Semiparametric modeling is a hybrid of the parametric and nonparametric modelings where some function forms are known and others are unknown. In this dissertation, we have made several contributions to semiparametric modeling based on the single index model related to the following three topics: the first is to propose a model for detecting change points simultaneously with estimating the unknown function; the second is to develop two models for spatially correlated data; and the third is to further develop two models for spatially-temporally correlated data. To address the first topic, we propose a unified approach in its ability to simultaneously estimate the nonlinear relationship and change points. We propose a single index change point model as our unified approach by adjusting for several other covariates. We nonparametrically estimate the unknown function using kernel smoothing and also provide a permutation based testing procedure to detect multiple change points. We show the asymptotic properties of the permutation testing based procedure. The advantage of our approach is demonstrated using the mortality data of Seoul, Korea from January, 2000 to December, 2007. On the second topic, we propose two semiparametric single index models for spatially correlated data. One additively separates the nonparametric function and spatially correlated random effects, while the other does not separate the nonparametric function and spatially correlated random effects. We estimate these two models using two algorithms based on Markov Chain Expectation Maximization algorithm. Our approaches are compared using simulations, suggesting that the semiparametric single index nonadditive model provides more accurate estimates of spatial correlation. The advantage of our approach is demonstrated using the mortality data of six cities, Korea from January, 2000 to December, 2007. The third topic involves proposing two semiparametric single index models for spatially and temporally correlated data. Our first model has the nonparametric function which can separate from spatially and temporally correlated random effects. We refer it to "semiparametric spatio-temporal separable single index model (SSTS-SIM)", while the second model does not separate the nonparametric function from spatially correlated random effects but separates the time random effects. We refer our second model to "semiparametric nonseparable single index model (SSTN-SIM)". Two algorithms based on Markov Chain Expectation Maximization algorithm are introduced to simultaneously estimate parameters, spatial effects, and times effects. The proposed models are then applied to the mortality data of six major cities in Korea. Our results suggest that SSTN-SIM is more flexible than SSTS-SIM because it can estimate various nonparametric functions while SSTS-SIM enforces the similar nonparametric curves. SSTN-SIM also provides better estimation and prediction. / Ph. D.

One of the major applications of wireless sensor networks is to sense accurate and reliable data from the physical environment with or without a priori knowledge of data statistics. To extract accurate data from the physical environment, we investigate spatial data correlation among sensor nodes to develop data accuracy models. We propose three data accuracy models namely Estimated Data Accuracy (EDA) model, Cluster based Data Accuracy (CDA) model and Distributed Cluster based Data Accuracy (DCDA) model with a priori knowledge of data statistics. Due to the deployment of high density of sensor nodes, observed data are highly correlated among sensor nodes which form distributed clusters in space. We describe two clustering algorithms called Deterministic Distributed Clustering (DDC) algorithm and Spatial Data Correlation based Distributed Clustering (SDCDC) algorithm implemented under CDA model and DCDA model respectively. Moreover, due to data correlation in the network, it has redundancy in data collected by sensor nodes. Hence, it is not necessary for all sensor nodes to transmit their highly correlated data to the central node (sink node or cluster head node). Even an optimal set of sensor nodes are capable of measuring accurate data and transmitting the accurate, precise data to the central node. This reduces data redundancy, energy consumption and data transmission cost to increase the lifetime of sensor networks. Finally, we propose a fourth accuracy model called Adaptive Data Accuracy (ADA) model that doesn't require any a priori knowledge of data statistics. ADA model can sense continuous data stream at regular time intervals to estimate accurate data from the environment and select an optimal set of sensor nodes for data transmission to the network. Data transmission can be further reduced for these optimal sensor nodes by transmitting a subset of sensor data using a methodology called Spatio-Temporal Data Prediction (STDP) model under data reduction strategies. Furthermore, we implement data accuracy model when the network is under a threat of malicious attack.