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In multiple linear regression models, the explanatory variables should be uncorrelated within each other but this assumption is violated in most of the cases. Generally, ordinary least square (OLS) estimator produces larger variances when explanatory variables are highly multicollinear. So, in this paper, we propose some new ridge parameters under Bayesian perspective relative to different loss functions, using Tierney and Kadane (T-K) approximation technique to overcome the effect of multicollinearity. We conduct the simulation study to compare the performance of the proposed estimators with OLS estimator and ordinary ridge estimator with some available best ridge parameters using mean squared error as the performance evaluation criterion. A real application is also consider to show the superiority of proposed estimators against competitive estimators. Based on the results of simulation and real application, we conclude that Bayesian ridge parameter estimated under general entropy loss function is better as compared to the OLS estimator and ordinary ridge estimator, when explanatory variables are small. This statement is also true for larger explanatory variables with small sample size. While for larger sample sizes and explanatory variables, the ordinary ridge estimator with best ridge parameter gives the better performance as others. [ABSTRACT FROM AUTHOR]

This paper discusses new approaches to parameter estimation of gamma distribution based on representative points. In the first part, the existence and uniqueness of gamma mean squared error representative points (MSE-RPs) are discussed theoretically. In the second part, by comparing three types of representative points, we show that gamma MSE-RPs perform well in parameter estimation and simulation. The last part proposes a new Harrel–Davis sample standardization technique. Simulation studies reveal that the standardized samples can be used to improve estimation performance or generate MSE-RPs. In addition, a real data analysis illustrates that the proposed technique yields efficient estimates for gamma parameters. [ABSTRACT FROM AUTHOR]

In this paper, a new two-type parameter estimator is proposed. This estimator is a generalization of the new two parameter (NTP) estimator introduced by Yang and Chang, which includes the ordinary least squares (OLS), the generalized ridge (GR) and the generalized Liu (GL) estimators, as special cases. Here, the performance of this new estimator is, theoretically, investigated over the OLS, the GR, the GL and the NTP estimators in terms of mean squared error matrix criterion. Furthermore, the estimation of the biasing parameters is obtained to minimize the scalar mean squared error. In addition, a complementary algorithm is proposed for the estimator presented by Yang and Chang. As well, a numerical example is given and a simulation study is done. [ABSTRACT FROM AUTHOR]

In linear regression modeling, the presence of multicollinearity among the explanatory variables has undesirable effects on the maximum likelihood estimator (MLE). To overcome this effect, we proposed some new ridge parameters under Bayesian paradigm. Moreover, we also compare these ridge parameters with Bayesian approach under different loss functions. To access the performance of new ridge parameters, we conduct a Monte Carlo simulation study where mean squared error (MSE) is considered as an evaluation criterion. In addition, a real life example is also provided to assess the superiority of the proposed estimators on the basis of MSE and cross-validation approaches. The simulation and real application results show that the Bayesian ridge parameter estimated under Precautionary loss function is better as compared to the other loss functions as well as the MLE and ordinary ridge regression estimator. [ABSTRACT FROM AUTHOR]

This paper presents an estimation approach within the framework of uplink massive machine-type-communications (mMTC) that considers the energy limitations of the devices. We focus on a scenario where a group of sensors observe a set of parameters and send the measured information to a collector node (CN). The CN is responsible for estimating the original observations, which are spatially correlated and corrupted by measurement and quantization noise. Given the use of Gaussian sources, the minimum mean squared error (MSE) estimation is employed and, when considering temporal evolution, the use of Kalman filters is studied. Based on that, we propose a device selection strategy to reduce the number of active sensors and a quantization scheme with adjustable number of bits to minimize the overall payload. The set of selected sensors and quantization levels are, thus, designed to minimize the MSE. For a more realistic analysis, communication errors are also included by averaging the MSE over the error decoding probabilities. We evaluate the performance of our strategy in a practical mMTC system with synthetic and real databases. Simulation results show that the optimization of the payload and the set of active devices can reduce the power consumption without compromising the estimation accuracy. [ABSTRACT FROM AUTHOR]

In this article, we obtain maximum likelihood and Bayes estimates of the parameters, reliability and hazard functions for generalized Rayleigh distribution when progressive type-II censored sample is available. Bayes estimates are derived under three loss functions: squared error, LINEX and generalized entropy. It is assumed that the parameters have independent gamma prior distributions. The estimates cannot be obtained in closed form, and hence the method of Lindley's approximation is employed in obtaining the desired Bayes estimates. The highest posterior density credible intervals of the model parameters are computed using importance sampling procedure. Moreover, approximate confidence intervals are constructed based on the normal approximation to maximum likelihood estimate and log-transformed maximum likelihood estimate. In order to construct the asymptotic confidence interval of the reliability and hazard functions, it is required to find their variances. These are approximated by delta method. A numerical study is performed to compare the proposed estimates with respect to their average values and mean squared error using Monte Carlo simulations. Further, based on the asymptotic normality of the maximum likelihood estimates, we provide the coverage probabilities for some defined pivotal quantities for model parameters. Finally, a real life dataset is considered to compute the proposed estimates. [ABSTRACT FROM AUTHOR]

In ordinary ridge regression, the estimation of the ridge parameter is a significant topic. This article generalizes some different methods for estimating the ridge parameter by considering the work of Kibria (2003), Khalaf and Shukur (2005), Alkhamisi, Khalaf, and Shukur (2006), Alkhamisi and Shukur (2008) and Muniz et al. (2012) in generalized linear models. The superiority of these estimators are assessed by the estimated mean squared error via Monte Carlo simulation study and real data set where the response follows gamma distribution with log link function. In this simulation study, it is chosen to vary the degree of correlation, the sample size, the number of explanatory variables and the different shape parameter for gamma response. [ABSTRACT FROM AUTHOR]

Double sampling technique and control charts are used for predicting about unknown parameters of the big population and developing algorithms for imposing control over growth factor. This sampling procedure has two approaches like sub-sample and independent sample. Aim is to estimate mean filesize by both and to find out which approach is better in big data setup. Comparative mathematical tools used herein are mean squared error, confidence interval, relative confidence interval length measure and control charts of digital file-size for monitoring. Estimation strategies are proposed and confidence intervals are computed over multiple points of time. At each time, it was found that confidence intervals are catching the true values. First kind of approach (as case I) of double sampling found better than the second. A new simulation strategy is proposed who is observed efficient for comparison purpose. Single-valued simulated confidence intervals are obtained using the new simulation strategy and found covering the truth in its range. As an application of outcomes, control charts are developed to monitor the parametric growth over long duration. Upper and Lower control limits are drawn for business managers to keep a watch on digital file-size estimates whether their growth under control? Outcomes may be extended for reliability evaluation under discrete time domain. The content herein is a piece of thought, idea and analysis developed by deriving motivation from past references to handle big data using double sampling. Findings of the study can be used for developing software based monitoring system using process control charts for managers. [ABSTRACT FROM AUTHOR]

A fundamental issue in statistics is parameter estimation, where the first step is to select estimators under some measure of estimation error. The commonly used measure is the mean squared error, which is simple, intuitive and highly interpretable, but it has some drawbacks, often creating confusions in evaluating estimators. To solve these problems, we propose two invariance properties and the sufficiency principle as the prerequisite for any reasonable measure. Then, the mean relative entropy is established as an invariant measure of estimation error. [ABSTRACT FROM AUTHOR]

Generalized estimating equations are routinely utilized for the marginal analysis of longitudinal data. In order to obtain consistent regression parameter estimates, these estimating equations must be unbiased. However, when certain types of time-dependent covariates are presented, these equations can be biased unless the working independence structure is used. Unfortunately, regression parameter estimation can be very inefficient with this structure because not all valid moment conditions are incorporated within the corresponding equations. Therefore, approaches have been proposed to utilize all valid moment conditions. However, these approaches assume that the data analyst knows the type of time-dependent covariate, although this likely is not the case in practice. Whereas hypothesis testing has been used to determine covariate type, we propose a novel strategy to select a working covariate type in order to avoid potentially high type II error rates with these hypothesis testing procedures. Parameter estimates resulting from our proposed method are consistent and have overall improved mean squared error relative to hypothesis testing approaches. Existing and proposed methods are compared in a simulation study and application example. [ABSTRACT FROM AUTHOR]

In this note, we consider the problem of estimation of coefficient of dispersion of a study variable by making use of known value of the coefficient of dispersion of an auxiliary variable. We propose ratio and regression-type estimators. We derive expressions of bias and variance of the proposed estimators to the first order of approximation. The relative efficiencies of the ratio and regression-type estimators with respect to the naïve estimator are investigated through a simulation study. [ABSTRACT FROM AUTHOR]

The occurrence of nonresponse is very much plebeian in surveys, which troubles the analysis, and hence, an inappropriate inference is left out. To counterbalance the sour effects of the incompleteness, fresh imputation techniques have been proposed with the aid of multi-auxiliary variates for the estimation of population mean on successive waves. Properties of the proposed estimators have been elaborated, and they have been compared with the work of Priyanka et al. (2015). Detailed simulation study is carried out to substantiate the empirical and theoretical results. Several possible cases have been addressed in which nonresponse can occur. [ABSTRACT FROM AUTHOR]

This article addresses the problem of estimating the proportion πS of the population belonging to a sensitive group using optional randomized response technique in stratified sampling based on Mangat model that has proportional and Neyman allocation and larger gain in efficiency. Numerically, it is found that the suggested model is more efficient than Kim and Warde stratified randomized response model and Mangat model. [ABSTRACT FROM AUTHOR]

In the context of estimating regression coefficients of an ill-conditioned binary logistic regression model, we develop a new biased estimator having two parameters for estimating the regression vector parameter β when it is subjected to lie in the linear subspace restrictionHβ =h. The matrix mean squared error and mean squared error (MSE) functions of these newly defined estimators are derived. Moreover, a method to choose the two parameters is proposed. Then, the performance of the proposed estimator is compared to that of the restricted maximum likelihood estimator and some other existing estimators in the sense of MSE via a Monte Carlo simulation study. According to the simulation results, the performance of the estimators depends on the sample size, number of explanatory variables, and degree of correlation. The superiority region of our proposed estimator is identified based on the biasing parameters, numerically. It is concluded that the new estimator is superior to the others in most of the situations considered and it is recommended to the researchers. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of estimating a general parameter using information on an auxiliary variableX. We have suggested a class of exponential-type ratio estimators for the parameter and its properties are studied. It is identified that the estimators due to Upadhyaya et al. [Journal of Statistical Theory and Practice (2011), 5(2), 285–302] and Yadav and Kadilar [Revista Columbiana de Estadistica, (2013), 36(1), 145–152] are members of the proposed estimator. We have also shown that the suggested estimator is more efficient than the estimators of Upadhyaya et al. (2011) and Yadav and Kadilar (2013). Numerical illustration is provided in support of the present study. [ABSTRACT FROM AUTHOR]

We considered a sensor formation problem for target localization based on the time difference of arrival (TDOA) data. It is assumed that the target is located far off from the sensors while the sensors are relatively close to each other. The estimators of the target location expressed in terms of the spherical coordinates are found to be uncorrelated when the sensors are arranged in a concentric ring formation. The proposed optimal formation of sensors is in the concentric ring formation and is shown to change in accordance with sensors' angular positions with respect to the line-of-sight vector from the reference sensor to the target. The proposed optimal sensor formations are compared in the context of estimation accuracy both in theory and by numerical experiments. They are shown optimal in general through refined numerical experiments. [ABSTRACT FROM AUTHOR]

This article suggests the class of estimators of population mean of study variable using various parameters related to an auxiliary variable with its properties in simple random sampling. It has been identified that the some existing estimator/classes of estimators are members of suggested class. It has been found theoretically as well as empirically that the suggested class is better than the existing methods. [ABSTRACT FROM AUTHOR]

In this paper, we propose a parameter estimation method for the three-parameter lognormal distribution based on Type-II right censored data. In the proposed method, under mild conditions, the estimates always exist uniquely in the entire parameter space, and the estimators also have consistency over the entire parameter space. Through Monte Carlo simulations, we further show that the proposed method performs very well compared to a prominent method of estimation in terms of bias and root mean squared error (RMSE) in small-sample situations. Finally, two examples based on real data sets are presented for illustrating the proposed method. [ABSTRACT FROM AUTHOR]

This paper is concerned with the parameter estimation in partial linear model and we proposed a difference-based almost unbiased Liu estimator (DBAULE) for the vector ofβin partial linear model. Necessary and sufficient conditions for the DBAULE over the difference-based estimator and difference-based Liu estimator under the mean squared error sense are derived. Finally, a method is given to select the biasing parameter. A numerical example and a simulation study are given to explain the performance of the estimators. [ABSTRACT FROM PUBLISHER]

In the preset study, a new identifier system has been proposed for optimal model estimation of Solid Oxide Fuel Cell (SOFC) stacks. To afford an appropriate identification system, the voltage-current profile of the system has been considered. The main idea is to minimize the Mean Squared Error (MSE) value between the actual output voltage of the stack and the output value achieved by the proposed model. Here, the MSE minimization has been established based on a new improved metaheuristic technique, called Fractional-order Social Network Search algorithm. The main advantage of the proposed technique is that it provides better trade-off between the global optimum and local optimum values. After system designing, it has been implemented to a studied case and its results are put in comparison with several latest techniques with considering two scenarios. One scenario with constant pressure and variable temperature and one other scenario with constant pressure and variable temperature. Final results indicate that the presented identification system provides satisfying results against the other compared methods in optimum system identification of the SOFCs. • New model identification of Solid Oxide Fuel Cell (SOFC) stacks based on a new metaheuristic. • Fractional-order Social Network Search algorithm is used as the new metaheuristic technique. • Voltage-current profile of the system is considered for identification. • The idea is to minimize the MSE between the model output data and empirical data. [ABSTRACT FROM AUTHOR]

In this paper, we investigate threshold effects associated with the swapping of signal and noise subspaces in estimating signal parameters from compressed noisy data. The term threshold effect refers to a sharp departure of mean-squared error from the Cramér–Rao bound when the signal-to-noise ratio falls below a threshold SNR. In many cases, the threshold effect is caused by a subspace swap event, when the measured data (or its sample covariance) is better approximated by a subset of components of an orthogonal subspace than by the components of a signal subspace. We derive analytical lower bounds on the probability of a subspace swap in compressively measured noisy data in two canonical models: a first-order model and a second-order model. In the first-order model, the parameters to be estimated modulate the mean of a complex multivariate normal set of measurements. In the second-order model, the parameters modulate the covariance of complex multivariate measurements. In both cases, the probability bounds are tail probabilities of F-distributions, and they apply to any linear compression scheme. These lower bounds guide our understanding of threshold effects and performance breakdowns for parameter estimation using compression. In particular, they can be used to quantify the increase in threshold SNR as a function of a compression ratio C. We demonstrate numerically that this increase in threshold SNR is roughly 10\log10 \ C dB, which is consistent with the performance loss that one would expect when measurements in Gaussian noise are compressed by a factor C. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a new method of estimation for the parameters and quantiles of the three-parameter Weibull distribution based on Type-II right censored data. The method, based on a data transformation, overcomes the problem of unbounded likelihood. In the proposed method, under mild conditions, the estimates always exist uniquely, and the estimators are also consistent over the entire parameter space. Through Monte Carlo simulations, we further show that the proposed method of estimation performs well compared to some prominent methods in terms of bias and root mean squared error in small-sample situations. Finally, two real data sets are used to illustrate the proposed method of estimation. [ABSTRACT FROM PUBLISHER]

This paper suggested an alternative ratio-cum-product type class of estimators of population mean using exponentiation method in simple random sampling. Approximate bias and mean squared error formulae of the suggested class of estimators have been obtained up to the first order of approximation. Asymptotic optimum estimator in the suggested class of estimators has been obtained with its mean squared error formula. Regions of preferences have been obtained under which the suggested class of estimators has been better than the usual unbiased, ratio and product estimators and the estimators according to Singh and Agnihotri (2008). Some examples are cited with numerical study. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a neural tree classifier, called the convex objective function neural tree (COF-NT), which has a specialized perceptron at each node. The specialized perceptron is a single layer feed-forward perceptron which calculates the errors before the neuron’s non-linear activation function instead of after them. Thus, the network parameters are independent of non-linear activation functions, and subsequently, the objective function is a convex objective function. The solution can be easily obtained by solving a system of linear equations which will require less computational power than conventional iterative methods. During the training, the proposed neural tree classifier divides the training set into smaller subsets by adding new levels to the tree. Each child perceptron takes forward the task of training done by its parent perceptron on the superset of this subset. Thus, the training is done by a number of single layer perceptrons (each perceptron carrying forward the work done by its ancestors) that reach the global minima in a finite number of steps. The proposed algorithm has been tested on available benchmark datasets and the results are promising in terms of classification accuracy and training time. [ABSTRACT FROM AUTHOR]

This article suggests an improved class of estimators for estimating the general population parameter using information on an auxiliary variable. The properties of the suggested class of estimators have been studied under large sample approximation. The general results are then applied to estimate the population coefficient of variation of study variable using auxiliary information. An empirical study is given in support of the theoretical results. [ABSTRACT FROM PUBLISHER]

Motivated from analysis of positive data such as income, revenue, harvests and production, the paper suggests the parametric transformed Fay–Herriot model in small-area estimation. When the dual power transformation is used as the parametric transformation, we provide consistent estimators of the transformation parameter, the regression coefficients and the variance component. The empirical best linear unbiased predictors which plug in those consistent estimators are suggested, and their mean squared errors (MSE) are asymptotically evaluated. A second-order unbiased estimator of the MSE is also given through the parametric bootstrap. Finally, performances of the suggested procedures are investigated through simulation and empirical studies. [ABSTRACT FROM AUTHOR]

This work is devoted to robust principal component analysis (PCA). We give a comparison between some multivariate estimators of location and scatter by computing the influence functions of the sensitivity coefficient ρ corresponding to these estimators, and the mean squared error (MSE) of estimators of ρ. The coefficient ρ measures the closeness between the subspaces spanned by the initial eigenvectors and their corresponding version derived from an infinitesimal perturbation of the data distribution. [ABSTRACT FROM PUBLISHER]

In the paper, we continue the investigation of the tail index estimators that are based on maxima over blocks of data and were proposed in [V. Paulauskas, A new estimator for tail index, Acta Appl. Math.,79:55-67, 2003; V. Paulauskas and M. Vaičiulis, Several modifications of DPR estimator of the tail index, Lith. Math. J., 51:36-50, 2011; V. Paulauskas and M. Vaičiulis, Estimation of the tail index in the max-aggregation scheme, Lith. Math. J., 52:297-315, 2012]. We construct a new tail index estimator based on local maxima and prove the weak consistency and asymptotic normality of this new estimator in the case of i.i.d. observations. We also prove the weak consistency in the case where data are generated by a nonstationary max-MA(q) process. Monte Carlo simulations show that our estimator is competitive with some popular estimators. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we propose an improved estimator of finite population mean using information on two auxiliary attributes under simple random sampling (SRS) and two-phase sampling schemes. The bias and mean squared error (MSE) expressions of the proposed estimators are obtained up to first order of approximation. It is shown theoretically, that the proposed estimator is more efficient than the ratio-product type estimator, regression estimator, difference type estimator and Malik and Singh (2013) [13] estimator in both SRS and two phase sampling. An empirical study using two data sets is also conducted to support the theoretical findings. [Copyright &y& Elsevier]

Abstract: We propose a two parameter ratio-product-ratio estimator for estimating a finite population variance based on simple random sampling without replacement. The bias and mean square error of the proposed estimator are obtained to the first degree of approximation. We have derived the conditions for the parameters under which the proposed estimator has smaller mean square error than the sample variance, ratio and product estimators. We carry out an application showing that the proposed estimator outperforms the traditional estimators using different data sets. [Copyright &y& Elsevier]

The gamma distribution is an important probability distribution in statistics. The maximum likelihood estimator (MLE) of its shape parameter is well known to be considerably biased, so that it has some modified versions. A new modified MLE of the shape for the gamma distribution is proposed in this paper, which is consistent, asymptotically normal and efficient. For finite-sample behavior, the new estimator improves the traditional MLE not only for reducing bias but also for gaining estimation efficiency significantly. In terms of estimation efficiency, it dominates other existing modified estimators. [ABSTRACT FROM AUTHOR]

Abstract: We develop empirical best estimators for small area event rates based on the hierarchical Poisson model with log-normal mixing distribution, when the basic data consists of area level measurements. We derive an approximate expression to the mean squared error of the estimators and we provide a method for estimating this expression. [Copyright &y& Elsevier]

Abstract: The empirical best linear unbiased predictor (EBLUP) in the linear mixed model (LMM) is useful for the small area estimation, and the estimation of the mean squared error (MSE) of EBLUP is important as a measure of uncertainty of EBLUP. To obtain a second-order unbiased estimator of the MSE, the second-order bias correction has been derived based on Taylor series expansions. However, this approach is hard to implement in complicated models with many unknown parameters like variance components, since we need to compute asymptotic bias, variance and covariance for estimators of unknown parameters as well as partial derivatives of some quantities. A similar difficulty occurs in the construction of confidence intervals based on EBLUP with second-order correction and in the derivation of second-order bias correction in the Akaike Information Criterion (AIC) and the conditional AIC. To avoid such difficulty in the derivation of second-order bias correction in these problems, the parametric bootstrap methods are suggested in this paper, and their second-order justifications are established. Finally, performances of the suggested procedures are numerically investigated in comparison with some existing procedures given in the literature. [Copyright &y& Elsevier]

Generalized least squares (GLS) for model parameter estimation has a long and successful history dating to its development by Gauss in 1795. Alternatives can outperform GLS in some settings, and alternatives to GLS are sometimes sought when GLS exhibits curious behavior, such as in Peelle's Pertinent Puzzle (PPP). PPP was described in 1987 in the context of estimating fundamental parameters that arise in nuclear interaction experiments. In PPP, GLS estimates fell outside the range of the data, eliciting concerns that GLS was somehow flawed. These concerns have led to suggested alternatives to GLS estimators. This paper defends GLS in the PPP context, investigates when PPP can occur, illustrates when PPP can be beneficial for parameter estimation, reviews optimality properties of GLS estimators, and gives an example in which PPP does occur. [ABSTRACT FROM AUTHOR]

Abstract: During the early stage of cancer clinical trials, when it is not convenient to construct an explicit hypothesis testing, a study on a new therapy often calls for a response rate (p) estimation concurrently with or right before a typical phase II study. We consider a two-stage process, where the acquired information from Stage I (with a small sample size (m)) would be utilized for sample size (n) recommendation for Stage II study aiming for a more accurate estimation. Once a sample size design and a parameter estimation protocol are applied, we study the overall utility (cost-effectiveness) in connection with the cost due to patient recruitment and treatment as well as the loss due to mean squared error from parameter estimation. Two approaches will be investigated including the posterior mixture method (a Bayesian approach) and the empirical variance method (a frequentist approach). We also discuss response rate estimation under truncated parameter space using maximum likelihood estimation with regard to sample size and mean squared error. The profiles of p-specific expected sample size, mean squared error and risk under different approaches motivate us to introduce the concept of “admissible sample size (design)". [ABSTRACT FROM AUTHOR]

Abstract: We consider the problem of estimating the scale parameter of the shifted exponential distribution with unknown location based on a type II progressively censored sample. Under a large class of bowl-shaped loss functions, a smooth estimator, that dominates the minimum risk equivariant estimator of , is proposed. A numerical study is performed and shows that the improved estimator yields significant risk reduction over the MRE. [Copyright &y& Elsevier]

This article examines a methodology to improve the efficiency of surveys to locate and estimate characteristics of rare populations. Two multiplicity counting rules are compared with a conventional rule in terms of reporting errors, sample variances, and survey yields. The analysis is based on data from two survey field experiments with diagnosed cancer patients and a subsample of their siblings or children who reside outside their households. The article concludes with a brief discussion of the circumstances in which a multiplicity counting rule is the preferred methodology and those in which other approaches should be pursued. [ABSTRACT FROM AUTHOR]