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This paper concerns with the estimation of a fixed effects panel data partially linear regression model with the idiosyncratic errors being an autoregressive process. For fixed effects short time series panel data, the commonly used autoregressive error structure fitting method will not result in a consistent estimator of the autoregressive coefficients. Here we propose an alternative estimation and show that the resulting estimator of the autoregressive coefficients is consistent
and this method is workable for any order autoregressive error structure. Moreover, combining the B-spline approximation, profile least squares dummy variable (PLSDV) technique and consistently estimated the autoregressive error structure, we develop a weighted PLSDV estimator for the parametric component and a weighted B-spline series (BS) estimator for the nonparametric component. The weighted PLSDV estimator is shown to be asymptotically normal and more asymptotically efficient than the one which ignores the error autoregressive structure. In addition, this paper derives the asymptotic bias of the weighted BS estimator and establish its asymptotic normality as well. Simulation studies and an example of application are conducted to illustrate the finite sample performance of the proposed procedures.
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In order to solve the problem of testing multidimensional diffusion models, we develop a test statistic based on Multi-Dimensional Tail Condition Expectations (CTEs). Although it is almost impossible to estimate the transition density matrix of a multidimensional diffusion model directly, the transition density of each component can be estimated and each component can be combined by the CTE to establish a true multidimensional statistics. Finally, the performance of the test is evaluated through simulation.
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This paper considers the asymptotics of randomly weighted sums and their maxima, where the increments {X_i,i\geq1\} is a sequence of independent, identically distributed and real-valued random variables and the weights {\theta_i,i\geq1\} form another sequence of non-negative and independent random variables, and the two sequences of random variables follow some dependence structures. When the common distribution F of the increments belongs to dominant variation class, we obtain some weakly asymptotic estimations for the tail probability of randomly weighted sums and their maxima. In particular, when the F
belongs to consistent variation class, some asymptotic formulas is presented. Finally, these results are applied to the asymptotic estimation for the ruin probability.
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Homogeneity of variance and correlation coefficients is one of assumptions in the analysis of longitudinal data.However, the assumption can be challenged. In this paper, we mainly propose and analyze nonlinear mixed effects models for longitudinal data with exponential correlation covariance structure, intend to introduce Huber's function in the log likelihood function and get robust estimation (M-estimation) by Fisher scoring method. Score test statistics for homogeneity of variance and correlation coefficient based on M-estimation are then studied. A simulation study is carried to assess the performance of test statistics and the method we proposed in the paper is illustrated by an actual data example.
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In this paper, a new H\'{a}jek-R\'{e}nyi-type inequality for mean zero associated random variables is obtained, which generalizes and improves the result of Theorem 2.2 of \ncite{9}. In addition, a Brunk-Prokhorov-type strong law of large numbers is also given.
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There're about 10^{11} neurons in the human brain.Through the synaptic junction, neurons have formed a highly complex network.And it is really important to figure out the information expressed in the network, which will contribute to the resolution of the prevention and diagnosis of cognitive disorder of human beings. This paper uses the schizophrenia and healthy controlled subjects' fMRI data to construct the brain network model, in order to explores abnormal topological properties of schizophrenics' brain network based on graph theory. When studying the human brain network information traditionally by the basement of graph theory, it's all assure that the human brain network model has invariance, so it takes the whole period of time series data in constructing human network
model, which is a kind static network. However, it's hard to ensure this because of the nonstationarity of fMRI functional time series data. Thus, when constructing human brain network model, we should take its time-variation into consideration, then construct a dynamic brain network. We can explore
the brain network information better. In this research, we segment the time series data, using time windows, to constructing dynamic brain network model,
then analyze it combined with the knowledge of graph theory, thereby reducing effects that the nonstationarity of fMRI functional time series data will
have. Comparing dynamic brain network of the schizophrenic patients with normal controls subjects' in different level, the results show that there are difference in single node property, group network property of schizophrenic patients and normal control subjects' whole brain dynamic functional connectivity network. The discovery of these difference in network topological properties has provide new clues for the further study on the pathological mechanism of schizophrenia.
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The heteroscedasticity is inevitable for the panel data modeling in economics. The two-stage estimation method is a better means to study the heteroscedasticity, in which the basis is to select only one independent variable for samples grouping, it can cause the information used is incomplete. In this paper, we propose to select several variables for grouping using variable selection method, then k-mean algorithm is used to cluster, so the samples classification can be achieved and the heteroscedasticity estimation can be obtained. The results of real example analysis show that the method presented in this paper has obvious advantages in effectiveness and feasibility.
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In the situation of \rho-mixing dependent sequences, this paper studied the mean square error and the optimal bandwidth of distribution kernel estimator nu_{p,h} of VaR. And the optimal bandwidth minimized the mean square error. The density function of Laplace distribution is used in the calculation of bandwidth
and we adopt the method of interpolation to compute specific value of bandwidth in this paper. According to the numerical simulations, the distribution kernel estimator is more accurate by comparing the performance of VaR distribution kernel estimation with a common order statistic. Finally, Shangzheng A-share index and Shenzheng B-share index are chosen for an empirical research, which concludes that the risk of the latter is significantly higher than that of the former.
