Expansion of Brownian Motion Functionals and Its Application in Econometric Estimation

Two types of Brownian motion functionals, both time-homogeneous and time-inhomogeneous, are expanded in terms of orthonormal bases in respective Hilbert spaces. Meanwhile, different time horizons are treated from the applicability point of view. Moreover, the degrees of approximation of truncation series to the corresponding series are established. An asymptotic theory is established. Both the proposed expansions and asymptotic theory are applied to establish consistent estimators in a class of time series econometric models.Asymptotic theory; Brownian motion; econometric estimation, series expansion.

Expansion of Lévy Process Functionals and Its Application in Statistical Estimation

In this paper, expansions of functionals of Lévy processes are established under some Hilbert spaces and their orthogonal bases. From practical standpoint, both time-homogeneous and time-inhomogeneous functionals of Lévy processes are considered. Several expansions and rates of convergence are established. In order to state asymptotic distributions for statistical estimators of unknown parameters involved in a general regression model, we develop a general asymptotic theory for partial sums of functionals of Lévy processes. The results show that these estimators of the unknown parameters in different situations converge to quite different random variables. In addition, the rates of convergence depend on various factors rather than just the sample size.Expansion, Lévy Process, Orthogonal Series, Statistical Estimation.

Semiparametric penalty function method in partially linear model selection

Model selection in nonparametric and semiparametric regression is of both theoretical and practical interest. Gao and Tong (2004) proposed a semiparametric leave–more–out cross–validation selection procedure for the choice of both the parametric and nonparametric regressors in a nonlinear time series regression model. As recognized by the authors, the implementation of the proposed procedure requires the availability of relatively large sample sizes. In order to address the model selection problem with small or medium sample sizes, we propose a model selection procedure for practical use. By extending the so–called penalty function method proposed in Zheng and Loh (1995, 1997) through the incorporation of features of the leave-one-out cross-validation approach, we develop a semiparametric, consistent selection procedure suitable for the choice of optimum subsets in a partially linear model. The newly proposed method is implemented using the full set of data, and simulations show that it works well for both small and medium sample sizes.Linear model; model selection; nonparametric method; partially linear model; semiparametric method

Smoothing the Nonsmoothness

To tackle difficulties for theoretical studies in situations involving nonsmooth functions, we propose a sequence of infinitely differentiable functions to approximate the nonsmooth function under consideration. A rate of approximation is established and an illustration of its application is then provided

Estimation of Semiparametric Multi-Index Models Using Deep Neural Networks

In this paper, we consider estimation and inference for both the multi-index parameters and the link function involved in a class of semiparametric multi-index models via deep neural networks (DNNs). We contribute to the design of DNN by i) providing more transparency for practical implementation, ii) defining different types of sparsity, iii) showing the differentiability, iv) pointing out the set of effective parameters, and v) offering a new variant of rectified linear activation function (ReLU), etc. Asymptotic properties for the joint estimates of both the index parameters and the link functions are established, and a feasible procedure for the purpose of inference is also proposed. We conduct extensive numerical studies to examine the finite-sample performance of the estimation methods, and we also evaluate the empirical relevance and applicability of the proposed models and estimation methods to real data

Estimation in a semiparametric panel data model with nonstationarity

<p>In this paper, we consider a partially linear panel data model with nonstationarity and certain cross-sectional dependence. Accounting for the explosive feature of the nonstationary time series, we particularly employ Hermite orthogonal functions in this study. Under a general spatial error dependence structure, we then establish some consistent closed-form estimates for both the unknown parameters and the unknown functions for the cases where <i>N</i> and <i>T</i> go jointly to infinity. Rates of convergence and asymptotic normalities are established for the proposed estimators. Both the finite sample performance and the empirical applications show that the proposed estimation methods work well.</p

Embolization of a Bleeding Maxillary Arteriovenous Malformation via the Superficial Temporal Artery after External Carotid Artery Ligation

We report a new approach of embolization in a 15-year-old boy that presented with a massive hemorrhage from a maxillary arteriovenous malformation. Rebleeding occurred after emergent ligation of the external carotid artery. The bleeding was successfully controlled by embolization via the superficial temporal artery

High throughput Single-cell Cultivation on Microfluidic Streak Plates

This paper describes the microfluidic streak plate (MSP), a facile method for high-throughput microbial cell separation and cultivation in nanoliter sessile droplets. The MSP method builds upon the conventional streak plate technique by using microfluidic devices to generate nanoliter droplets that can be streaked manually or robotically onto petri dishes prefilled with carrier oil for cultivation of single cells. In addition, chemical gradients could be encoded in the droplet array for comprehensive dose-response analysis. The MSP method was validated by using single-cell isolation of Escherichia coli and antimicrobial susceptibility testing of Pseudomonas aeruginosa PAO1. The robustness of the MSP work flow was demonstrated by cultivating a soil community that degrades polycyclic aromatic hydrocarbons. Cultivation in droplets enabled detection of the richest species diversity with better coverage of rare species. Moreover, isolation and cultivation of bacterial strains by MSP led to the discovery of several species with high degradation efficiency, including four Mycobacterium isolates and a previously unknown fluoranthene-degrading Blastococcus species

Association of Aortic Stiffness and Cognitive Decline: A Systematic Review and Meta-Analysis

Background: Increased aortic stiffness has been found to be associated with cognitive function decline, but the evidence is still under debate. It is of great significance to elucidate the evidence in this debate to help make primary prevention decisions to slow cognitive decline in our routine clinical practice.Methods: Electronic databases of PubMed, EMBASE, and Cochrane Library were systematically searched to identify peer-reviewed articles published in English from January 1, 1986, to March 16, 2020, that reported the association between aortic stiffness and cognitive function. Studies that reported the association between aortic pulse wave velocity (PWV) and cognitive function, cognitive impairment, and dementia were included in the analysis.Results: Thirty-nine studies were included in the qualitative analysis, and 29 studies were included in the quantitative analysis. The aortic PWV was inversely associated with memory and processing speed in the cross-sectional analysis. In the longitudinal analysis, the high category of aortic PWV was 44% increased risk of cognitive impairment (OR 1.44; 95% CI 1.24–1.85) compared with low PWV, and the risk of cognitive impairment increased 3.9% (OR 1.039; 95% CI 1.005–1.073) per 1 m/s increase in aortic PWV. Besides, meta-regression analysis showed that age significantly increased the association between high aortic PWV and cognitive impairment risk.Conclusion: Aortic stiffness measured by aortic PWV was inversely associated with memory and processing speed and could be an independent predictor for cognitive impairment, especially for older individuals

Expansion of Lévy process functionals and its application in econometric estimation.

This research focuses on the estimation of a class of econometric models for involved unknown nonlinear functionals of nonstationary processes. The proxy of nonstationary processes studied here is Lévy processes including Brownian motion as a particular one. A Lévy process is a càdlàg stochastic process which starts at zero almost surely, which has independent increments over disjoint intervals, which has stationary increment distribution meaning that under shift the distributions of increments are identical, which has stochastic continuous trajectory. Obviously, Brownian motion, Poisson process, Gamma process and Pascal process are fundamental examples of Lévy processes. Lévy processes (Z(t); t >0) studied in this thesis possess density or probability distribution functions which verify some properties stated in the text.Thesis (Ph.D.) -- University of Adelaide, School of Economics, 201