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AbstractA simple yet effective way of modeling survival data with cure fraction is by considering Box-Cox transformation cure model (BCTM) that unifies mixture and promotion time cure models. In this article, we numerically study the statistical properties of the BCTM when applied to interval censored data. Time-to-events associated with susceptible subjects are modeled through proportional hazards structure that allows for non-homogeneity across subjects, where the baseline hazard function is estimated by distribution-free piecewise linear function with varied degrees of non-parametricity. Due to missing cured statuses for right censored subjects, maximum likelihood estimates of model parameters are obtained by developing an expectation-maximization (EM) algorithm. Under the EM framework, the conditional expectation of the complete data log-likelihood function is maximized by considering all parameters (including the Box-Cox transformation parameter α) simultaneously, in contrast to conventional profile-likelihood technique of estimating α. The robustness and accuracy of the model and estimation method are established through a detailed simulation study under various parameter settings, and an analysis of real-life data obtained from a smoking cessation study. [ABSTRACT FROM AUTHOR]

Computational data analysis is an essential component of modern statistics. The most important challenge in classical statistics was an estimation of the location parameter. In addition, the selection of estimators among potential estimators is another problem in the computational data analysis. Therefore, the main objective of this study is to develop a location estimator that has been modified compared to all common location estimators. In order to ensure the objective of the new estimator, combinations weighted mean (Alex-mean) was developed and computed with R version 3.6.3. Further, the properties of a good location estimator diagnosed with all location estimators compared to Alex-mean with a COVID-19 new case data set. In addition, the new estimator was compared with mean, median and trimmed-mean based on relative efficiency and bootstrap simulation techniques. The new estimator is better than the mean, median and trimmed-mean of relative efficiency estimated using bootstrap and simulation techniques. The sensitivity graph shows that Alex-mean is insensitive to the outlier and is computed on the basis of all observations. Thus, the researcher suggested that Alex-mean is the good location estimator than all common measures of central tendency since it is undisturbed by extreme values. [ABSTRACT FROM AUTHOR]

In complex survey design, the resampling method is often used for assessing the variability and confidence interval of non-linear estimators which is a function of several estimated means or totals. A well-known resampling method, called the re-scaling bootstrap technique was originated by Rao and Wu (1988). This article is an attempt to propose a re-scaling bootstrap technique in estimating the parameters of rare and clustered population for a complex survey design. Adaptive cluster sampling design is a probabilistic approach to reach out to the rare and clustered units. Thompson (1990) introduced this design. Chaudhuri (2000) extended this design for varying probability sampling. In practice, the final sample size of adaptive sampling may be exorbitantly large. From this realistic point of view, Chaudhuri, Bose, and Dihidar (2005) developed the size-constrained adaptive sampling design, in varying probability sampling. We first describe here, how this well-known re-scaling bootstrap technique may be employed for non-linear estimators of the population total, in the case of rare and clustered population. It has been found that there is a need to develop an alternative re-scaling bootstrap procedure to avoid complications in computation to cover Chaudhuri, Bose, and Dihidar (2005). A simulation study has been carried out to demonstrate the proposed methods. [ABSTRACT FROM AUTHOR]

The randomness of the biases of parameter estimates, residuals and some variables is seldom considered for calculating covariance matrix of parameter estimates in total least squares (TLS) iterative algorithm. There are few studies on the precision estimation with the approximate probability distribution method of function in the TLS. In order to get more reasonable precision information for the TLS adjustment, the derivative-free Sterling interpolation method is introduced and implemented. The errors-in-variables (EIV) model and its TLS algorithm are introduced. The TLS iterative algorithm is combined with the Sterling interpolation, and two kinds of schemes for calculating biases of the TLS parameter estimates and approximate mean squared error matrix are designed. The method is used to four examples: line fitting model, coordinate transformation model, auto-regression model and variation function model. Comparing the results with the scaled unscented transformation (SUT) method, the feasibility and effectiveness of the Sterling interpolation method in the TLS precision estimation are verified. The Sterling interpolation method has fewer parameters than the SUT method, and it is simpler to implement. And the scheme two in this paper can be applied to the case where some matrix elements are nonlinear functions of the observation. The application of the precision estimation is expanded by this method, and the theory for precision estimation of TLS is further improved. [ABSTRACT FROM AUTHOR]

Gibbs samplings is a Markov Chain Monte Carlo technique for estimating conditional probabilities in Bayesian networks. A major problem of Gibbs sampling is the dependency of the generated chain of samples. Thus the estimates are biased unless the initial value of the chain is drawn from the target distribution. One elegant method to overcome the initial bias is regenerative samplings. We reported elsewhere the "stationary minorization condition" that makes any Markov Chain Monte Carlo technique regenerative. In this paper, we show how this condition can be easily met in the simulations of any Bayesian network. [ABSTRACT FROM AUTHOR]

Estimation of sensitive issues is an adversely challenging task as it is highly influenced by social desirability bias leading to untrue response many times. Hence, the possible way out for these problems are randomized response technique or scrambled response technique or the item sum technique etc. The proposed work is a methodological advancement in estimation of quantitative sensitive mean in two move successive sampling by modifying the item sum technique. Detailed properties of new IST estimators have been discussed in general sampling design with applications in different sampling designs on successive moves. Theoretical considerations have been integrated with simulation studies to show the working version of modified IST on two move successive sampling. [ABSTRACT FROM AUTHOR]

In this work we propose a novel method for treatment selection based on individual covariate information when the treatment response is multivariate and data are available from a crossover design. Our method covers any number of treatments and it can be applied for a broad set of models. The proposed method uses a rank aggregation technique to estimate an ordering of treatments based on ranked lists of treatment performance measures such as smooth conditional means and conditional probability of a response for one treatment dominating others. An empirical study demonstrates the performance of the proposed method in finite samples. [ABSTRACT FROM AUTHOR]

Functional polynomial multiple-index model which includes the functional linear model, functional quadratic model and functional single index model as the special cases is considered. In this paper we propose an iterative technique to estimate the link function and polynomial coefficients nonparametrically. Simulations show that the proposed methods have good prediction performances. The proposed model is also illustrated with tecator data. [ABSTRACT FROM AUTHOR]

Few studies have been conducted on the precision estimation of weighted total least squares (WTLS) by using the approximate function probability distribution method. And the existing Monte Carlo method needs to simulate a lot, the amount of calculation is large and the results obtained are uncertain. In order to further improve the total least squares precision estimation theory, this paper introduces the Jackknife method into Geomatics data processing. Combining the Jackknife method and WTLS method, the delete-1 Jackknife method and delete-d Jackknife method are proposed. The biases and standard deviations or covariance of parameter estimations are calculated by these proposed methods. And the specific steps of the precision estimation of these two methods are given. Applying these methods to the linear regression model and the coordinate transformation model, and comparing with the approximate function method and the Monte Carlo method, we can see that the Jackknife methods for precision estimation can obtain more stable and reasonable precision results and are very adaptive. In order to get more reasonable precision results, the Jackknife method does spend much more time over total least squares when the amount of the observed data is large. But compared with Monte Carlo method, it can reduce the amount of calculation and improve the computational efficiency. The method in this paper could provide an idea for further study on the precision estimation for total least squares. [ABSTRACT FROM AUTHOR]

This paper presents a robust version of partial residuals technique to estimate parametric and nonparametric components in semiparametric partially linear model. The robust estimation of the parametric component is constructed by using an M-estimation after eliminating the effect of the nonparametric component on both the response and covariates based on the pseudo data. Finally, the nonparametric component is estimated robustly by using the residuals from the obtained M-estimation of the parametric component. Simulation studies and a real data analysis illustrate that the proposed estimator performs better than the existing estimations when outliers in the dataset or errors with heavy tails. [ABSTRACT FROM AUTHOR]

Autoregressive Moving Average (ARMA) time series model fitting is a procedure often based on aggregate data, where parameter estimation plays a key role. Therefore, we analyze the effect of temporal aggregation on the accuracy of parameter estimation of mixed ARMA and MA models. We derive the expressions required to compute the parameter values of the aggregate models as functions of the basic model parameters in order to compare their estimation accuracy. To this end, a simulation experiment shows that aggregation causes a severe accuracy loss that increases with the order of aggregation, leading to poor accuracy. [ABSTRACT FROM AUTHOR]

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 is proposed. The scalarmean squared error of the proposed estimator is derived and its properties are investigated. Finally, a numerical example and a simulation study are presented to show the performance of the proposed estimator. [ABSTRACT FROM AUTHOR]

The binomial exponential 2 (BE2) distributionwas proposed by Bakouch et al. as a distribution of a random sum of independent exponential random variables, when the sample size has a zero truncated binomial distribution. In this article, we introduce a generalization of BE2 distribution which offers a more flexible model for lifetime data than the BE2 distribution. The hazard rate function of the proposed distribution can be decreasing, increasing, decreasing-increasing-decreasing and unimodal, so it turns out to be quite flexible for analyzing non-negative real life data. Some statistical properties and parameters estimation of the distribution are investigated. Three different algorithms are proposed for generating random data from the new distribution. Two real data applications regarding the strength data and Proschan's air-conditioner data are used to show that the new distribution is better than the BE2 distribution and some other well-known distributions in modeling lifetime data. [ABSTRACT FROM AUTHOR]

The likelihood of a generalized linear mixed model (GLMM) often involves high-dimensional integrals, which in general cannot be computed explicitly. When direct computation is not available, method of simulated moments (MSM) is a fairly simpleway to estimate the parameters of interest. In this research, we compared parametric bootstrap (PB) and nonparametric bootstrapmethods (NPB) in estimating the standard errors of MSM estimators for GLMM. Simulation results show that when the group size is large, the PB and NPB perform similarly; when group size is medium, NPB performs better than PB in estimating standard errors of the mean. [ABSTRACT FROM AUTHOR]

This article is devoted to study the problem of estimation in the periodic restricted exponential autoregressive EXPAR(1) models. The estimation procedure that is used is the least-square method. Simulation studies are carried out in order to check the asymptotic properties. An application to monthly flow data for the Fraser River in British Columbia is included. [ABSTRACT FROM AUTHOR]

In this article, main characteristics of a generalized Gumbel (GG) distribution are derived. Parameter estimation with method of moments, maximum likelihood, and Bayesian approaches are demonstrated. Due to the ranges of its skewness and kurtosis, it is satisfactory for fitting a wide variety of datasets. Also, it can be used to model block maxima or minima data due to its close connection with the standard Gumbel distribution. It is demonstrated that the GG distribution fits more accurately than both of the standard Gumbel and generalized extreme value distributions to block maxima data under specific conditions. [ABSTRACT FROM AUTHOR]

Estimation of common location parameter of two exponential populations is considered when the scale parameters are ordered using type-II censored samples. A general inadmissibility result is proved which helps in deriving improved estimators. Further, a class of estimators dominating the MLE has been derived by an application of integrated expression of risk difference (IERD) approach of Kubokawa. A discussion regarding extending the results to a general k( ⩾ 2) populations has been done. Finally, all the proposed estimators are compared through simulation. [ABSTRACT FROM AUTHOR]

In profile monitoring, control charts are proposed to detect unanticipated changes, and it is usually assumed that the in-control parameters are known. However, due to the characteristics of a system or process, the prespecified changes would appear in the process. Moreover, in most applications, the in-control parameters are usually unknown. To overcome these issues, we develop the zone control charts with estimated parameters to detect small shifts of these prespecified changes. The effects of estimation error have been investigated on the performance of the proposed charts. To account for the practitioner-to-practitioner variability, the expected average run length (ARL) and the standard deviation of the average run length (SDARL) is used as the performance metrics. Our results show that the estimation error results in the significant variation in the ARL distribution. Furthermore, in order to adequately reduce the variability, more phase I samples are required in terms of the SDARL metric than that in terms of the expected ARL metric. In addition, more observations on each sampled profile are suggested to improve the charts' performance, especially for small phase I sample sizes. Finally, an illustrative example is given to show the performance of the proposed zone control charts. [ABSTRACT FROM AUTHOR]

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

In this article, we consider a linear regression model with AR(p) error terms with the assumption that the error terms have a t distribution as a heavy-tailed alternative to the normal distribution.We obtain the estimators for the model parameters by using the conditional maximum likelihood (CML) method. We conduct an iteratively reweighting algorithm (IRA) to find the estimates for the parameters of interest. We provide a simulation study and three real data examples to illustrate the performance of the proposed robust estimators based on t distribution. [ABSTRACT FROM AUTHOR]

In this paper, we briefly overview different zero-inflated probability distributions. We compare the performance of the estimates of Poisson, Generalized Poisson, ZIP, ZIGP and ZINB models through Mean square error (MSE), bias and Standard error (SE) when the samples are generated from ZIP distribution. We propose a new estimator referred to as probability estimator (PE) of inflation parameter of ZIP distribution based on moment estimator (ME) of the mean parameter and compare its performance with ME andmaximum likelihood estimator (MLE) through a simulation study.We use the PE along with ME and MLE to fit ZIP distribution to various zero-inflated datasets and observe that the results do not differ significantly. We recommend using PE in place of MLE since it is easy to calculate and the simulation study in this paper demonstrates that the PE performs as good as MLE irrespective of the sample size. [ABSTRACT FROM AUTHOR]

The existing synthetic exponential control charts are based on the assumption of known in-control parameter. However, the in-control parameter has to be estimated from a Phase I dataset. In this article, we use the exact probability distribution, especially the percentiles, mean, and standard deviation of the conditional average run length (ARL) to evaluate the effect of parameter estimation on the performance of the Phase II synthetic exponential charts. This approach accounts for the variability in the conditional ARL values of the synthetic chart obtained by different practitioners. Since parameter estimation results in more false alarms than expected, we develop an exact method to design the adjusted synthetic charts with desired conditional in-control performance. Results of known and unknownin-control parameter cases show that the control limit of the conforming run length sub-chart of the synthetic chart should be as small as possible. [ABSTRACT FROM AUTHOR]

Skew normal distribution is an alternative distribution to the normal distribution to accommodate asymmetry. Since then extensive studies have been done on applying Azzalini's skewness mechanism to other well-known distributions, such as skew-t distribution, which is more flexible and can better accommodate long tailed data than the skew normal one. The Kumaraswamy generalized distribution (Kw - F) is another new class of distribution which is capable of fitting skewed data that can not be fitted well by existing distributions. Such a distribution has been widely studied and various versions of generalization of this distribution family have been introduced. In this article, we introduce a new generalization of the skew-t distribution based on the Kumaraswamy generalized distribution. The new class of distribution, whichwe call the Kumaraswamy skew-t (KwST ) has the ability of fitting skewed, long, and heavy-tailed data and is more flexible than the skew-t distribution as it contains the skew-t distribution as a special case. Related properties of this distribution family such as mathematical properties, moments, and order statistics are discussed. The proposed distribution is applied to a real dataset to illustrate the estimation procedure. [ABSTRACT FROM AUTHOR]

In this article, we studied the identification of significant predictors in partially linear model in which some regressors are contaminated with random errors. Moreover, the dimension of parametric component is divergent and the regression coefficients are sparse. We applied difference technique to remove the nonparametric component for circumventing the selection of bandwidth, and constructed a bias-corrected shrinking estimator for the coefficient by using smoothly clipped absolute deviation (SCAD) penalty. Then, we derived the estimating and selecting consistency and established the asymptotic distribution for the identified significant estimators. Finally, Monte Carlo studies illustrate the performance of our approach. [ABSTRACT FROM AUTHOR]

In this article, we develop estimation procedures for partially linear quantile regression models, where some of the responses are censored by another random variable. The nonparametric function is estimated by basis function approximations. The estimation procedure is easy to implement through existing weighted quantile regression, and it requires no specification of the error distributions. We show the largesample properties of the resulting estimates, the proposed estimator of the regression parameter is root-n consistent and asymptotically normal and the estimator of the functional component achieves the optimal convergence rate of the nonparametric function. The proposed method is studied via simulations and illustrated with the analysis of a primary biliary cirrhosis (BPC) data. [ABSTRACT FROM AUTHOR]

The continuous threshold expectile regression model could capture the effect of a covariate on the response variable with two different straight lines, while intersecting an unknown threshold needed be estimated. This article proposes a new estimation method via a linearization technique to estimate the regression coefficients and the threshold simultaneously. Statistical inferences of the proposed estimators are easily derived from the existing theory. Moreover, the estimation procedure is readily implemented by the current software. Simulation studies and an application on GDP per capita and quality of electricity supply data illustrate the proposed method. [ABSTRACT FROM AUTHOR]

The fact of estimating how a model output is influenced by the variations of inputs has become an important problematic in reliability and sensitivity analysis. This article is interested in estimating sensitivity indices useful to quantify the contribution of inputs to the variance of model output. A multivariate mixed kernel estimator is investigated since, until now, discrete and continuous inputs have been separately considered in kernel estimation of sensitivity indices. To illustrate the differences between the influence of mixed, discrete, and continuous inputs, analytical expressions of Sobol sensitivity indices are expressed in these three cases for the Ishigami test function. Besides, the performance of the mixed kernel estimator is illustrated through simulations in which the Bayesian procedure is applied for bandwidth parameter choice. An application is also realized on a real example. Finally, the use of an appropriate kernel estimator according to the type of inputs is found to be influential on the accuracy of sensitivity indices estimates. [ABSTRACT FROM AUTHOR]

This study introduces fast marginal maximum likelihood (MML) algorithms for estimating the tuning (shrinkage) parameter(s) of the ridge and power ridge regression models, and an automatic plug-in MML estimator for the generalized ridge regression model, in a Bayesian framework. These methods are applicable to multicollinear or singular covariate design matrices, including matrices where the number of covariates exceeds the sample size. According to analyses of many real and simulated datasets, these MML-based ridge methods tend to compare favorably to other tuning parameter selection methods, in terms of computation speed, prediction accuracy, and ability to detect relevant covariates. [ABSTRACT FROM AUTHOR]

This article focuses on estimating regression coefficients in the high dimensional seemingly unrelated regression model. When the number of equations exceeds that of the observations, both the maximum likelihood estimator and Zellner's two-stage estimator do not exist. As an alternative, we propose a two-stage conditional expectation improved estimator. The new estimator is further improved by the high-correlated residuals, and the high correlation is determined by hypothesis testings. Simulations show that the new estimator outperforms the ordinary least-squares estimator in terms of mean square errors, especially when high-correlated residuals exist between the equations. [ABSTRACT FROM AUTHOR]

This article is concerned with statistically and computationally efficient estimation in a hierarchical data setting with unequal cluster sizes and an AR(1) covariance structure. Maximum likelihood estimation for AR(1) requires numerical iteration when cluster sizes are unequal. A near optimal non-iterative procedure is proposed. Pseudo-likelihood and split-sample methods are used, resulting in computing weights to combine cluster size specific parameter estimates. Results show that the method is statistically nearly as efficient as maximum likelihood, but shows great savings in computation time. [ABSTRACT FROM AUTHOR]

In this article, a new class of variance function estimators is proposed in the setting of heteroscedastic nonparametric regression models. To obtain a variance function estimator, the main proposal is to smooth the product of the response variable and residuals as opposed to the squared residuals. The asymptotic properties of the proposed methodology are investigated in order to compare its asymptotic behavior with that of the existing methods. The finite sample performance of the proposed estimator is studied through simulation studies. The effect of the curvature of the mean function on its finite sample behavior is also discussed. [ABSTRACT FROM AUTHOR]

This article addresses the various properties and different methods of estimation of the unknown parameter of length and area-biased Maxwell distributions. Although, our main focus is on estimation from both frequentist and Bayesian point of view, yet, various mathematical and statistical properties of length and area-biased Maxwell distributions (such as moments, moment-generating function (mgf), hazard rate function, mean residual lifetime function, residual lifetime function, reversed residual life function, conditional moments and conditional mgf, stochastic ordering, and measures of uncertainty) are derived. We briefly describe different frequentist approaches, namely, maximum likelihood estimator, moments estimator, least-square and weighted least-square estimators, maximum product of spacings estimator and compare them using extensive numerical simulations. Next we consider Bayes estimation under different types of loss function (symmetric and asymmetric loss functions) using inverted gamma prior for the scale parameter. Furthermore, Bayes estimators and their respective posterior risks are computed and compared using Markov chain Monte Carlo (MCMC) algorithm. Also, bootstrap confidence intervals using frequentist approaches are provided to compare with Bayes credible intervals. Finally, a real dataset has been analyzed for illustrative purposes. [ABSTRACT FROM AUTHOR]

This work presents a new linear calibration model with replication by assuming that the error of the model follows a skew scale mixture of the normal distributions family, which is a class of asymmetric thick-tailed distributions that includes the skew normal distribution and symmetric distributions. In the literature, most calibration models assume that the errors are normally distributed. However, the normal distribution is not suitable when there are atypical observations and asymmetry. The estimation of the calibration model parameters are done numerically by the EM algorithm. A simulation study is carried out to verify the properties of the maximum likelihood estimators. This new approach is applied to a real dataset from a chemical analysis. [ABSTRACT FROM AUTHOR]

In this paper, a one-stage multiple comparison procedures with the average for exponential location parameters based on the doubly censored sample under heteroscedasticity is proposed. These intervals can be used to identify a subset which includes all no-worse-than-the-average treatments in an experimental design and to identify better-than-the-average, worse-than-the-average and not-much-different-from-the-average products in agriculture, emerging market, pharmaceutical industries. The critical values are tabulated in a table for practical use. A simulation study on the confidence length and coverage probabilities is done. At last, an example of comparing four drugs in the treatment of leukemia is given to demonstrate the proposed procedures. [ABSTRACT FROM AUTHOR]

Among the many analytical techniques that have been published to analyze the significance of the effects in the absence of replications, two have emerged as the most widely used in text books as well as statistical software packages: The Lenth's method and the estimation of the variance of the effects from the values of those considered negligible. This article shows that neither is better than the other in all cases, and by analyzing the results obtained in a wide variety of situations it provides guidelines on when it is preferable to use one or the other technique. [ABSTRACT FROM AUTHOR]

This article addresses two methods of estimation of the probability density function (PDF) and cumulative distribution function (CDF) for the Lindley distribution. Following estimation methods are considered: uniformly minimum variance unbiased estimator (UMVUE) and maximum likelihood estimator (MLE). Since the Lindley distribution is more flexible than the exponential distribution, the same estimators have been found out for the exponential distribution and compared. Monte Carlo simulations and a real data analysis are performed to compare the performances of the proposed methods of estimation. [ABSTRACT FROM AUTHOR]

In applications of multivariate finite mixture models, estimating the number of unknown components is often difficult. We propose a bootstrap information criterion, whereby we calculate the expected log-likelihood at maximum a posteriori estimates for model selection. Accurate estimation using the bootstrap requires a large number of bootstrap replicates. We accelerate this computation by employing parallel processing with graphics processing units (GPUs) on the Compute Unified Device Architecture (CUDA) platform. We conducted a runtime comparison of CUDA algorithms between implementation on the GPU and that on a CPU. The results showed significant performance gains in the proposed CUDA algorithms over multithread CPUs. [ABSTRACT FROM AUTHOR]

The ordinary least-square estimators for linear regression analysis with multicollinearity and outliers lead to unfavorable results. In this article, we propose a new robust modified ridge M-estimator (MRME) based on M-estimator (ME) to deal with the combined problem resulting from multicollinearity and outliers in the y-direction. MRME outperforms modified ridge estimator, robust ridge estimator and ME, according to mean squares error criterion. Furthermore, a numerical example and a Monte Carlo simulation experiment are given to illustrate some of the theoretical results. [ABSTRACT FROM AUTHOR]

In this article, the estimation problem of the multicomponent stress-strength reliability parameter is considered where the stress and the strength systems have arbitrary fixed numbers of independent and non-identical parallel components. It is assumed that the distribution functions of the stress and the strength components satisfy the proportional reversed hazard rate model. The study is done in more details when the baseline distributions are exponential. Maximum likelihood and uniformly minimum variance unbiased estimators are obtained and compared. Also, Bayes and empirical Bayes estimators are discussed and Monte Carlo simulations are carried out to compare their performances. [ABSTRACT FROM AUTHOR]

In the field of computer virus, a growing number of mathematical models have been published during the last decade. In this paper, we consider several estimation methods under two parametric models, the random constant scanning model and the nonhomogeneous random scanning model, to propose a comparison of the estimators’ performances based on the simulation of random populations. We conclude our work with an application of the different estimation methods to a real data set of worm propagation. [ABSTRACT FROM AUTHOR]

This article proposes nonparametric Bayesian approaches to monotone function estimation. This approach uses a hierarchical Bayes framework and a characterization of stick-breaking process that allows unconstrained estimation of the monotone function. In order to avoid the limitation of parametric modeling, a general class of prior distributions, called stick-breaking priors, is considered. It accommodates much more flexible forms and can easily deal with skewness, multimodality, etc., of the dependent variable response. The proposed approach is incorporated to model the catch ratio based on automatic weather station (AWS) data. [ABSTRACT FROM AUTHOR]

We postulate a spatiotemporal multilevel model and estimate using forward search algorithm and MLE imbedded into the backfitting algorithm. Forward search algorithm ensures robustness of the estimates by filtering the effect of temporary structural changes in the estimation of the group-level covariates, the individual-level covariates and spatial parameters. Backfitting algorithm provides computational efficiency of estimation procedure assuming an additive model. Simulation studies show that estimates are robust even in the presence of structural changes induced for example by epidemic outbreak. The model also produced robust estimates even for small sample and short time series common in epidemiological settings. [ABSTRACT FROM AUTHOR]

We develop a simple methodology that allows practitioners to test for the presence of a unit root without a priori knowledge regarding the occurrence of a break under the null hypothesis. We use a pre-test that is readily available in the estimated regression used to calculate the unit root statistics, and so our methodology is very easy to implement. The t-statistic corresponding to the impulse dummy variables evaluated at break date estimator is used as a pre-test to ascertain whether a break exists under the null hypothesis. Finite sample simulations show that our methodology yields tests that maintain their size. [ABSTRACT FROM AUTHOR]

This article mainly considers a new class of anticipated BSDEs driven by Brownian motion and continuous increasing process, which are called generalized anticipated backward stochastic differential equations(GABSDEs). We first give the form of GABSDEs. Then, existence and uniqueness result for GABSDEs is established as well as a comparison theorem is obtained under the certain assumptions. At last, we give an application about the duality between SDDEs and GABSDEs. [ABSTRACT FROM AUTHOR]

The motivation of this study is to evaluate the American put option on zero-coupon bond, when the interest rate model is governed by a fractional CIR (FCIR) interest rate model. Since the existence of fractional Brownian motion, leading to create the arbitrage, we employ the transaction cost for eliminating the arbitrage. We first of all apply the Leland's hedging strategy for a self-financing portfolio that contains an American option and zero-coupon bond and derive a formula for the transaction cost. We perform the least-square Monte Carlo (LSM) method for pricing American option under the proposed interest rate model. [ABSTRACT FROM AUTHOR]

This article mainly considers a new class of anticipated BSDEs driven by Brownian motion and continuous increasing process, which are called generalized anticipated backward stochastic differential equations(GABSDEs). We first give the form of GABSDEs. Then, existence and uniqueness result for GABSDEs is established as well as a comparison theorem is obtained under the certain assumptions. At last, we give an application about the duality between SDDEs and GABSDEs. [ABSTRACT FROM AUTHOR]

The study proposes a weighted bootstrap control chart based on the strata and determines suitable weights for each stratum by measuring the relative error of estimated Type I risks (Err). In addition to validating the detection effectiveness of the proposed control chart, this study also compares several types of control charts for detecting the Type I, Type II risks, and median run lengths. The proposed control chart shows superior detection effectiveness in six skewed distributions compared to other types of control charts. [ABSTRACT FROM PUBLISHER]

This article investigates the problem of establishing best linear unbiased predictors and best linear unbiased estimators of all unknown parameters in a group of linear models with random coefficients and correlated covariance matrix. We shall derive a variety of fundamental statistical properties of the predictors and estimators by using some matrix analysis tools. In particular, we shall establish necessary and sufficient conditions for the predictors and estimators to be equivalent under single and combined equations in the group of models by using the method of matrix equations, matrix rank formulas, and partitioned matrix calculations. [ABSTRACT FROM PUBLISHER]

The least-squares regression estimator can be very sensitive in the presence of multicollinearity and outliers in the data. We introduce a new robust estimator based on the MM estimator. By considering weights, also the resulting MM-Liu estimator is highly robust, but also the estimation of the biasing parameter is robustified. Also for high-dimensional data, a robust Liu-type estimator is introduced, based on the Partial Robust M-estimator. Simulation experiments and a real dataset show the advantages over the standard estimators and other robustness proposals. [ABSTRACT FROM PUBLISHER]

Diagnostic odds ratio is defined as the ratio of the odds of the positivity of a diagnostic test results in the diseased population relative to that in the non-diseased population. It is a function of sensitivity and specificity, which can be seen as an indicator of the diagnostic accuracy for the evaluation of a biomarker/test. The naïve estimator of diagnostic odds ratio fails when either sensitivity or specificity is close to one, which leads the denominator of diagnostic odds ratio equal to zero. We propose several methods to adjust for such situation. Agresti and Coull’s adjustment is a common and straightforward way for extreme binomial proportions. Alternatively, estimation methods based on a more advanced sampling design can be applied, which systematically selects samples from underlying population based on judgment ranks. Under such design, the odds can be estimated by the sum of indicator functions and thus avoid the situation of dividing by zero and provide a valid estimation. The asymptotic mean and variance of the proposed estimators are derived. All methods are readily applied for the confidence interval estimation and hypothesis testing for diagnostic odds ratio. A simulation study is conducted to compare the efficiency of the proposed methods. Finally, the proposed methods are illustrated using a real dataset. [ABSTRACT FROM PUBLISHER]