CONSERVATIVE ESTIMATING FUNCTION IN THE NONLINEAR REGRESSION MODEL WITH AGGREGATED DATA

The purpose of this paper is to study the theory of conservative estimating functions in nonlinear regression model with aggregated data. In this model, a quasi-score function with aggregated data is defined. When this function happens to be conservative, it is projection of the true score function onto a class of estimation functions. By constructing, the potential function for the projected score with aggregated data is obtained, which have some properties of log-likelihood function.

A Study of EM Algorithm as an Imputation Method: A Model-Based Simulation Study with Application to a Synthetic Compositional Data

Compositional data, such as relative information, is a crucial aspect of machine learning and other related fields. It is typically recorded as closed data or sums to a constant, like 100%. The statistical linear model is the most used technique for identifying hidden relationships between underlying random variables of interest. However, data quality is a significant challenge in machine learning, especially when missing data is present. The linear regression model is a commonly used statistical modeling technique used in various applications to find relationships between variables of interest. When estimating linear regression parameters which are useful for things like future prediction and partial effects analysis of independent variables, maximum likelihood estimation (MLE) is the method of choice. However, many datasets contain missing observations, which can lead to costly and time-consuming data recovery. To address this issue, the expectation-maximization (EM) algorithm has been suggested as a solution for situations including missing data. The EM algorithm repeatedly finds the best estimates of parameters in statistical models that depend on variables or data that have not been observed. This is called maximum likelihood or maximum a posteriori (MAP). Using the present estimate as input, the expectation (E) step constructs a log-likelihood function. Finding the parameters that maximize the anticipated log-likelihood, as determined in the E step, is the job of the maximization (M) phase. This study looked at how well the EM algorithm worked on a made-up compositional dataset with missing observations. It used both the robust least square version and ordinary least square regression techniques. The efficacy of the EM algorithm was compared with two alternative imputation techniques, k-Nearest Neighbor (k-NN) and mean imputation (), in terms of Aitchison distances and covariance.

ESTIMATION FOR THE AYMPTOTIC VARIANCE OF PARAMETRIC ESTIMATES IN PARTIAL LINEAR MODEL WITH CENSORED DATA

Consider tile partial linear model Y=Xβ+ g(T) + e. Wilers Y is at risk of being censored from the right, g is an unknown smoothing function on [0,1], β is a 1-dimensional parameter to be estimated and e is an unobserved error. In Ref[1,2], it wes proved that the estimator for the asymptotic variance of βn(βn) is consistent. In this paper, we establish the limit distribution and the law of the iterated logarithm for,En, and obtain the convergest rates for En and the strong uniform convergent rates for gn(gn).

EMPIRICAL LIKELIHOOD-BASED INFERENCE IN LINEAR MODELS WITH INTERVAL CENSORED DATA

An empirical likelihood approach to estimate the coefficients in linear model with interval censored responses is developed in this paper. By constructing unbiased transformation of interval censored data,an empirical log-likelihood function with asymptotic X^2 is derived. The confidence regions for the coefficients are constructed. Some simulation results indicate that the method performs better than the normal approximation method in term of coverage accuracies.

ESTIMATORS AND SOME BEHAVIORS FORA PARTIALLY LINEAR MODEL WITH CENSORED DATA

This paper considers the local linear regression estimators for partially linear model with censored data. Which have some nice large-sample behaviors and are easy to implement. By many simulation runs, the author also found that the estimators show remarkable in the small sample case yet.

Empirical Likelihood Inference for Generalized Partially Linear Models with Longitudinal Data

In this article, we propose a generalized empirical likelihood inference for the parametric component in semiparametric generalized partially linear models with longitudinal data. Based on the extended score vector, a generalized empirical likelihood ratios function is defined, which integrates the within-cluster?correlation meanwhile avoids direct estimating the nuisance parameters in the correlation matrix. We show that the proposed statistics are asymptotically?Chi-squared under some suitable conditions, and hence it can be used to construct the confidence region of parameters. In addition, the maximum empirical likelihood estimates of parameters and the corresponding asymptotic normality are obtained. Simulation studies demonstrate the performance of the proposed method.

Database-oriented storage based on LMDB and linear octree for massive block model

Data organization requires high efficiency for large amount of data applied in the digital mine system. A new method of storing massive data of block model is proposed to meet the characteristics of the database, including ACID-compliant, concurrency support, data sharing, and efficient access. Each block model is organized by linear octree, stored in LMDB（lightning memory-mapped database）. Geological attribute can be queried at any point of 3D space by comparison algorithm of location code and conversion algorithm from address code of geometry space to location code of storage. The performance and robustness of querying geological attribute at 3D spatial region are enhanced greatly by the transformation from 3D to 2D and the method of 2D grid scanning to screen the inner and outer points. Experimental results showed that this method can access the massive data of block model, meeting the database characteristics. The method with LMDB is at least 3 times faster than that with etree, especially when it is used to read. In addition, the larger the amount of data is processed, the more efficient the method would be.

The Improvement Made by a Modified TLM in 4DVAR with a Geophysical Boundary Layer Model

The strong nonlinearity of boundary layer parameterizations in atmospheric and oceanic models can cause difficulty for tangent linear models in approximating nonlinear perturbations when the time integration grows longer. Consequently, the related 4—D variational data assimilation problems could be difficult to solve. A modified tangent linear model is built on the Mellor-Yamada turbulent closure (level 2.5) for 4-D variational data assimilation. For oceanic mixed layer model settings, the modified tangent linear model produces better finite amplitude, nonlinear perturbation than the full and simplified tangent linear models when the integration time is longer than one day. The corresponding variational data assimilation performances based on the adjoint of the modified tangent linear model are also improved compared with those adjoints of the full and simplified tangent linear models.

ASYMPTOTIC PROPERTIES OF ESTIMATORS IN PARTIALLY LINEAR SINGLE-INDEX MODEL FOR LONGITUDINAL DATA

In this article, a partially linear single-index model /or longitudinal data is investigated. The generalized penalized spline least squares estimates of the unknown parameters are suggested. All parameters can be estimated simultaneously by the proposed method while the feature of longitudinal data is considered. The existence, strong consistency and asymptotic normality of the estimators are proved under suitable conditions. A simulation study is conducted to investigate the finite sample performance of the proposed method. Our approach can also be used to study the pure single-index model for longitudinal data.

Use of Linear Spectral Mixture Model to Estimate Rice Planted Area Based on MODIS Data

MODIS （Moderate Resolution Imaging Spectroradiometer） is a key instrument aboard the Terra （EOS AM） and Aqua （EOS PM） satellites. Linear spectral mixture models are applied to MOIDS data for the sub-pixel classification of land covers. Shaoxing county of Zhejiang Province in China was chosen to be the study site and early rice was selected as the study crop. The derived proportions of land covers from MODIS pixel using linear spectral mixture models were compared with unsupervised classification derived from TM data acquired on the same day, which implies that MODIS data could be used as satellite data source for rice cultivation area estimation, possibly rice growth monitoring and yield forecasting on the regional scale.

Data perturbation analysis of a linear model

The linear model features were carefully studied in the cases of data perturbation and mean shift perturbation. Some important features were also proved mathematically. The results show that the mean shift perturbation is equivalent to the data perturbation, that is, adding a parameter to an observation equation means that this set of data is deleted from the data set. The estimate of this parameter is its predicted residual in fact.

ROBUST ESTIMATION IN PARTIAL LINEAR MIXED MODEL FOR LONGITUDINAL DATA

In this article, robust generalized estimating equation for the analysis of partial linear mixed model for longitudinal data is used. The authors approximate the nonparametric function by a regression spline. Under some regular conditions, the asymptotic properties of the estimators are obtained. To avoid the computation of high-dimensional integral, a robust Monte Carlo Newton-Raphson algorithm is used. Some simulations are carried out to study the performance of the proposed robust estimators. In addition, the authors also study the robustness and the efficiency of the proposed estimators by simulation. Finally, two real longitudinal data sets are analyzed.

On use of the alpha stable self-similar stochastic process to model aggregated VBR video traffic

The alpha stable self-similar stochastic process has been proved an effective model for high variable data traffic. A deep insight into some special issues and considerations on use of the process to model aggregated VBR video traffic is made. Different methods to estimate stability parameter a and self-similar parameter H are compared. Processes to generate the linear fractional stable noise （LFSN） and the alpha stable random variables are provided. Model construction and the quantitative comparisons with fractional Brown motion （FBM） and real traffic are also examined. Open problems and future directions are also given with thoughtful discussions.

An analysis of longitudinal binary data using generalized linear models

Objective: To analyze longitudinal binary data by using generalized linear models. The correlation between repeated measures were considered. The general method for analyzing longitudinal binary data was given. Methods: Generalized estimating equations (GEE) proposed by Zeger and Liang was used. For sevens covariance structures, one method was given for estimating regression and correlation parameters. Results: Regression and coerelation parameters were estimated simultaneously. A Set of program was finished and an example was illustrated. Conclusion: Longitudinal dsta often occur in medical researches and clinical trials. For solving the problem of correlation between repeated measures, it is necessary to use some special methods to cope with this Kind of data.

Clustered Federated Learning with Weighted Model Aggregation for Imbalanced Data

As a promising edge learning framework in future 6G networks,federated learning(FL)faces a number of technical challenges due to the heterogeneous network environment and diversified user behaviors.Data imbalance is one of these challenges that can significantly degrade the learning efficiency.To deal with data imbalance issue,this work proposes a new learning framework,called clustered federated learning with weighted model aggregation(weighted CFL).Compared with traditional FL,our weighted CFL adaptively clusters the participating edge devices based on the cosine similarity of their local gradients at each training iteration,and then performs weighted per-cluster model aggregation.Therein,the similarity threshold for clustering is adaptive over iterations in response to the time-varying divergence of local gradients.Moreover,the weights for per-cluster model aggregation are adjusted according to the data balance feature so as to speed up the convergence rate.Experimental results show that the proposed weighted CFL achieves a faster model convergence rate and greater learning accuracy than benchmark methods under the imbalanced data scenario.

A two-step rectification algorithm for airborne linear images with POS data

Rectification for airborne linear images is an indispensable preprocessing step. This paper presents in detail a two-step rectification algorithm. The first step is to establish the model of direct georeference position using the data provided by the Po- sitioning and Orientation System (POS) and obtain the mathematical relationships between the image points and ground reference points. The second step is to apply polynomial distortion model and Bilinear Interpolation to get the final precise rectified images. In this step, a reference image is required and some ground control points (GCPs) are selected. Experiments showed that the final rectified images are satisfactory, and that our two-step rectification algorithm is very effective.

Shrinkage Estimation of Semiparametric Model with Missing Responses for Cluster Data

This paper simultaneously investigates variable selection and imputation estimation of semiparametric partially linear varying-coefficient model in that case where there exist missing responses for cluster data. As is well known, commonly used approach to deal with missing data is complete-case data. Combined the idea of complete-case data with a discussion of shrinkage estimation is made on different cluster. In order to avoid the biased results as well as improve the estimation efficiency, this article introduces Group Least Absolute Shrinkage and Selection Operator (Group Lasso) to semiparametric model. That is to say, the method combines the approach of local polynomial smoothing and the Least Absolute Shrinkage and Selection Operator. In that case, it can conduct nonparametric estimation and variable selection in a computationally efficient manner. According to the same criterion, the parametric estimators are also obtained. Additionally, for each cluster, the nonparametric and parametric estimators are derived, and then compute the weighted average per cluster as finally estimators. Moreover, the large sample properties of estimators are also derived respectively.

Some Additional Moment Conditions for a Dynamic Count Panel Data Model with Predetermined Explanatory Variables

This paper proposes some additional moment conditions for the linear feedback model with explanatory variables being predetermined, which is proposed by [1] for the purpose of dealing with count panel data. The newly proposed moment conditions include those associated with the equidispersion, the Negbin I-type model and the stationarity. The GMM estimators are constructed incorporating the additional moment conditions. Some Monte Carlo experiments indicate that the GMM estimators incorporating the additional moment conditions perform well, compared to that using only the conventional moment conditions proposed by [2,3].

Zero Truncated Bivariate Poisson Model: Marginal-Conditional Modeling Approach with an Application to Traffic Accident Data

A new covariate dependent zero-truncated bivariate Poisson model is proposed in this paper employing generalized linear model. A marginal-conditional approach is used to show the bivariate model. The proposed model with estimation procedure and tests for goodness-of-fit and under (or over) dispersion are shown and applied to road safety data. Two correlated outcome variables considered in this study are number of cars involved in an accident and number of casualties for given number of cars.

Fault tolerant synchronization of chaotic systems based on T-S fuzzy model with fuzzy sampled-data controller

In this paper the fault tolerant synchronization of two chaotic systems based on fuzzy model and sample data is investigated. The problem of fault tolerant synchronization is formulated to study the global asymptotical stability of the error system with the fuzzy sampled-data controller which contains a state feedback controller and a fault compensator. The synchronization can be achieved no matter whether the fault occurs or not. To investigate the stability of the error system and facilitate the design of the fuzzy sampled-data controller, a Takagi Sugeno （T-S） fuzzy model is employed to represent the chaotic system dynamics. To acquire good performance and produce a less conservative analysis result, a new parameter-dependent Lyapunov-Krasovksii functional and a relaxed stabilization technique are considered. The stability conditions based on linear matrix inequality are obtained to achieve the fault tolerant synchronization of the chaotic systems. Finally, a numerical simulation is shown to verify the results.