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To compare clinical effects of different postoperative rehabilitation modes on lumbar degenerative diseases, and explore influence of rehabilitation mode and other factors on postoperative effect.From June 2013 to July 2016, totally 900 patients were admitted from nine tertiary hospitals in Beijing to perform single segment bone grafting and internal fixation due to lumbar degenerative diseases were prospectively analyzed. There were 428 males and 472 females, the age of patient over 18 years old, with an average of (51.42±12.41) years old;according to patients' subjective wishes and actual residence conditions, all patients were divided into three groups, named as observation group 1 (performed integrated rehabilitation approach and orthopedic treatment model intervention), observation group 2 (performed integrated rehabilitation approach and orthopedic treatment, classified rehabilitation model intervention), and control group(performed routine rehabilitation model intervention). Visual analogue scale(VAS), Oswestry Disability Index(ODI) and Japanese Orthopaedic Association (JOA) were used to evaluate postoperative efficacy among three groups at 24 weeks. Possible factors affecting the postoperative efficacy including age, age grouping, gender, body mass index (BMI), BMI grouping, education level, visiting hospital, payment method of medical expenses, preoperative complications, preoperative JOA score, clinical diagnosis, surgery section, operative method, intraoperative bleeding volume, postoperative complications and rehabilitation mode were listed as independent variables, and postoperative ODI score at 24 weeks as dependent variables. Univariate analysis was used to analyze relationship between influencing factors and postoperative efficacy. Multiple linear regression was used to analyze relationship between influencing factors, rehabilitation mode and postoperative ODI score at 24 weeks, in further to find out the main reasons which affect postoperative efficacy, and to analyze impact of rehabilitation mode on postoperative efficacy.All patients were followed up for 24 weeks after operation. All incisions healed at stage I with stable internal fixation. (1)Evaluation of postoperative efficacy:① There were no statistical differences in preoperative VAS and ODI among three groups(Preoperative JOA score, gender, age could predict postoperative clinical effects of lumbar degenerative diseases in varying degrees treated with single level bone graft fusion and internal fixation. Different rehabilitation modes could improve clinical effects. Intergrated rehabilitation orthopedic treatment model and integrated rehabilitation approach and orthopedic treatment with classifiedrehabilitation model are superior to conventional rehabilitation model in improving patients' postoperative function and relieving pain, which is worthy of promoting in clinical.

Based on Vector Aitken (VA) method, we propose an acceleration Expectation-Maximization (EM) algorithm, VA-accelerated EM algorithm, whose convergence speed is faster than that of EM algorithm. The VA-accelerated EM algorithm does not use the information matrix but only uses the sequence of estimates obtained from iterations of the EM algorithm, thus it keeps the flexibility and simplicity of the EM algorithm. Considering Steffensen iterative process, we have also given the Steffensen form of the VA-accelerated EM algorithm. It can be proved that the reform process is quadratic convergence. Numerical analysis illustrate the proposed methods are efficient and faster than EM algorithm.

Research on species interactions has generally assumed that species have a fixed interaction and therefore linear or non-linear parametric regression models (e.g. exponential, logistic) have been widely used to describe the species interaction. However, these models that describe the relationship between interacting species as a specific functional response might not be appropriate for real biological communities, for instance, in a chaotic system, when the species relationship varies among different situations. To allow a more accurate description of the relationship, we developed a species correlation model with varying coefficient analysis, in which a non-parametric estimation is applied to identify, as a function of related factors, variation in the correlation coefficient. This was applied to a fig-fig wasp model system. When the effect of the factors on the relationship can be described with parameters, the new method reduces to traditional parametric correlation analysis. In this way, the new method is more general and flexible for empirical data analyses, but different by allowing investigation of whether a species interaction varies with respect to factors, and of the factors that maintain or change the species interaction. This method will have important applications in both theoretical and applied research (e.g. epidemiology, community management).

Linear mixed models (LMMs) have become an important statistical method for analyzing cluster or longitudinal data. In most cases, it is assumed that the distributions of the random effects and the errors are normal. This paper removes this restrictions and replace them by the moment conditions. We show that the least square estimators of fixed effects are consistent and asymptotically normal in general LMMs. A closed-form estimator of the covariance matrix for the random effect is constructed and its consistent is shown. Based on this, the consistent estimate for the error variance is also obtained. A simulation study and a real data analysis show that the procedure is effective.

In this paper, we consider whether the random effect exists in linear mixed models (LMMs) when only moment conditions are assumed. Based on the estimators of parameters and their asymptotic properties, a Wald-type test is constructed. It is consistent against global alternatives and is sensitive to the local alternatives converging to the null hypothesis at parametric rates, a fastest possibly rate for goodness-of-fit testing. Moreover, a simulation study shows the performance of the test is good. The procedure also applies to a real data.

In this paper, we construct an empirical process-based test to examine the adequacy of a varying-coefficient model. A Monte Carlo approach is applied to approximate the null distribution of the test. Beyond the desired features that are shared by the existing empirical process-based tests, the Monte Carlo approximation makes the test self-invariant such that studentisation for the test statistic is not needed. Thus, the variance of residuals, as a studentising constant that is model dependent and may deteriorate the power of test, is no need to estimate. Simulations and an example are provided to illustrate our methodology.

We construct an empirical process-based test to examine the adequacy of varying-coefficient models. A Monte Carlo approach is applied to approximate the null distribution of the test. Due to the use of the Monte Carlo test procedure, beyond the desired features that are shared by the existing empirical process-based tests, our test is self-invariant, which overcomes the difficulty of estimating the variance of the test. Simulations are provided to illustrate our methodology.

The issue of selection of bandwidth in kernel smoothing method is considered within the context of partially linear models. In this paper, we study the asymptotic behavior of the bandwidth choice based on generalized cross-validation (GCV) approach and prove that this bandwidth choice is asymptotically optimal. Numerical simulation are also conducted to investigate the empirical performance of generalized cross-validation.