Sliced Average Variance Estimation for Tensor Data

Tensor data have been widely used in many fields,e.g.,modern biomedical imaging,chemometrics,and economics,but often suffer from some common issues as in high dimensional statistics.How to find their low-dimensional latent structure has been of great interest for statisticians.To this end,we develop two efficient tensor sufficient dimension reduction methods based on the sliced average variance estimation(SAVE)to estimate the corresponding dimension reduction subspaces.The first one,entitled tensor sliced average variance estimation(TSAVE),works well when the response is discrete or takes finite values,but is not■consistent for continuous response;the second one,named bias-correction tensor sliced average variance estimation(CTSAVE),is a de-biased version of the TSAVE method.The asymptotic properties of both methods are derived under mild conditions.Simulations and real data examples are also provided to show the superiority of the efficiency of the developed methods.

Linear minimum variance estimation fusion

This paper shows that a general multisensor unbiased linearly weighted estimation fusion essentially is the linear minimum variance (LMV) estimation with linear equality constraint, and the general estimation fusion formula is developed by extending the Gauss-Markov estimation to the random parameter under estimation. First, we formulate the problem of distributed estimation fusion in the LMV setting. In this setting, the fused estimator is a weighted sum of local estimates with a matrix weight. We show that the set of weights is optimal if and only if it is a solution of a matrix quadratic optimization problem subject to a convex linear equality constraint. Second, we present a unique solution to the above optimization problem, which depends only on the covariance matrix Ck.Third, if a priori information, the expectation and covariance, of the estimated quantity is unknown, a necessary and sufficient condition for the above LMV fusion becoming the best unbiased LMV estimation with known prior information as the above is presented. We also discuss the generality and usefulness of the LMV fusion formulas developed. Finally, we provide an off-line recursion of Ck for a class of multisensor linear systems with coupled measurement noises.

Nonlinear total least-squares variance component estimation for GM(1,1)model

The solution of the grey model(GM(1,1)model)generally involves equal-precision observations,and the(co)variance matrix is established from the prior information.However,the data are generally available with unequal-precision measurements in reality.To deal with the errors of all observations for GM(1,1)model with errors-in-variables(EIV)structure,we exploit the total least-squares(TLS)algorithm to estimate the parameters of GM(1,1)model in this paper.Ignoring that the effect of the improper prior stochastic model and the homologous observations may degrade the accuracy of parameter estimation,we further present a nonlinear total least-squares variance component estimation approach for GM(1,1)model,which resorts to the minimum norm quadratic unbiased estimation(MINQUE).The practical and simulative experiments indicate that the presented approach has significant merits in improving the predictive accuracy in comparison with control methods.

Robust Variance Components Estimation in the PERG Mixed Distributions of Empirical Variances—PEROBVC Method

A mixed distribution of empirical variances, composed of two distributions the basic and contaminating ones, and referred to as PERG mixed distribution of empirical variances, is considered. In the paper a robust inverse problem solution is given, namely a (new) robust method for estimation of variances of both distributions—PEROBVC Method, as well as the estimates for the numbers of observations for both distributions and, in this way also the estimate of contamination degree.

A New Class of L-Moments Based Calibration Variance Estimators

Variance is one of themost important measures of descriptive statistics and commonly used for statistical analysis.The traditional second-order central moment based variance estimation is a widely utilized methodology.However,traditional variance estimator is highly affected in the presence of extreme values.So this paper initially,proposes two classes of calibration estimators based on an adaptation of the estimators recently proposed by Koyuncu and then presents a new class of L-Moments based calibration variance estimators utilizing L-Moments characteristics(L-location,Lscale,L-CV)and auxiliary information.It is demonstrated that the proposed L-Moments based calibration variance estimators are more efficient than adapted ones.Artificial data is considered for assessing the performance of the proposed estimators.We also demonstrated an application related to apple fruit for purposes of the article.Using artificial and real data sets,percentage relative efficiency(PRE)of the proposed class of estimators with respect to adapted ones are calculated.The PRE results indicate to the superiority of the proposed class over adapted ones in the presence of extreme values.In this manner,the proposed class of estimators could be applied over an expansive range of survey sampling whenever auxiliary information is available in the presence of extreme values.

L-Moments Based Calibrated Variance Estimators Using Double Stratified Sampling

Variance is one of the most vital measures of dispersion widely employed in practical aspects.A commonly used approach for variance estimation is the traditional method of moments that is strongly influenced by the presence of extreme values,and thus its results cannot be relied on.Finding momentum from Koyuncu’s recent work,the present paper focuses first on proposing two classes of variance estimators based on linear moments(L-moments),and then employing them with auxiliary data under double stratified sampling to introduce a new class of calibration variance estimators using important properties of L-moments(L-location,L-cv,L-variance).Three populations are taken into account to assess the efficiency of the new estimators.The first and second populations are concerned with artificial data,and the third populations is concerned with real data.The percentage relative efficiency of the proposed estimators over existing ones is evaluated.In the presence of extreme values,our findings depict the superiority and high efficiency of the proposed classes over traditional classes.Hence,when auxiliary data is available along with extreme values,the proposed classes of estimators may be implemented in an extensive variety of sampling surveys.

Sampling Error Estimation in Stratified Surveys

Many operations carried out by official statistical institutes use large-scale surveys obtained by stratified random sampling without replacement. Variables commonly examined in this type of surveys are binary, categorical and continuous, and hence, the estimates of interest involve estimates of proportions, totals and means. The problem of approximating the sampling relative error of this kind of estimates is studied in this paper. Some new jackknife methods are proposed and compared with plug-in and bootstrap methods. An extensive simulation study is carried out to compare the behavior of all the methods considered in this paper.

DISTRIBUTED MONITORING SYSTEM RELIABILITY ESTIMATION WITH CONSIDERATION OF STATISTICAL UNCERTAINTY

Taking into account the whole system structure and the component reliability estimation uncertainty, a system reliability estimation method based on probability and statistical theory for distributed monitoring systems is presented. The variance and confidence intervals of the system reliability estimation are obtained by expressing system reliability as a linear sum of products of higher order moments of component reliability estimates when the number of component or system survivals obeys binomial distribution. The eigenfunction of binomial distribution is used to determine the moments of component reliability estimates, and a symbolic matrix which can facilitate the search of explicit system reliability estimates is proposed. Furthermore, a case of application is used to illustrate the procedure, and with the help of this example, various issues such as the applicability of this estimation model, and measures to improve system reliability of monitoring systems are discussed.

A Geometric Approach to Conditioning and the Search for Minimum Variance Unbiased Estimators

Our purpose is twofold: to present a prototypical example of the conditioning technique to obtain the best estimator of a parameter and to show that this technique resides in the structure of an inner product space. The technique uses conditioning of an unbiased estimator on a sufficient statistic. This procedure is founded upon the conditional variance formula, which leads to an inner product space and a geometric interpretation. The example clearly illustrates the dependence on the sampling methodology. These advantages show the power and centrality of this process.

Comparison of REML and MINQUE for Estimated Variance Components and Predicted Random Effects

Linear mixed model (LMM) approaches have been widely applied in many areas of research data analysis because they offer great flexibility for different data structures and linear model systems. In this study, emphasis is placed on comparing the properties of two LMM approaches: restricted maximum likelihood (REML) and minimum norm quadratic unbiased estimation (MINQUE) with and without resampling techniques being included. Bias, testing power, Type I error, and computing time were compared between REML and MINQUE approaches with and without Jackknife technique based on 500 simulated data sets. Results showed that MINQUE and REML methods performed equally regarding bias, Type I error, and power. Jackknife-based MINQUE and REML greatly improved power compared to non-Jackknife based linear mixed model approaches. Results also showed that MINQUE is more time-saving compared to REML, especially with the use of resampling techniques and large data set analysis. Results from the actual cotton data analysis were in agreement with our simulated results. Therefore, Jackknife-based MINQUE approaches could be recommended to achieve desirable power with reduced time for a large data analysis and model simulations.

Recent Advances in the Geodesy Data Processing

Geodetic functional models,stochastic models,and model parameter estimation theory are fundamental for geodetic data processing.In the past five years,through the unremitting efforts of Chinese scholars in the field of geodetic data processing,according to the application and practice of geodesy,they have made significant contributions in the fields of hypothesis testing theory,un-modeled error,outlier detection,and robust estimation,variance component estimation,complex least squares,and ill-posed problems treatment.Many functional models such as the nonlinear adjustment model,EIV model,and mixed additive and multiplicative random error model are also constructed and improved.Geodetic data inversion is an important part of geodetic data processing,and Chinese scholars have done a lot of work in geodetic data inversion in the past five years,such as seismic slide distribution inversion,intelligent inversion algorithm,multi-source data joint inversion,water reserve change and satellite gravity inversion.This paper introduces the achievements of Chinese scholars in the field of geodetic data processing in the past five years,analyzes the methods used by scholars and the problems solved,and looks forward to the unsolved problems in geodetic data processing and the direction that needs further research in the future.

The mathematical weighting of GNSS observations based on different types of receivers/antennas and environmental conditions

Stochastic models play an important role in achieving high accuracy in positioning,the ideal estimator in the least-squares(LS)can be obtained only by using the suitable stochastic model.This study investigates the role of variance component estimation(VCE)in the LS method for Precise Point Positioning(PPP).This estimation is performed by considering the ionospheric-free(IF)functional model for code and the phase observation of Global Positioning System(GPS).The strategy for estimating the accuracy of these observations was evaluated to check the effect of the stochastic model in four modes:a)antenna type,b)receiver type,c)the tropospheric effect,and d)the ionosphere effect.The results show that using empirical variance for code and phase observations in some cases caused erroneous estimation of unknown components in the PPP model.This is because a constant empirical variance may not be suitable for various receivers and antennas under different conditions.Coordinates were compared in two cases using the stochastic model of nominal weight and weight estimated by LS-VCE.The position error difference for the east-west,north-south,and height components was 1.5 cm,4 mm,and 1.8 cm,respectively.Therefore,weight estimation with LS-VCE can provide more appropriate results.Eventually,the convergence time based on four elevation-dependent models was evaluated using nominal weight and LS-VCE weight.According to the results,the LS-VCE has a higher convergence rate than the nominal weight.The weight estimation using LS-VCE improves the convergence time in four elevation-dependent models by 11,13,12,and 9 min,respectively.

Variable Selection of Partially Linear Single-index Models

In this article, we study the variable selection of partially linear single-index model(PLSIM). Based on the minimized average variance estimation, the variable selection of PLSIM is done by minimizing average variance with adaptive l1 penalty. Implementation algorithm is given. Under some regular conditions, we demonstrate the oracle properties of aLASSO procedure for PLSIM. Simulations are used to investigate the effectiveness of the proposed method for variable selection of PLSIM.

Self-tuning weighted measurement fusion Kalman filter and its convergence

For multisensor systems,when the model parameters and the noise variances are unknown,the consistent fused estimators of the model parameters and noise variances are obtained,based on the system identification algorithm,correlation method and least squares fusion criterion.Substituting these consistent estimators into the optimal weighted measurement fusion Kalman filter,a self-tuning weighted measurement fusion Kalman filter is presented.Using the dynamic error system analysis （DESA） method,the convergence of the self-tuning weighted measurement fusion Kalman filter is proved,i.e.,the self-tuning Kalman filter converges to the corresponding optimal Kalman filter in a realization.Therefore,the self-tuning weighted measurement fusion Kalman filter has asymptotic global optimality.One simulation example for a 4-sensor target tracking system verifies its effectiveness.

Improving Energy and Power Efficiency Using NComputing and Approaches for Predicting Reliability of Complex Computing Systems

Opting to follow the computing-design philosophy that the best way to reduce power consumption and increase energy efficiency is to reduce waste, we propose an architecture with a very simple ready-implementation by using an NComputing device that can allow multi-users but only one computer is needed. This intuitively can save energy, space as well as cost. In this paper, we propose a simple and realistic NComputing architecture to study the energy and power-efficient consumption of desktop computer systems by using the NComputing device. We also propose new approaches to estimate the reliability of k-out-of-n systems based on the delta method. The k-out-of-n system consisting of n subsystems works if and only if at least k-of-the-n subsystems work. More specificly, we develop approaches to obtain the reliability estimation for the k-out-of-n systems which is composed of n independent and identically distributed subsystems where each subsystem （or energy-efficient usage application） can be assumed to follow a two-parameter exponential lifetime distribution function. The detailed derivations of reliability estimation of k-out-of-n systems based on the biased-corrected estimator, known as delta method, the uniformly minimum variance unbiased estimate （UMVUE） and maximum likelihood estimate （MLE） are discussed. An energy-management NComputing application is discussed to illustrate the reliability results in terms of the energy consumption usages of a computer system with qua（t-core, 8 GB of RAM, and a GeForce 9800GX-2 graphics card to perform various complex applications. The estimated reliability values of systems based on the UMVUE and the delta method differ only slightly. Often the UMVUE of reliability for a complex system is a lot more difficult to obtain, if not impossible. The delta method seems to be a simple and better approach to obtain the reliability estimation of complex systems. The results of this study also show that, in practice, the NComputing architecture improves both energy cost saving and energy efficient living spaces.

Model-free adaptive robust control method for high-speed trains

Aiming at the robustness issue in high-speed trains(HSTs)operation control,this article proposes a model-free adaptive control(MFAC)scheme to suppress disturbance.Firstly,the dynamic linearization data model of train system under the action of measurement disturbance is given,and the Kalman filter(KF)based on this model is derived under the minimum variance estimation criterion.Then,according to the KF,an anti-interference MFAC scheme is designed.This scheme only needs the input and output data of the controlled system to realize the MFAC of the train under strong disturbance.Finally,the simulation experiment of CRH380A HSTs is carried out and compared with the traditional MFAC and the MFAC with attenuation factor.The proposed control algorithm can effectively suppress the measurement disturbance,and obtain smaller tracking error and larger signal to noise ratio with better applicability.

Binomial Proportion Estimation in Longitudinal Data with Non-ignorable Non-response

Non-random missing data poses serious problems in longitudinal studies. The binomial distribution parameter becomes to be unidentifiable without any other auxiliary information or assumption when it suffers from ignorable missing data. Existing methods are mostly based on the log-linear regression model. In this article, a model is proposed for longitudinal data with non-ignorable non-response. It is considered to use the pre-test baseline data to improve the identifiability of the post-test parameter. Furthermore, we derive the identified estimation （IE）, the maximum likelihood estimation （MLE） and its associated variance for the post-test parameter. The simulation study based on the model of this paper shows that the proposed approach gives promising results.

Model-based small area estimation with no samples within the areas,by benchmarking to marginal cross-sectional and time-series estimates

Official monthly U.S.labour force estimation at the sub-State level(mostly counties)is based on what is known as the‘Handbook’(HB)method,one of the earliest uses of administrative data for small area estimation.The administrative data,however,are poor in coverage and have conceptual deficiencies.Past attempts to correct for the resulting bias of the HB estimates by informal(implicit)modelling have not been successful,due to the absence of regular direct monthly survey estimates at the sub-State level.Benchmarking the sub-State HB estimates each month to the State model dependent estimates helps to correct for an overall bias,but not in individual areas.In this article we propose benchmarking additionally to the annual model-dependent area estimates.The annual models include known administrative data as covariates,and are used to define corresponding monthly sub-State models,which in turn enable producing monthly synthetic estimates as possible substitutes for the HB estimates in real time production.Variance estimates,which account for sampling errors and the errors of the model dependent estimators are developed.Data for sub-State areas in the State of Arizona are used for illustration.Although the methodology developed in this article stems from a particular(but very important)application,it is general and applicable to other similar problems.

Performance analysis of SBAS ephemeris corrections and integrity algorithms in China region

Satellite Based Augmentation Systems(SBASs)improve the positioning accuracy and integrity by broadcasting to the civil aviation community the corrections and integrity parameters.A snapshot algorithm based on the minimum variance estimation is investigated in this study to calculate the satellite clock and orbit corrections.A chi-square test is performed on the remaining errors in the corrected ephemeris to guarantee the integrity.User Differential Range Error(UDRE)and scaling matrix contained in Message Type 28 are derived using the covariance information based on the assumption that one of the reference stations failed.A software package is developed and applied in the real data collected at 26 stations.International GNSS(Global Navigation Satellite System)Service(IGS)precise clock and orbit products are taken as the references to assess the accuracy of corrections.For both Global Positioning System(GPS)and BeiDou Navigation Satellite System(BDS),the range accuracy of 0.10 m can be achieved with the employment of the derived corrections.No obvious performance difference between GPS and BDS is found.UDREs for all visible satellites are generated with the maximum index of 12 and minimum index of 3.The geometric range differences calculated with IGS precise products and broadcast ephemeris are employed to assess the integrity of UDRE.It is found that the UDRE is able to bound the residuals with 99.9%confidence which meet the requirement of aviation users.With ionospheric delay corrected by Global Ionosphere Map(GIM),the positioning accuracy of 0.98 m with GPS corrections and 0.80 m with multi-constellation augmentation can be achieved which indicates a significant improvement of GPS standalone results.

Multimodel inference based on smoothed information criteria

The multimodel inference makes statistical inferences from a set of plausible models rather than from a single model.In this paper,we focus on the multimodel inference based on smoothed information criteria proposed by seminal monographs(see Buckland et al.(1997)and Burnham and Anderson(2003)),which are termed as smoothed Akaike information criterion(SAIC)and smoothed Bayesian information criterion(SBIC)methods.Due to their simplicity and applicability,these methods are very widely used in many fields.By using an illustrative example and deriving limiting properties for the weights in the linear regression,we find that the existing variance estimation for SAIC is not applicable because of a restrictive condition,but for SBIC it is applicable.Especially,we propose a simulation-based inference for SAIC based on the limiting properties.Both the simulation study and the real data example show the promising performance of the proposed simulationbased inference.