The Generalized Method of Moments for Mixture and Mixed Models

Mixture models can be found in a wide variety of statistical applications. However, undertaking statistical inference in mixture models, especially non-parametric mixture models, can be challenging. A general, or nonparametric, mixture model has effectively an infinite dimensional parameter space. In frequentist statistics, the maximum likelihood estimator with an infinite dimensional parameter may not be consistent or efficient in the sense that the Cramer-Rao bound is not attained even asymptotically. In Bayesian statistics, a prior on an infinite dimensional space is not well defined and can be highly informative even with large amounts of data. In this thesis, we mainly consider mixture and mixed-effects models, when the mixing distribution is non-parametric. Following the dimensionality reduction idea in [Marriott, 2002], we propose a reparameterization-approximation framework with a complete orthonormal basis in a Hilbert space. The parameters in the reparameterized models are interpreted as the generalized moments of a mixing distribution. We consider different orthonormal bases, including the families of orthogonal polynomials and the eigenfunctions of positive self-adjoint integral operators. We also study the approximation errors of the truncation approximations of the reparameterized models in some special cases. The generalized moments in the truncated approximations of the reparameterized models have a natural parameter space, called the generalized moment space. We study the geometric properties of the generalized moment space and obtain two important geometric properties: the positive representation and the gradient characterization. The positive representation reveals the identifiability of the mixing distribution by its generalized moments and provides an upper bound of the number of the support points of the mixing distribution. On the other hand, the gradient characterization provides the foundation of the class of gradient-based algorithms when the feasible set is the generalized moment space. Next, we aim to fit a non-parametric mixture model by a set of generalized moment conditions, which are from the proposed reparameterization-approximation procedure. We propose a new estimation method, called the generalized method of moments for mixture models. The proposed estimation method involves minimizing a quadratic objective function over the generalized moment space. The proposed estimators can be easily computed through the gradient-based algorithms. We show the convergence rate of the mean squared error of the proposed estimators, as the sample size goes to infinity. Moreover, we design the quadratic objective function to ensure that the proposed estimators are robust to the outliers. Compared to the other existing estimation methods for mixture models, the GMM for mixture models is more computationally friendly and robust to outliers. Lastly, we consider the hypothesis testing problem on the regression parameter in a mixed-effects model with univariate random effects. Through our new procedures, we obtain a series of estimating equations parameterized in the regression parameter and the generalized moments of the random-effects distribution. These parameters are estimated under the framework of the generalized method of moments. In the case that the number of the generalized moments diverges with the sample size and the dimension of the regression parameter is fixed, we compute the convergence rate of the generalized method of moments estimators for the mixed-effects models with univariate random effects. Since the regularity conditions in [Wilks, 1938] fail under our context, it is challenging to construct an asymptotically $\chi^2$ test statistic. We propose using ensemble inference, in which an asymptotically $\chi^2$ test statistic is constructed from a series of the estimators obtained from the generalized estimating equations with different working correlation matrices

Local Mixture Model in Hilbert Space

In this thesis, we study local mixture models with a Hilbert space structure. First, we consider the fibre bundle structure of local mixture models in a Hilbert space. Next, the spectral decomposition is introduced in order to construct local mixture models. We analyze the approximation error asymptotically in the Hilbert space. After that, we will discuss the convexity structure of local mixture models. There are two forms of convexity conditions to consider, first due to positivity in the $-1$-affine structure and the second by points having to lie inside the convex hull of a parametric family. It is shown that the set of mixture densities is located inside the intersection of the sets defined by these two convexities. Finally, we discuss the impact of the approximation error in the Hilbert space when the domain of mixing variable changes

Identifying Schistosoma japonicum Excretory/Secretory Proteins and Their Interactions with Host Immune System

Schistosoma japonicum is a major infectious agent of schistosomiasis. It has been reported that large number of proteins excreted and secreted by S. japonicum during its life cycle are important for its infection and survival in definitive hosts. These proteins can be used as ideal candidates for vaccines or drug targets. In this work, we analyzed the protein sequences of S. japonicum and found that compared with other proteins in S. japonicum, excretory/secretory (ES) proteins are generally longer, more likely to be stable and enzyme, more likely to contain immune-related binding peptides and more likely to be involved in regulation and metabolism processes. Based on the sequence difference between ES and non-ES proteins, we trained a support vector machine (SVM) with much higher accuracy than existing approaches. Using this SVM, we identified 191 new ES proteins in S. japonicum, and further predicted 7 potential interactions between these ES proteins and human immune proteins. Our results are useful to understand the pathogenesis of schistosomiasis and can serve as a new resource for vaccine or drug targets discovery for anti-schistosome

Impacts of Biochar and Vermicompost Addition on Physicochemical Characteristics, Metal Availability, and Microbial Communities in Soil Contaminated with Potentially Toxic Elements

In the current work, the effects of biochar, vermicompost, as well as their combined application on ammonia-oxidizing archaea (AOA) and ammonia-oxidizing bacteria (AOB) in soils contaminated with potentially toxic elements (PTEs) were investigated. In this regard, four treatments were performed; among them, treatment A served as a control without additive, treatment B with vermicompost (2%), treatment C with biochar (2%), and treatment D with biochar (2%) plus vermicompost (2%). In addition, the abundance and structure of the AOA and AOB amoA gene were measured using quantitative PCR and high-throughput sequencing. The relationships between the microbial community, physicochemical parameters, and CaCl2-extractable PTEs were analyzed using the Pearson correlation method. We found that adding biochar and vermicompost promoted the immobilization of PTEs and nitrogen biotransformation. The rational use of biochar and vermicompost is beneficial for the growth of bacterial and fungal communities in soils polluted by PTEs. AOA and AOB amoA genes were stimulated by biochar, vermicompost, and their combination, but their structure was hardly affected

Stochastic interest model driven by compound Poisson process andBrownian motion with applications in life contingencies

In this paper, we introduce a class of stochastic interest model driven by a compoundPoisson process and a Brownian motion, in which the jumping times of force of interest obeyscompound Poisson process and the continuous tiny fluctuations are described by Brownian motion, andthe adjustment in each jump of interest force is assumed to be random. Based on the proposed interestmodel, we discuss the expected discounted function, the validity of the model and actuarial presentvalues of life annuities and life insurances under different parameters and distribution settings. Ournumerical results show actuarial values could be sensitive to the parameters and distribution settings,which shows the importance of introducing this kind interest model

Intra-articular delivery of tetramethylpyrazine microspheres with enhanced articular cavity retention for treating osteoarthritis

Tetramethylpyrazine (TMP) is a traditional Chinese herbal medicine with strong anti-inflammatory and cartilage protection activities, and thus a promising candidate for treating osteoarthritis. However, TMP is rapidly cleared from the joint cavity after intra-articular injection and requires multiple injections to maintain efficacy. The aim of this study was to encapsulate TMP into poly (lactic-co-glycolic acid) (PLGA) microspheres to enhance the TMP retention in the joint, reducing injection frequencies and decreasing dosage. TMP microspheres were prepared by emulsion/solvent evaporation method. The intra-articular retention of the drug was assessed by detecting the drug concentration distributed in the joint tissue at different time points. The therapeutic effect of TMP microspheres was evaluated by the swelling of knee joints and histologic analysis in papain-induced OA rat model. The prepared freeze-dried microspheres with a particle size of about 10 µm can effectively prolong the retention time of the drug in the articular cavity to 30 d, which is 4.7 times that of the TMP solution. Intra-articular injection of TMP microspheres efficiently relieved inflammatory symptoms, improved joint lesions and decreased the depletion of proteoglycan. In conclusion, intra-articular injection of TMP loaded microspheres was a promising therapeutic method in the treatment of OA. Keywords: Osteoarthritis, Tetramethylpyrazine, Intra-articular injection, PLGA microspheres, Retention, Pharmacodynamic

The Role of Toll-like Receptor Agonists and Their Nanomedicines for Tumor Immunotherapy

Toll-like receptors (TLRs) are a class of pattern recognition receptors that play a critical role in innate and adaptive immunity. Toll-like receptor agonists (TLRa) as vaccine adjuvant candidates have become one of the recent research hotspots in the cancer immunomodulatory field. Nevertheless, numerous current systemic deliveries of TLRa are inappropriate for clinical adoption due to their low efficiency and systemic adverse reactions. TLRa-loaded nanoparticles are capable of ameliorating the risk of immune-related toxicity and of strengthening tumor suppression and eradication. Herein, we first briefly depict the patterns of TLRa, followed by the mechanism of agonists at those targets. Second, we summarize the emerging applications of TLRa-loaded nanomedicines as state-of-the-art strategies to advance cancer immunotherapy. Additionally, we outline perspectives related to the development of nanomedicine-based TLRa combined with other therapeutic modalities for malignancies immunotherapy