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Suppose we are interested in the effect of a treatment in a clinical trial. The efficiency of inference may be limited due to small sample size. However, external control data are often available from historical studies. Motivated by an application to Helicobacter pylori infection, we show how to borrow strength from such data to improve efficiency of inference in the clinical trial. Under an exchangeability assumption about the potential outcome mean, we show that the semiparametric efficiency bound for estimating the average treatment effect can be reduced by incorporating both the clinical trial data and external controls. We then derive a doubly robust and locally efficient estimator. The improvement in efficiency is prominent especially when the external control dataset has a large sample size and small variability. Our method allows for a relaxed overlap assumption, and we illustrate with the case where the clinical trial only contains a treated group. We also develop doubly robust and locally efficient approaches that extrapolate the causal effect in the clinical trial to the external population and the overall population. Our results also offer a meaningful implication for trial design and data collection. We evaluate the finite-sample performance of the proposed estimators via simulation. In the Helicobacter pylori infection application, our approach shows that the combination treatment has potential efficacy advantages over the triple therapy., Accepted for publication in Biometrics; 1 figure, 3 tables

In this manuscript, we investigate the estimation of the unknown reliability measure R = P [Y

This study proposes an efficient estimator and uses it to estimate the health of a lithium-ion battery and a supercapacitor in the hybrid energy storage system (HESS). A new type of online health estimator that uses a fuzzy brain emotional learning neural network (FBELNN) is proposed. This neural network is different to a conventional brain emotional learning neural network where the fuzzy inference system and a new reward signal are used. The effect capacity fading on the output of energy storage components is also determined. The proposed method uses a discrete wavelet transform (DWT) and principal component analysis (PCA) to extract features from the response signal for the impulse load. The DWT-PCA can reduce the workload for feature extraction. The parameter adaptation laws and convergence analysis for the FBELNN are derived and the internal parameters for the FBELNN are optimized using a genetic algorithm (GA). A neural network estimates the capacity of a supercapacitor and lithium-ion battery in real-time to better ensure the safety of HESS. The sample set is collected from the voltage response signal in the HESS simulation platform and practical experimental platform. Simulation and experimental results show that the proposed method has a faster learning speed and is more accurate than other methods.

It is well known that the ordinary least squares (OLS) regression estimator is not robust. Many robust regression estimators have been proposed and inferential methods based on these estimators have been derived. However, for two independent groups, let θj(X) be some conditional measure of location for the jth group, given X, based on some robust regression estimator. An issue that has not been addressed is computing a 1 − α confidence interval for θ1(X) − θ2(X) in a manner that allows both within group and between group hetereoscedasticity. The paper reports the finite sample properties of a simple method for accomplishing this goal. Simulations indicate that, in terms of controlling the probability of a Type I error, the method performs very well for a wide range of situations, even with a relatively small sample size. In principle, any robust regression estimator can be used. The simulations are focused primarily on the Theil–Sen estimator, but some results using Yohai’s MM-estimator, as well as the Koenker and Bassett quantile regression estimator, are noted. Data from the Well Elderly II study, dealing with measures of meaningful activity using the cortisol awakening response as a covariate, are used to illustrate that the choice between an extant method based on a nonparametric regression estimator, and the method suggested here, can make a practical difference.

A basic assumption concerned with general linear regression model is that there is no correlation (or no multicollinearity) between the explanatory variables. When this assumption is not satisfied, the least squares estimators have large variances and become unstable and may have a wrong sign. Therefore, we resort to biased regression methods, which stabilize the parameter estimates. Ridge regression (RR) and principal component regression (PCR) are two of the most popular biased regression methods which can be used in case of multicollinearity. But the r-k class estimator, which is composed by combining the RR estimator and the PCR estimator into a single estimator gives the better estimates of the regression coefficients than the RR estimator and PCR estimator.This paper explores the multiple regression technique using r-k class estimator between TFR and other socio-economic and demographic variables and the data has been taken from the National Family Health Survey-III (NFHS-III): 29 states of India. The analysis shows that use of contraceptive devices shares the greatest impact on fertility rate followed by maternal care, use of improved water, female age at marriage and spacing between births.

For estimating bivariate survival function under random censor- ship, it is commonly believed that the Dabrowska estimator is among the best ones while the Volterra estimator is far from being computational ef- ficiency. As we will see, the Volterra estimator is a natural extension of the Kaplan-Meier estimator to bivariate data setting. We believe that the computational 'inefficiency' of the Volterra estimator is largely due to the formidable computational complexity of the traditional recursion method. In this paper, we show by numerical study as well as theoretical analysis that the Volterra estimator, once computed by dynamic programming technique, is more computationally efficient than the Dabrowska estimator. Therefore, the Volterra estimator with dynamic programming would be quite recom- mendable in applications owing to its significant computational advantages.

A modified form of the population mean estimator suggested by Anieting and Enang (2020) in stratified double sampling in the presence of nonresponse using a single auxiliary variable has been proposed. The Mean Squared Error (MSE) and the bias of the proposed estimator have been given using large sample approximation. The empirical study shows that the MSE of the suggested estimator is more efficient than all other existing estimators in the same scheme. Determination of the optimal values of the first and second phases samples has also been done

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 select...

3-D target localization based on multi-input and multioutput radar systems is studied in this letter by utilizing time delay and angle of arrival measurements, which can be obtained by some local sensor signal processing methods. For such a positioning problem, the typical closed-form solution first establishes pseudolinear equation and then, applies the weighted least squares (WLS) technique to determine the final position. However, the WLS solution often suffers from performance degradation when the noise is large. To alleviate this problem, the cost function of the WLS is represented, and a quadratic constraint is imposed such that the expectation of the cost function can attain the minimum value at the true position. Moreover, simulation experiments show that the proposed method performs better than the state-of-art algorithms.

Unified approach (Chen and Chen in J R Stat Soc B 62(3):449–460, 2000) uses a working regression model to extract information from auxiliary variables in two-stage study for computing an efficient estimator of regression parameter. As far as we know, the method is limited to deal with missing complete at random data in a simple monotone missing data pattern. In this research, we extend the unified approach to estimate regression models with nonmonotone missing at random data. We describe an inverse probability weighting estimator condition on estimators from a set of working regression models which contains information from incomplete data and auxiliary variables. The proposed method is flexible and can easily accommodate incomplete data and auxiliary variables. We investigate the finite-sample performance of the proposed estimators using simulation studies and further illustrate the estimation method on a case–control study investigating the risk factors of hip fractures.

Markov chain algorithms are ubiquitous in machine learning and statistics and many other disciplines. Typically, these algorithms can be formulated as acceptance rejection methods. In this work, we...

Error variance estimation plays a key role in the analysis of homogeneous non‐parametric regression models. For a random design model, most methods in the literature for error variance estimation assume the independence between the predictor variable X and the error e. In this work, we derive the optimal semi‐parametric efficiency bound for the error variance σ2=var(ϵ) without such an independence assumption. A residual‐based efficient estimator for σ2 is proposed and its asymptotic normality is established. An extensive simulation study is conducted, which shows that our proposed estimator works very favourably against competitors. A simple real‐data example is also presented.

In this article, we are concerned with the utilization of ranks of original auxiliary variable as an additional auxiliary variable and thus we propose an efficient estimator of population variance....

In this paper, the credit scoring problem is studied by incorporating networked information, where the advantages of such incorporation are investigated theoretically in two scenarios. Firstly, a Bayesian optimal filter is proposed to provide risk prediction for lenders assuming that published credit scores are estimated merely from structured financial data. Such prediction can then be used as a monitoring indicator for the risk management in lenders' future decisions. Secondly, a recursive Bayes estimator is further proposed to improve the precision of credit scoring by incorporating the dynamic interaction topology of clients. It is shown that under the proposed evolution framework, the designed estimator has a higher precision than any efficient estimator, and the mean square errors are strictly smaller than the Cram\'er-Rao lower bound for clients within a certain range of scores. Finally, simulation results for a special case illustrate the feasibility and effectiveness of the proposed algorithms., Comment: 19 pages, simulations and discussion added, motivation clarified, references updated

This paper investigates the state estimation problem for a class of fractional-order memristive neural networks (FOMNNs) with leakage and time delay. The main objective of this study is to construct an efficient estimator such that the state of the corresponding estimation error is globally stable. Distinct to the previous studies, the state estimation problem of FOMNNs is investigated through fractional-order Lyapunov direct method. The sufficient conditions that ensure the global stability of the error system has been derived as a set of solvable linear matrix inequalities. In order to validate the effectiveness of the proposed theoretical results, two numerical examples have been illustrated.

Summary Advances in digital technology and wearables have made it possible to deliver behavioural mobile health interventions to individuals in their everyday lives. Micro-randomized trials are increasingly used to provide data to inform the construction of these interventions. In a micro-randomized trial, each individual is repeatedly randomized among multiple intervention options, often hundreds or even thousands of times over the course of the trial. The work reported in this article is motivated by multiple micro-randomized trials that have been conducted or are currently in the field, in which the primary outcome is a longitudinal binary outcome. The primary aim of such micro-randomized trials is to examine whether a particular time-varying intervention has an effect on the longitudinal binary outcome, often marginally over all, but a small subset of the individual’s data. We propose the concept of causal excursion effect, which can be used in such a primary-aim analysis for micro-randomized trials with binary outcomes. Under rather restrictive assumptions one can derive, based on existing literature, a semiparametric, locally efficient estimator of the causal effect. Starting from this estimator, we develop an estimator that can be used as the basis of a primary-aim analysis under more plausible assumptions. Simulation studies are conducted to compare the estimators. We illustrate the proposed methods using data from the micro-randomized trial BariFit, the goal of which is to support weight maintenance for individuals who have undergone bariatric surgery.

Estimation of the four generalized lambda distribution parameters is not straightforward, and available estimators that perform best have large computation times. In this paper, we introduce a simp...

In this paper we study blind source localization problem based on the joint received signal strength difference (RSSD) and angle of arrival (AOA) measurements with unknown transmit power of source. Since RSSD and AOA measurements are uncorrelated, combining two methods leads to a better performance for source localization. This paper focus on the pseudo linear estimator (PLE) with a closed-form and low complexity solution. One of the main limitations in this estimator is the bias created from the correlation between system matrix and error vector, which is not vanished by increasing the number of measurements. To overcome this problem first, we present a bias compensated PLE using the closed instrumental variable (IV). Then, for improving the localization performance a weighting IV estimator (WIV) is presented. Finally, for achieving the Cramer–Rao lower bound (CRLB) an improved WIV (IWIV) estimator is used based on the known relation between the estimated parameters of WIV estimator. The proposed IWIV estimator is proved to be asymptotically efficient (i.e., obtaining zero bias and the Cramer–Rao lower bound). Numerical simulations also verify the theoretical development and show source localization using hybrid information RSSD/AOA has a superior performance than RSSD and AOA solely.

This paper is concerned with the robust state estimation problem for a class of delayed fractional-order bidirectional associative memory (FOBAM) neural networks (NNs) with norm-bounded uncertainties. The objective of the study is to construct an efficient estimator in such a way that the behavior of the corresponding error state is stable in the Mittag-Leffler sense. Distinct to the previous studies, the state estimation problem of FOBAM NNs is investigated through fractional-order Lyapunov direct method. The sufficient conditions that ensure the global Mittag-Leffler stability of the error system are derived as a set of solvable linear matrix inequalities (LMIs) without uncertainties. The proposed stability conditions are further extended to the FOBAM NNs by considering the effect of uncertainties. In order to validate the effectiveness of the proposed theoretical results, two numerical examples have been illustrated.

This paper studies the estimation and inference problems of time-invariant restrictions on certain known functions of the stochastic volatility process. We first develop a more efficient GMM estimator and derive the efficiency bound under such restrictions. Then we construct an integrated Hausman-type test by summing up the squared differences between this more efficient estimator and the unrestricted estimator computed at different time points. Although less efficient under the null, the latter estimator is consistent under both the null and the alternative. The efficient GMM estimator can also be used to update an existing Bierens-type test and simplify the calculation of the asymptotic variance. Since the quadratic function puts more weight on large values, the Hausman-type test can have superior power than the Bierens-type test, which is based on a linear function of the differences. The simulation study shows that except for very small local window sizes, the Hausman-type test has good size and superior power. We finally apply these tests to studying the constant beta hypothesis using empirical data and find substantial evidence against this hypothesis.

Summary Mediation analysis in causal inference has traditionally focused on binary exposures and deterministic interventions, and a decomposition of the average treatment effect in terms of direct and indirect effects. We present an analogous decomposition of the population intervention effect, defined through stochastic interventions on the exposure. Population intervention effects provide a generalized framework in which a variety of interesting causal contrasts can be defined, including effects for continuous and categorical exposures. We show that identification of direct and indirect effects for the population intervention effect requires weaker assumptions than its average treatment effect counterpart, under the assumption of no mediator–outcome confounders affected by exposure. In particular, identification of direct effects is guaranteed in experiments that randomize the exposure and the mediator. We propose various estimators of the direct and indirect effects, including substitution, reweighted and efficient estimators based on flexible regression techniques, allowing for multivariate mediators. Our efficient estimator is asymptotically linear under a condition requiring n1/4-consistency of certain regression functions. We perform a simulation study in which we assess the finite sample properties of our proposed estimators. We present the results of an illustrative study where we assess the effect of participation in a sports team on the body mass index among children, using mediators such as exercise habits, daily consumption of snacks and overweight status.

In this paper, a novel algebraic closed-form method is proposed to estimate the position and velocity of a moving target in distributed multiple-input multiple-output radar systems with erroneous sensor locations by utilizing time delay and Doppler shift measurements. Unlike the existing methods that introduce nuisance parameters to build the pseudo-linear equations, the proposed method uses the singular value decomposition approach to establish new linear equations with regard to the target location with no nuisance parameters, and then derives a weighted least-squares (WLS) solution. To further improve the localization accuracy, the solution is refined through estimating the error by another WLS estimator. Based on the theoretical derivation and numerical simulations, the proposed estimator is demonstrated to be approximately unbiased and can attain the CRLB under small noise conditions. Moreover, the simulation results show that the proposed method achieves better target location accuracy than the state-of-the-art algorithms.

We propose a computationally efficient estimator for multi-dimensional linear space-invariant system dynamics with periodic boundary conditions that attains low mean squared error from very few temporal steps. By exploiting the inherent redundancy found in many real-world spatiotemporal systems, the estimator performance improves with the dimensionality of the system. This paper provides a detailed analysis of maximum likelihood estimation of the state transition operator in linear space-invariant systems driven by Gaussian noise. The key result of this work is that, by incorporating the space-invariance prior, the mean squared error of a estimator normalized to the number of parameters is upper bounded by $N^{-1}M^{-1} + O(N^{-1} M^{-2})$ , where $N$ is the number of spatial points, and $M$ is the number of observed timesteps after the initial value.

Panel data analysis is often faced with the issue of errors having arbitrary correlation across time for a particular individual “I” (serial correlation) and/or errors having arbitrary correlation across individuals at a moment in time (spatial correlation) with error disturbances having non constant variance. This study examined some panel data estimators in the presence of serial and spatial autocorrelation with panel heteroscedasticity. The study was done using two different sets of data simulated separately with ?=0.95 & 0.50. For each set of simulations short and long panels were considered for different sample sizes. The analysis considered two settings were rho is considered to be panel-specific (?i) and where rho is considered to be common for all panels (?). The estimators were examined based on bias, overconfidence and relative efficiency. The results produced evidence that the size of the autocorrelation coefficient ? affects the general performance of an estimator. Comparison of the estimators showed that Panel Corrected Standard Error Estimator (PCSE) produced better results than the other estimators considered in this work. But it was seen not to do very well in small samples and short panels. In terms of relative efficiency Park-Kmenta estimator was found to be more efficient that PCSE and PWLS (Panel Weighted Least Square Estimator). This paper has been able to show that the size of rho at the long run has an impact on the performance of the estimators, it showed that a small size of rho tends to increase overconfidence. The paper also revealed that Park-Kmenta estimator even with its flaws is still the most efficient estimator compared to the PCSE and PWLS. and it also substantiated the fact that PCSE performs badly in samples especially when N>T.

We consider the estimation of the transition matrix of a hidden Markovian process by using information geometry with respect to transition matrices. In this paper, only the histogram of k-memory data is used for the estimation. To establish our method, we focus on a partial observation model with the Markovian process and we propose an efficient estimator whose asymptotic estimation error is given as the inverse of projective Fisher information of transition matrices. This estimator is applied to the estimation of the transition matrix of the hidden Markovian process. In this application, we carefully discuss the equivalence problem for hidden Markovian process on the tangent space.

In this letter, an efficient estimator for 3-D target localization in distributed multiple-input multiple-output (MIMO) radars using time delay (TD) and angle of arrival (AOA) measurements is proposed. First, an approximately equivalent maximum likelihood (ML) estimation problem is formulated. Then, the aforementioned ML problem is recast into a convex optimization problem for which we derive a semi closed-form solution that eventually boils down to finding the roots of certain polynomials. Using numerical simulations, we demonstrate that the proposed estimator reaches the Cramer-Rao lower bound (CRLB) up to relatively high Gaussian measurement noise levels. Furthermore, the proposed method is shown to outperform the state-of-the-art algorithms under the above-mentioned noise model.

In this paper, we generalize the property of local asymptotic normality (LAN) to an enlarged neighborhood, under the name of rescaled local asymptotic normality (RLAN). We obtain sufficient conditions for a regular parametric model to satisfy RLAN. We show that RLAN supports the construction of a statistically efficient estimator which maximizes a cubic approximation to the log-likelihood on this enlarged neighborhood. In the context of Monte Carlo inference, we find that this maximum cubic likelihood estimator can maintain its statistical efficiency in the presence of asymptotically increasing Monte Carlo error in likelihood evaluation., Comment: 41 pages, 1 figure

Motivated by recent work involving the analysis of biomedical imaging data, we present a novel procedure for constructing simultaneous confidence corridors for the mean of imaging data. We propose to use flexible bivariate splines over triangulations to handle irregular domain of the images that is common in brain imaging studies and in other biomedical imaging applications. The proposed spline estimators of the mean functions are shown to be consistent and asymptotically normal under some regularity conditions. We also provide a computationally efficient estimator of the covariance function and derive its uniform consistency. The procedure is also extended to the two-sample case in which we focus on comparing the mean functions from two populations of imaging data. Through Monte Carlo simulation studies we examine the finite-sample performance of the proposed method. Finally, the proposed method is applied to analyze brain Positron Emission Tomography (PET) data in two different studies. One dataset used in preparation of this article was obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database.

In regression modeling, it has become very common to deal with missing data, which render the statistical analysis more difficult. It is then of interest to develop robust methods toward statistical inference for the regression coefficients in the presence of missing data. From this, a generalized signed-rank estimator of the regression coefficients in a model with non-ignorable missing responses is studied. The generalized signed-rank objective function covers a large class of existing objective functions such as the least squares, the signed-rank, the least absolute deviation among others. Under mild regularity conditions, the consistency and the limiting distribution of the proposed estimator are established. Finite-samples simulation studies are carried out to assess the performance of the proposed estimation method, and a practical real data application is given to illustrate our method. Results of these studies show that the proposed approach results in a robust and more efficient estimator compared to the least squares and least absolute deviation approaches, when dealing with heavy-tailed, contaminated model error distributions and/or when data contain gross outliers in the response space. Under the standard normal model error distribution, while the least squares and the proposed estimator have a similar performance, the least absolute deviation is inefficient.

Çok değişkenli veri setlerinde aykırı değerlerin varlığı anakütle parametre tahminini zorlaştırmakta ve hata varyansını arttırarak kullanılan istatistiki testin gücünü azaltmaktadır. Bu durum, değişkenlerin eşit varyansa ve çok değişkenli normal dağılıma sahip olduğu varsayımlarından sapmalara sebep olmaktadır. Çok değişkenli aykırı değer tespitinde kullanılan tekniklerden biri olan Mahalanobis uzaklığı, aykırı değişkenlere karşı hassas ölçütler olan çok değişkenli ortalamalar ve kovaryans matrisine dayalı olarak hesaplanmakta; çok değişkenli veri setlerinde aykırı gözlemlerin tespitinin engellenmesi veya normal gözlemlerin aykırı gözlem olarak tespit edilmesi problemlerine karşı dayanıklı ölçütlerle de kullanılmaktadır. Bu çalışmada, çok değişkenli aykırı değer tespitinde kullanılan klasik ve dayanıklı Mahalanobis ölçütlerinin aykırı gözlem tespitlerinin karşılaştırılması amaçlanmıştır. Uygulama verisi olarak, Ocak 2013 – Aralık 2017 döneminde New York ve NASDAQ borsasında yatırımcılar tarafından gerçekleştirilen 1.239.507 adet hisse senedi alım ve satım işlemi kullanılmıştır. Aykırı işlemlerin tespitinde miktar ve hacim değişkenleri ele alınarak, her bir işlem için klasik ve dayanıklı ölçütlere dayalı uzaklık skorları hesaplanarak, söz konusu teknikler karşılaştırılmıştır. Çalışma sonucunda, klasik Mahalanobis ölçütü ve En Küçük Hacimli Elipsoid ile tespit edilemeyen maskelenmiş aykırı gözlemlerin, Hızlı Minimum Kovaryans Determinant yöntemiyle tespit edilmiş olduğu; söz konusu yöntemin finans uygulama alanında çok değişkenli veri setlerinde aykırı gözlemlerin tespiti için kullanılabilecek etkin bir yöntem olduğu sonucuna ulaşılmıştır.

Double Extreme Ranked Set Sampling (DERSS) was first introduced by Samawi (2002) as a modification to the well-known Ranked Set Sampling (RSS) and Extreme Ranked Set Sampling (ERSS). In this article, we provide a modification to DERSS scheme with ranking based on an easy-to-rank baseline auxiliary variable known to be associated with survival time. We show that using the modified DERSS improves the performance of the Accelerated failure time (AFT) survival model and provides a more efficient estimator of the hazard ratio than that based on their counter parts simple random sample (SRS), RSS and ERSS, which results in reducing the sample size required and hence the total cost of the study. Our theoretical and simulation studies show the superiority of using the modified DERSS for AFT survival models compared with using SRS, RSS and ERSS. A numerical example based on Worcester Heart Attack Study is presented to illustrate the implementation of the DERSS.

This study considers the problem of adaptive detection for a multichannel signal in the presence of spatially and temporally correlated compound-Gaussian disturbance. By modelling the disturbance as a multichannel autoregressive process, the authors resort to a parametric generalised likelihood ratio test (PGLRT) with the capability of dimension reduction. In the derivation, due to treating the random texture components of disturbance as deterministic unknown parameters, the test requires no a priori knowledge about the disturbance statistics. Moreover, the involving highly non-linear maximum-likelihood (ML) estimation procedure underlying the PGLRT is subtly addressed by ad hoc ML estimators. Accordingly, the derived detector applies to challenging cases with limited or even no training signals for parameter estimation. Such cases (especially when training-free case) are attractive for signal detection in heterogeneous or fast changing environments. In simulations, the performance evaluations are conducted by means of Monte Carlo trials. Numerical results investigate the issues of the estimator efficiency, detection and false alarm probabilities in terms of several concerned cases. Compared to the existing and benchmark detectors, the proposed PGLRT achieves improved detection performance, in general.

In this paper, a novel solution for the problem of joint moving target and antenna localization in the distributed multiple-input multiple-output (MIMO) radar systems is proposed. The localization problem in the presence of antenna location uncertainty is formulated as a maximum likelihood (ML) estimation problem, which is then recast into convex form by defining some auxiliary variables and applying semidefinite relation (SDR) technique. Next, an algebraic closed-form estimator is proposed to jointly estimate the target and the antennas error terms and refine their uncertain values. The proposed method is shown analytically and verified by the numerical simulations to be an efficient estimator, which can achieve the Cramer–Rao lower bound (CRLB) performance for both the target and antenna estimations under small error conditions. Furthermore, the results of numerical simulations demonstrate that the proposed estimator outperforms the state-of-the-art methods presented for moving target localization in MIMO radars.

Case-controls studies are popular epidemiological designs for detecting gene–environment interactions in the etiology of complex diseases, where the genetic susceptibility and environmental exposures may often be reasonably assumed independent in the source population. Various papers have presented analytical methods exploiting gene–environment independence to achieve better efficiency, all of which require either a rare disease assumption or a distributional assumption on the genetic variables. We relax both assumptions. We construct a semiparametric estimator in case-control studies exploiting gene–environment independence, while the distributions of genetic susceptibility and environmental exposures are both unspecified and the disease rate is assumed unknown and is not required to be close to zero. The resulting estimator is semiparametric efficient and its superiority over prospective logistic regression, the usual analysis in case-control studies, is demonstrated in various numerical illustrations.

This paper describes a method for estimation and inference with a nonparametric varying coefficients panel data model that allows for cross-sectional dependence and heteroscedasticity, wherein the time series length T is larger than the cross-sectional size N. We first eliminate fixed effects by taking the cross-sectional average, and then use a local linear approach to obtain the initial estimator of the unknown coefficient functions. However, the initial estimator ignores the cross-sectional dependence and heteroscedasticity, which will lead to a loss of efficiency. Thus, we propose a weighted local linear method to obtain a more efficient estimator. In the theoretical part of the paper, we derive the asymptotic theory of the resulting estimator. Simulation results and a real data analysis are provided to illustrate the finite sample performance of the proposed method.

In this study, we have observed some situations in which modified maximum likelihood estimation becomes inappropriate to develop the robust and efficient estimator of the population mean. To cope w...

It is well known that the use of prior information in the logistic regression improves the estimates of regression coefficients when multicollinearity presents. This prior information may be in the form of exact or stochastic linear restrictions. In this article, in the presence of stochastic linear restrictions, we propose a new efficient estimator, named Stochastic restricted optimal logistic estimator for the parameters in the logistic regression models when the multicollinearity presents. Further, conditions for the superiority of the new optimal estimator over some existing estimators are derived with respect to the mean square error matrix sense. Moreover, a Monte Carlo simulation study and a real data example are provided to illustrate the performance of the proposed optimal estimator in the scalar mean square error sense.

Poverty is an important issue that needs to be addressed by all countries. Poverty is related to a group of people earning a low income (lower-tail of the income distribution). In Malaysia, low-income earners are classified as the B40 group. This study aims to describe the behavior of the low-income distribution using the power law model. For this purpose, an inverse Pareto model was applied for describing the lower tail data of Malaysian household income. A robust and efficient estimator, called the probability integral transform statistic estimator, was utilized for estimating the shape parameter of the inverse Pareto distribution. Based on the fitted inverse Pareto model, not all households in the B40 group complied with the power law behavior. However, the power law was able to provide a good description for the group of B40 that was below the poverty line. Based on the inverse Pareto model, the parametric Lorenz curve and the Gini index were derived to provide a robust measure of the income inequality of poor households in Malaysia.

The estimation in a stationary heterogeneous panel model where unknown common factors are present is considered. A two-stage estimator is proposed and compared to existing alternative methods for the estimation of slope parameters in panels with a multifactor error structure. The asymptotic properties of this estimator are provided alongside the comparison of its finite-sample properties with those of a range of estimators by means of Monte Carlo experiments. The two-stage estimator affords a greater computational simplicity with respect to existing iterative estimators that fail to achieve convergence in a relevant number of cases considered. The proposed estimator is employed in the analysis of the determinants of Euro-denominated bonds in a framework of a heterogeneous panel data model with multifactor error structure.

In this paper, we consider the frequency synchronization issue in orthogonal frequency division multiplexing distributed antenna systems. There may exist multiple carrier frequency offsets (CFOs) between the transmitter and distributed receive antennas. To solve the multi-CFO estimation problem, we first derive the blind maximum likelihood estimator, which has superior estimation performance, but exhibits high computational complexity. Furthermore, we develop a blind pairing-based efficient estimator (PBEE), which divides the multiple antennas into pairs of two. The two CFOs in each pair are jointly estimated with a carefully designed cost function, which proves to be exactly a cosine function parameterized by the two CFOs even with the effect of noise. Consequently, the joint estimation of the two CFOs can be simplified to the one-dimensional search optimization problem. The PBEE can achieve better CFO estimation performance than the existing competitors. From the theoretical mean square error (MSE) analysis of PBEE, we further derive the optimal antenna pairing scheme by minimizing the signal-to-noise ratio degradation caused by the uncompensated residual CFOs. Finally, the Cramer-Rao bound of CFO estimation is derived and numerical results are provided to corroborate the proposed studies.

Recent results have proven the minimax optimality of LASSO and related algorithms for noisy linear regression. However, these results tend to rely on variance estimators that are inefficient or optimizations that are slower than LASSO itself. We propose an efficient estimator for the noise variance in high dimensional linear regression that is faster than LASSO, only requiring $p$ matrix-vector multiplications. We prove this estimator is consistent with a good rate of convergence, under the condition that the design matrix satisfies the Restricted Isometry Property (RIP). In practice, our estimator scales incredibly well into high dimensions, is highly parallelizable, and only incurs a modest bias., 17 pages, 7 figures

The quantile residual lifetime function provides comprehensive quantitative measures for residual life, especially when the distribution of the latter is skewed or heavy‐tailed and/or when the data contain outliers. In this paper, we propose a general class of semiparametric quantile residual life models for length‐biased right‐censored data. We use the inverse probability weighted method to correct the bias due to length‐biased sampling and informative censoring. Two estimating equations corresponding to the quantile regressions are constructed in two separate steps to obtain an efficient estimator. Consistency and asymptotic normality of the estimator are established. The main difficulty in implementing our proposed method is that the estimating equations associated with the quantiles are nondifferentiable, and we apply the majorize–minimize algorithm and estimate the asymptotic covariance using an efficient resampling method. We use simulation studies to evaluate the proposed method and illustrate its application by a real‐data example.

Based on the probability integral transform statistic, Finkelstein et al. (2006) have proposed a robust estimator for the shape parameter of Pareto distribution. In this paper, based on the same method, a robust and efficient estimator for the shape parameter of the inverse Pareto distribution is developed assuming that the threshold parameter is known. To study the robustness properties of this new estimator, we derive the asymptotic variance, breakdown point and gross error sensitivity. However, since the inverse Pareto distribution is literally an inverse of the Pareto distribution, some derivations and proofs for the probability integral transform statistic estimator presented in this paper are found closely related to those provided by Finkelstein et al. (2006). The performance of this new estimator and the maximum likelihood estimator is assessed through a simulation study. For the application, an inverse Pareto distribution is fitted to the lower tail data of Malaysian household incomes for the year of 2014, involving the proposed estimator in order to allow for the presence of outliers. Based on the inverse Pareto model, the parametric Lorenz curve is fitted and the Gini coefficient is estimated to measure the income inequality of poor households in Malaysia.

We consider nonlinear heteroscedastic single‐index models where the mean function is a parametric nonlinear model and the variance function depends on a single‐index structure. We develop an efficient estimation method for the parameters in the mean function by using the weighted least squares estimation, and we propose a “delete‐one‐component” estimator for the single‐index in the variance function based on absolute residuals. Asymptotic results of estimators are also investigated. The estimation methods for the error distribution based on the classical empirical distribution function and an empirical likelihood method are discussed. The empirical likelihood method allows for incorporation of the assumptions on the error distribution into the estimation. Simulations illustrate the results, and a real chemical data set is analyzed to demonstrate the performance of the proposed estimators.

We propose a consistent and locally efficient estimator to estimate the model parameters for a logistic mixed effect model with random slopes. Our approach relaxes two typical assumptions: the random effects being normally distributed, and the covariates and random effects being independent of each other. Adhering to these assumptions is particularly difficult in health studies where in many cases we have limited resources to design experiments and gather data in long-term studies, while new findings from other fields might emerge, suggesting the violation of such assumptions. So it is crucial if we could have an estimator robust to such violations and then we could make better use of current data harvested using various valuable resources. Our method generalizes the framework presented in Garcia & Ma (2016) which also deals with a logistic mixed effect model but only considers a random intercept. A simulation study reveals that our proposed estimator remains consistent even when the independence and normality assumptions are violated. This contrasts from the traditional maximum likelihood estimator which is likely to be inconsistent when there is dependence between the covariates and random effects. Application of this work to a Huntington disease study reveals that disease diagnosis can be further improved using assessments of cognitive performance.

When the distribution of the truncation time is known up to a finite-dimensional parameter vector, many researches have been conducted with the objective to improve the efficiency of estimation for nonparametric or semiparametric model with left-truncated and right-censored (LTRC) data. When the distribution of truncation times is unspecified, one approach is to use the conditional maximum likelihood estimators (cMLE) (Chen and Shen in Lifetime Data Anal https://doi.org/10.1007/s10985-016-9385-9 , 2017). Although the cMLE has nice asymptotic properties, it is not efficient since the conditional likelihood function does not incorporate information on the distribution of truncation time. In this article, we aim to develop a more efficient estimator by considering the full likelihood function. Following Turnbull (J R Stat Soc B 38:290–295, 1976) and Qin et al. (J Am Stat Assoc 106:1434–1449, 2011), we treat the unobserved (left-truncated) subpopulation as missing data and propose a two-stage approach for obtaining the pseudo maximum likelihood estimators (PMLE) of regression parameters. In the first stage, the distribution of left truncation time is estimated by the inverse-probability-weighted (IPW) estimator (Wang in J Am Stat Assoc 86:130–143, 1991). In the second stage, we obtain the pseudo complete-data likelihood function by replacing the distribution of truncation time with the IPW estimator in the full likelihood. We propose an expectation–maximization algorithm for obtaining the PMLE and establish the consistency of the PMLE. Simulation results show that the PMLE outperforms the cMLE in terms of mean squared error. The PMLE can also be used to analyze the length-biased data, where the truncation time is uniformly distributed. We demonstrate that the PMLE works more robust against the support assumption of truncation time for length-biased data compared with the MLE proposed by Qin et al. (2011). We apply our proposed method to the channing house data. While the PMLE is quite appealing under specific cases with independent censoring and time-invariant covariates, its applicability, as shown in simulation study, can be rather restricted for more general settings.

This paper mainly addresses maximum likelihood estimation for a response-selective stratified sampling scheme, the basic stratified sampling (BSS), in which the maximum subsample size in each stratum is fixed. We derived the complete-data likelihood for BSS, and extended it as a full-data likelihood by incorporating incomplete data. We also similarly extended the empirical proportion likelihood approach for consistent and efficient estimation. We conducted a simulation study to compare these two new approaches with the existing estimation methods in BSS. Our result indicates that they perform as well as the standard full information likelihood approach. Methods were illustrated using a growth model for fish size at age, including between-individual variability. One of our major conclusions is that the fully observed BSS data, the partially observed data used for stratification, and the sampling strategy are all important in constructing a consistent and efficient estimator.