INFLUENCE ANALYSIS IN NONLINEAR MODELS WITH RANDOM EFFECTS

In this paper,a unified diagnostic method for the nonlinear models with random effects based upon the joint likelihood given by Robinson in 1991 is presented.It is shown that the case deletion model is equivalent to the mean shift outlier model.From this point of view,several diagnostic measures,such as Cook distance,score statistics are derived.The local influence measure of Cook is also presented. A numerical example illustrates that the method is available.

SOME ASYMPTOTIC INFERENCE IN MULTINOMIAL NONLINEAR MODELS (A GEOMERIC APPROACH)

A geometric framework is proposed for multinomial nonlinear modelsbased on a modified version of the geometric structure presented by Bates & Watts[4]. We use this geometric framework to study some asymptotic inference in terms ofcurvatures for multinomial nonlinear models. Our previous results [15] for ordinarynonlinear regression models are extended to multinomial nonlinear models.

INFLUENCE ANALYSIS ON EXPONENTIAL NONLINEAR MODELS WITH RANDOM EFFECTS

This paper presents a unified diagnostic method for exponential nonlinear models with random effects based upon the joint likelihood given by Robinson in 1991. The authors show that the case deletion model is equivalent to mean shift outlier model. From this point of view, several diagnostic measures, such as Cook distance, score statistics are derived. The local influence measure of Cook is also presented. Numerical example illustrates that our method is available.

Rate of strong consistency of the maximum quasi-likelihood estimator in quasi-likelihood nonlinear models

Quasi-likelihood nonlinear models （QLNM） include generalized linear models as a special case. Under some regularity conditions, the rate of the strong consistency of the maximum quasi-likelihood estimation （MQLE） is obtained in QLNM. In an important case, this rate is O（n-^1/2（loglogn）^1/2）, which is just the rate of LIL of partial sums for i.i.d variables, and thus cannot be improved anymore.

Diagnostics in generalized nonlinear models based on maximum L_q-likelihood estimation

In order to detect whether the data conforms to the given model, it is necessary to diagnose the data in the statistical way. The diagnostic problem in generalized nonlinear models based on the maximum Lq-likelihood estimation is considered. Three diagnostic statistics are used to detect whether the outliers exist in the data set. Simulation results show that when the sample size is small, the values of diagnostic statistics based on the maximum Lq-likelihood estimation are greater than the values based on the maximum likelihood estimation. As the sample size increases, the difference between the values of the diagnostic statistics based on two estimation methods diminishes gradually. It means that the outliers can be distinguished easier through the maximum Lq-likelihood method than those through the maximum likelihood estimation method.

SOME ASYMPTOTIC INFERENCE IN QUASI-LIKELIHOOD NONLINEAR MODELS:A GEOMETRIC APPROACH

A modified Bates and Watts geometric framework is proposed for quasi\|likelihood nonlinear models in Euclidean inner product space.Based on the modified geometric framework,some asymptotic inference in terms of curvatures for quasi\|likelihood nonlinear models is studied.Several previous results for nonlinear regression models and exponential family nonlinear models etc.are extended to quasi\|likelihood nonlinear models.

APPROXIMATE POWER OF HETEROSCEDASTICITY TEST IN NONLINEAR MODELS WITH ARIMA（0,1,0） ERRORS

This paper presents an approach for estimating power of the score test, based on an asymptotic approximation to the power of the score test under contiguous alternatives. The method is applied to the problem of power calculations for the score test of heteroscedasticity in European rabbit data （Ratkowsky, 1983）. Simulation studies are presented which indicate that the asymptotic approximation to the finite-sample situation is good over a wide range of parameter configurations.

TESTING FOR VARYING DISPERSION IN DISCRETE EXPONENTIAL FAMILY NONLINEAR MODELS

It is necessary to test for varying dispersion in generalized nonlinear models.Wei,et al(1998) developed a likelihood ratio test,a score test and their adjustments to test for varying dispersion in continuous exponential family nonlinear models.This type of problem in the framework of general discrete exponential family nonlinear models is discussed.Two types of varying dispersion,which are random coefficients model and random effects model,are proposed,and corresponding score test statistics are constructed and expressed in simple,easy to use,matrix formulas.

Variable projection algorithms with sparse constraint for separable nonlinear models

Separable nonlinear models are widely used in various fields such as time series analysis, system modeling, and machine learning, due to their flexible structures and ability to capture nonlinear behavior of data. However, identifying the parameters of these models is challenging, especially when sparse models with better interpretability are desired by practitioners. Previous theoretical and practical studies have shown that variable projection (VP) is an efficient method for identifying separable nonlinear models, but these are based on \(L_2\) penalty of model parameters, which cannot be directly extended to deal with sparse constraint. Based on the exploration of the structural characteristics of separable models, this paper proposes gradient-based and trust-region-based variable projection algorithms, which mainly solve two key problems: how to eliminate linear parameters under sparse constraint;and how to deal with the coupling relationship between linear and nonlinear parameters in the model. Finally, numerical experiments on synthetic data and real time series data are conducted to verify the effectiveness of the proposed algorithms.

Estimation of Treatment Effects in Nonlinear Models with Unobserved Confounding

Estimation of treatment effects is one of the crucial mainstays in economics and sociology studies.The problem will become more serious and complicated if the treatment variable is endogenous for the presence of unobserved confounding.The estimation and conclusion are likely to be biased and misleading if the endogeny of treatment variable is ignored.In this article,we propose the pseudo maximum likelihood method to estimate treatment effects in nonlinear models.The proposed method allows the unobserved confounding and random error terms to exist in an arbitrary relationship(such as,add or multiply),and the unobserved confounding have different influence directions on treatment variables and outcome variables.The proposed estimator is consistent and asymptotically normally distributed.Simulation studies show that the proposed estimator performs better than the special regression estimator,and the proposed method is stable for various distribution of error terms.Finally,the proposed method is applied to the real data that studies the influence of individuals have health insurance on an individual’s decision to visit a doctor.

Nonlinear Characteristic Analysis of Gas-Interconnected Quasi-Zero Stiffness Pneumatic Suspension System:A Theoretical and Experimental Study

Because of significantly changed load and complex and variable driving road conditions of commercial vehicles,pneumatic suspension with lower natural frequencies is widely used in commercial vehicle suspension system.How ever,traditional pneumatic suspension system is hardly to respond the greatly changed load of commercial vehicles To address this issue,a new Gas-Interconnected Quasi-Zero Stiffness Pneumatic Suspension(GIQZSPS)is presented in this paper to improve the vibration isolation performance of commercial vehicle suspension systems under frequent load changes.This new structure adds negative stiffness air chambers on traditional pneumatic suspension to reduce the natural frequency of the suspension.It can adapt to different loads and road conditions by adjusting the solenoid valves between the negative stiffness air chambers.Firstly,a nonlinear mechanical model including the dimensionless stiffness characteristic and interconnected pipeline model is derived for GIQZSPS system.By the nonlinear mechanical model of GIQZSPS system,the force transmissibility rate is chosen as the evaluation index to analyze characteristics.Furthermore,a testing bench simulating 1/4 GIQZSPS system is designed,and the testing analysis of the model validation and isolating performance is carried out.The results show that compared to traditional pneumatic suspension,the GIQZSPS designed in the article has a lower natural frequency.And the system can achieve better vibration isolation performance under different load states by switching the solenoid valves between air chambers.

Smoothed Empirical Likelihood Inference for Nonlinear Quantile Regression Models with Missing Response

In this paper, three smoothed empirical log-likelihood ratio functions for the parameters of nonlinear models with missing response are suggested. Under some regular conditions, the corresponding Wilks phenomena are obtained and the confidence regions for the parameter can be constructed easily.

Comparison of nonlinear modeling methods for the composite rubber clamp

The cubic stiffness force model(CSFM)and Bouc-Wen model(BWM)are introduced and compared innovatively.The unknown coefficients of the nonlinear models are identified by the genetic algorithm combined with experiments.By fitting the identified nonlinear coefficients under different excitation amplitudes,the nonlinear vibration responses of the system are predicted.The results show that the accuracy of the BWM is higher than that of the CSFM,especially in the non-resonant region.However,the optimization time of the BWM is longer than that of the CSFM.

TESTING FOR VARYING DISPERSION OF LONGITUDINAL BINOMIAL DATA IN NONLINEAR LOGISTIC MODELS WITH RANDOM EFFECTS

In this paper, it is discussed that two tests for varying dispersion of binomial data in the framework of nonlinear logistic models with random effects, which are widely used in analyzing longitudinal binomial data. One is the individual test and power calculation for varying dispersion through testing the randomness of cluster effects, which is extensions of Dean(1992) and Commenges et al (1994). The second test is the composite test for varying dispersion through simultaneously testing the randomness of cluster effects and the equality of random-effect means. The score test statistics are constructed and expressed in simple, easy to use, matrix formulas. The authors illustrate their test methods using the insecticide data (Giltinan, Capizzi & Malani (1988)).

Consistency and Asymptotic Normality of the Maximum Quasi-likelihood Estimator in Quasi-likelihood Nonlinear Models with Random Regressors

This paper proposes some regularity conditions, which result in the existence, strong consistency and asymptotic normality of maximum quasi-likelihood estimator （MQLE） in quasi-likelihood nonlinear models （QLNM） with random regressors. The asymptotic results of generalized linear models （GLM） with random regressors are generalized to QLNM with random regressors.

Strong Consistency of Maximum Quasi-Likelihood Estimator in Quasi-Likelihood Nonlinear Models

This paper proposes some regularity conditions. On the basis of the proposed regularity conditions, we show the strong consistency of maximum quasi-likelihood estimation （MQLE） in quasi-likelihood nonlinear models （QLNM）. Our results may be regarded as a further generalization of the relevant results in Ref. [4].

Consistency and asymptotic normality of profilekernel and backfitting estimators in semiparametric reproductive dispersion nonlinear models

Semiparametric reproductive dispersion nonlinear model (SRDNM) is an extension of nonlinear reproductive dispersion models and semiparametric nonlinear regression models, and includes semiparametric nonlinear model and semiparametric generalized linear model as its special cases. Based on the local kernel estimate of nonparametric component, profile-kernel and backfitting estimators of parameters of interest are proposed in SRDNM, and theoretical comparison of both estimators is also investigated in this paper. Under some regularity conditions, strong consistency and asymptotic normality of two estimators are proved. It is shown that the backfitting method produces a larger asymptotic variance than that for the profile-kernel method. A simulation study and a real example are used to illustrate the proposed methodologies.

Statistical estimation in partially nonlinear models with random effects

In this article, a partially nonlinear model with random effects is proposed and its new estimation procession is provided. In order to estimate the link function, we propose generalised leastsquare estimate and B-splines estimate methods. Further, we also use the Gauss–Newton methodto construct the estimates of unknown parameters. Finally, we also consider the estimation forthe variance components. The consistency and the asymptotic normality of the estimator will beproved. Simulated and real examples are given to illustrate our proposed methodology, whichshows that our methods give effective estimation.

Maximal and total skew information for a two-qubit system using nonlinear interaction models

Maximal and total skew information is studied. For symmetric pure states of two-qubit, they are closely related to the linear entropy, the concurrence, and the spin squeezing parameter. For a two-qubit system implemented in three nonlinear interaction models with an external field, we give the exact state vectors and the expectation value （Sz） at any time t. Based on （Sz）2, we give the maximal and the total skew information and a condition in which the maximal and the total skew information can reach 1 and 2, respectively.

ON CONFIDENCE REGIONS OF SEMIPARAMETRIC NONLINEAR REGRESSION MODELS(A GEOMETRIC APPROACH)

A geometric framework is proposed for semiparametric nonlinear regression models based on the concept of least favorable curve, introduced by Severini and Wong (1992). The authors use this framework to drive three kinds of improved approximate confidence regions for the parameter and parameter subset in terms of curvatures. The results obtained by Hamilton et al. (1982), Hamilton (1986) and Wei (1994) are extended to semiparametric nonlinear regression models.