Sequential analysis could potentially reduce financial and human cost due to its capability of reaching an earlier conclusion. Since its introduction, sequential analysis has been widely applied to many areas such as statistical process control (SPC) and clinical design. However, nonparametric SPC cumulative sum (CUSUM) procedures for multivariate data and correlated observations are still rare in literatures, and there is little discussion in sequential classification for longitudinal data. In this dissertation we try to develop new sequential procedures for nonparametric statistical process control applicable to multivariate and serially correlated data, and sequential classifier for longitudinal data.

First, we develop two nonparametric multivariate CUSUM control charts based on spatial sign and data depth. These two procedures can be considered as the nonparametric counterparts of the two parametric multivariate CUSUM procedures developed in Crosier (1988). We show that the two proposed CUSUM procedures are affine-invariant and asymptotically distribution-free over a broad family of distributions. In our simulation studies, the proposed CUSUM procedures perform well across a broad range of settings, and compare favorably with existing CUSUM procedures for detecting location and scale changes.

Second, on the fundation of the above nonparameric multivariate CUSUM control charts, a nonparametric SPC procedure for correlated data is proposed. We incorporate wavelet decomposition with Box and Jenkins time series models and the above multivariate CUSUM control chart to obtain a procedure that is robust under correlated processes without distributional assumption. The procedure is also shown to be powerful in detecting location shift through extensive simulation studies.

Last, we develop a first of its kind sequential classification procedure for longitudinal data. The procedure adapts a neutral zone classifier framework, and attempts to reduce overall cost when the cost of time is considered. The sequential classifier evaluates each subject at each longitudinal time point for evidence of classification. A classification decision is not made until sufficient confidence is present or the last time point where the data can be collected is reached. The early decision property of the proposed classifier may aid the early diagnosis of severe disease diagnosis as in our real data example.

Comparing species assemblages at different times and locations provides useful

information regarding the ecosystem. Due to the unique structure

of abundance data often collected in species assemblage, appropriate

statistical tests are in need. In this thesis, we propose two types of tests,

one is data depth based nonparametric test, the other is a zero-inflated Poisson mixture model based test. These two types of tests are developed for different testing objectives and under different assumptions. We use simulation to demonstrate that their performance is better than that of the existing tests. We also discuss the differences of these two tests.

Combining multiple tests has many real world applications. However, most existing methods fail to directly take into account the underlying dependency among the tests. In the first project of this dissertation, we propose a novel procedure to combine dependent tests based on the notion of data depth. The proposed method can automatically incorporate the underlying dependency among the tests, and is nonparametric and completely data-driven. To demonstrate its application, we apply the proposed combining method to develop a new two-sample test for data of arbitrary types when the data can be metrizable and their information can be characterized by interpoint distances. Our simulation studies and real data analysis show that the proposed test based on the new combining method performs well across a broad range of settings and compares favorably with existing tests.

Count data monitoring has important applications in many fields. However, most of the existing control charts for monitoring count data are parametric. Parametric control charts can be problematic when the underlying parametric distributional assumption does not hold for the particular application. On the other hand, nonparametric control charts do not require such distributional assumptions, and are more desirable in real-world situations where the underlying distribution cannot be easily described using a parametric distribution. In the second project of this dissertation, we extend the nonparametric control chart for continuous data monitoring in Li (2021) to count data monitoring. To guarantee a desired in-control performance, we further adopt the bootstrap procedure from Gandy and Kvaløy (2013) to help determine the control limit of our proposed control chart. Our simulation studies and real data analysis show that the proposed control chart performs well across a variety of settings, and compares favorably with other existing nonparametric control charts for count data.

High performance computing and high resolution range sensor motivates the intelligent system innovations such as smart car, smart home/community and 3D motion games. Most importantly, 3D graphics technique requires high performance computation to provide high quality and vivid real-time videos. Accurate motion sensing requires high resolution radar sensor. However, in general, data transmission limits the large scale computation while high resolution radar signal processor limits the detection accuracy. Therefore, low power design for high speed data transmission and high resolution radar signal processor are desired.

Energy efficient transceivers have been aggressively demanded by high performance computing applications. Recently, data center has reached TB/s in 2015 and it would reach 20 TB/s in a few years. Therefore, low cost short range interconnects becomes one of the major limitations for high speed data transmission especially for processor-to-processor and processor-to-memory. Silicon photonics (SiP) has attracted great attentions for its low energy efficiency and less IO pins. In air interface, 15 cm sensing resolution and Gb/s data communication dual mode system enables a layer of network intelligence.

The first portion of the dissertation discusses the energy efficient transceiver

design for optical interconnects. A monolithic micro-ring modulator based transmitter is presented in 130 nm CMOS SOI. In this process, the data rate limitation of monolithic integration is on the eletrical driver. With optimized micro-ring modulator, the transmitter demonstrates 25 Gb/s data rate without pre-emphasis.

Secondly, the scaling trends from FD-SOI CMOS to FinFET process is discussed. Since the monolithic integration can not scale the energy efficiency as hybrid integration due to the limitation of optical devices development, hybrid integration keeps the energy efficiency scaling on behalf of the high fT device in advanced process. An optical and electrical co-design algorithm for the WDM link is proposed which focus on the energy efficiency optimization in hybrid integration. Link budget is analyzed and transceivers with planar 28 nm FD-SOI CMOS and 3D 14 nm FinFET are presented.

Thirdly, a high speed pulse compression radar (PCR) signal processor is presented in 90 nm CMOS. High speed analog correlation is proposed to replace the conventional digital correlation. This relaxes the high speed requirement in analog-to-digital converter (ADC) design. An analog correlation signal processor is implemented with a variable gain amplifier (VGA), a correlator, a delay-lock loop (DLL), a 4-bits DAC and a 4-bits ADC. Additionally, a new closed-loop calibration algorithm is proposed for DC offset and time misalignment.

Finally, a dual mode bidirectional pulse compression radar is proposed. The

radar signal processor is demonstrated in 90 nm CMOS. The system allows 3 Gb/s data transmission in passthrough mode and 10 cm range resolution in radar mode. This is the first demonstration of pulse compression radar signal processor with the features of wireless data communication and high resolution range sensing.

Missing data occur frequently in surveys, clinical trials as well as other real data studies. In the analysis of incomplete data, one needs to correctly identify the missing mechanism and then adopt appropriate statistical procedures. Recently, the analysis of missing data has gained more and more attention. People start to investigate the missing data analysis in several different areas. This dissertation concerns two projects. First, we propose a Bayesian solution to data analysis with non-ignorable missingness. The other one is the non-parametric test of missing mechanism for incomplete multivariate data.

First, Bayesian methods are proposed to detect non-ignorable missing and eliminate potential bias in estimators when non-ignorable missing presents. Two hierarchical linear models, pattern mixture model and selection model, are applied to a real data example: the National Assessment of Education Progress (NAEP) education survey data. The results show that the Bayesian methods can correctly recognize the missingness mechanism and provide model-based estimators which can eliminate the possible bias due to non-ignorable missing. We also evaluate the goodness-of-fit of these two proposed models using two methods: the comparison of the real data with the predictive posterior distribution and the residual analysis by cross validation. A simulation study compares the performance of the two proposed Bayesian methods with the traditional design-based methods under different missing mechanisms and show the good properties of the Bayesian methods. Further, we discuss the three commonly used model selection criteria: the Bayes factor, the deviance information criterion and the minimum posterior predictive loss approach. Due to the complicated calculation of the Bayes factor and the uncertainty of the DIC, we conduct the last approach, which fails to correctly detect the real model structure for the hierarchical linear model.

Second, as an alternative to the fully specified model-based Bayesian method, a novel non-parametric test is proposed to detect the missing mechanism for multivariate missing data. The proposed test does not need any distributional assumptions and is proven to be consistent. A simulation study demonstrates that it has well controlled type I error and satisfactory power against a variety of alternative hypotheses.

Allelic gene structure variations and alternative splicing are responsible for transcript structure variations. More than 75% of human genes have structural isoforms of transcripts, but to date few studies have been conducted to verify the alternative splicing systematically.

The present study used expressed sequence tags (ESTs) and EST tagged SNP patterns to examine the transcript structure variations resulting from allelic gene structure variations in the major human malaria vector, Anopheles gambiae. About 80% of 236,004 available A. gambiae ESTs were successfully aligned to A. gambiae reference genomes. More than 2,340 transcript structure variation events were detected. Because the current A. gambiae annotation is incomplete, we re-annotated the A. gambiae genome with an A. gambiae-specific gene model so that the effect of variations on gene coding could be better evaluated. A total of 15,962 genes were predicted. Among them, 3,873 were novel genes and 12,089 were previously identified genes. The gene completion rate improved from 60% to 84%. Based on EST support, 82.5% of gene structures were predicted correctly. In light of the new annotation, we found that ∼78% of transcript structure variations were located within the coding sequence (CDS) regions, and >65% of variations in the CDS regions have the same open-reading-frame. The association between transcript structure isoforms and SNPs indicated that more than 28% of transcript structure variation events were contributed by different gene alleles in A. gambiae.

We successfully expanded the A. gambiae genome annotation. We predicted and analyzed transcript structure variations in A. gambiae and found that allelic gene structure variation plays a major role in transcript diversity in this important human malaria vector.

In the first chapter of this thesis, we propose a penalized splines (P-splines) estimator for random effects panel data model. While being a nonparametric technique, one of the most attractive properties of splines methods is their analogous setup to parametric regression model. Compared to kernel-based methods, however, splines methods are far less developed at least for econometric models. The asymptotic results of our P-splines estimator are established in this chapter. Monte Carlo simulation is conducted to compare the performance of our P-splines estimator with different kernel-based estimators proposed in recent literature. It turns out that the P-splines estimator consistently performs well and is computationally efficient.

In the second chapter, we develop a general procedure to derive the asymptotic variance-covariance matrices of two-stage estimators that can be used to estimate simultaneous equation systems with a mixture of any number of binary and continuous dependent variables. To demonstrate the usefulness of our procedure, we apply our formulas to empirical data with one continuous and two binary dependent variables in the simultaneous equations system. Our results are expected to be of tremendous help to numerous practitioners of econometrics using two-stage procedures to estimate their simultaneous equations models.