. Extensive comparisons for simulated datasets, multivariate Swiss banknote and image segmentation examples show the new algorithm is competitive with and mostly superior to such state-of-the-art procedures as FastMCD and DetMCD for both Gaussian and heavy-tailed real-world data. Outlier detection for Swiss banknote and image segmentation data is presented. A corresponding R package is provided.

Liu-type shrinkage estimations in linear models

In this study, we present the preliminary test, Stein-type and positive part Stein-type Liu estimators in the linear models when the parameter vector is partitioned into two parts, namely, the main effects and the nuisance effects such that . We consider the case that a priori known or suspected set of the explanatory variables do not contribute to predict the response so that a sub-model may be enough for this purpose. Thus, the main interest is to estimate when is close to zero. Therefore, we investigate the performance of the suggested estimators asymptotically and via a Monte Carlo simulation study. Moreover, we present a real data example to evaluate the relative efficiency of the suggested estimators, where we demonstrate the superiority of the proposed estimators.

Prediction of mean wave overtopping at simple sloped breakwaters using kernel-based methods

Abstract The accurate prediction of the mean wave overtopping rate at breakwaters is vital for a safe design. Hence, providing a robust tool as a preliminary estimator can be useful for practitioners. Recently, soft computing tools such as artificial neural networks (ANN) have been developed as alternatives to traditional overtopping formulae. The goal of this paper is to assess the capabilities of two kernel-based methods, namely Gaussian process regression (GPR) and support vector regression for the prediction of mean wave overtopping rate at sloped breakwaters. An extensive dataset taken from the EurOtop database, including rubble mound structures with permeable core, straight slopes, without berm, and crown wall, was employed to develop the models. Different combinations of the important dimensionless parameters representing structural features and wave conditions were tested based on the sensitivity analysis for developing the models. The obtained results were compared with those of the ANN model and the existing empirical formulae. The modified Taylor diagram was used to compare the models graphically. The results showed the superiority of kernel-based models, especially the GPR model over the ANN model and empirical formulae. In addition, the optimal input combination was introduced based on accuracy and the number of input parameters criteria. Finally, the physical consistencies of developed models were investigated, the results of which demonstrated the reliability of kernel-based models in terms of delivering physics of overtopping phenomenon.

Robust penalized spline estimation with difference penalties

Penalized spline estimation with discrete difference penalties (P-splines) is a popular estimation method for semiparametric models, but the classical least-squares estimator is highly sensitive to deviations from its ideal model assumptions. To remedy this deficiency, a broad class of P-spline estimators based on general loss functions is introduced and studied. Robust estimators are obtained by well-chosen loss functions, such as the Huber or Tukey loss function. A preliminary scale estimator can also be included in the loss function. It is shown that this class of P-spline estimators enjoys the same optimal asymptotic properties as least-squares P-splines, thereby providing strong theoretical motivation for its use. The proposed estimators may be computed very efficiently through a simple adaptation of well-established iterative least squares algorithms and exhibit excellent performance even in finite samples, as evidenced by a numerical study and a real-data example.

Development of Preliminary Test Estimators and Confidence Interval for the Reliability Characteristics of Generalized Inverted Scale Family of Distribution based on Records

Development of Preliminary Test Estimators and Confidence Interval for the Reliability Characteristics of Generalized Inverted Scale Family of Distribution based on Records

Employ shrinkage technique during estimate normal distribution mean

The preliminary test shrinkage estimator for estimating the mean (α) of normal distribution was presented in this article when a prior guess (α0) of the actual (α) on hand using shrinkage weight factor Ψ(·) in addition to pretest region (R). Equations for Bias, Mean Squared Error and Relative Efficiency for the recommended estimator were resulting. Statistical outcome and discussions were drawn about collection different (constant) including in previous equations. Comparisons between optional estimator with usual and some existing works were given based on Bias and relative efficiency. Finally, the conclusions in this context are displayed.

Estimation and inference for policy relevant treatment effects

The policy relevant treatment effect (PRTE) measures the average effect of switching from a status-quo policy to a counterfactual policy under consideration. Estimation of the PRTE involves estimation of multiple preliminary parameters, including propensity scores, conditional expectation functions of the outcome and covariates given the propensity score, and marginal treatment effects. These preliminary estimators can affect the asymptotic distribution of the PRTE estimator in complicated and intractable manners. In this light, we propose an orthogonal score for double debiased estimation of the PRTE, whereby the asymptotic distribution of the PRTE estimator is obtained without any influence of preliminary parameter estimators as far as they satisfy mild requirements of convergence rates. To our knowledge, this paper is the first to develop limit distribution theories for inference about the PRTE.