My dissertation includes three essays that examine or relax classical restrictive assumptions used in econometrics estimation methods. The first chapter proposes methods for examining how a response variable is influenced by a covariate. Rather than focusing on the conditional mean I consider a test of whether a covariate has an effect on the entire conditional distribution of the response variable given the covariate and other conditioning variables. This type of analysis is useful in situations where the econometrician or policy maker is interested in knowing whether a variable or policy would improve the distribution of the response outcomes in a stochastic dominance sense. The response variable is assumed to be continuous, while both discrete and continuous covariate cases are considered. I derive the asymptotic distribution of the test statistics and show that they have simple known asymptotic distributions under the null by using and extending conditional empirical process results given by Horvath and Yandell (1988). Monte Carlo experiments are conducted, and the tests are shown to have good small sample behavior. The tests are applied to a study on father's labor supply. The second chapter is based on previous joint work with Jason Abrevaya. It considers estimation of censored panel-data models with individual-specific slope heterogeneity. The slope heterogeneity may be random (random-slopes model) or related to covariates (correlated-random-slopes model). Maximum likelihood and censored least-absolute deviations estimators are proposed for both models. Specification tests are provided to test the slope-heterogeneity models against nested alternatives. The proposed estimators and tests are used for an empirical study of Dutch household portfolio choice. Strong evidence of correlated random slopes for the age variables is found, indicating that the age profile of portfolio adjustment varies significantly with other household characteristics. The third chapter proposes specification tests in models with endogenous covariates. In empirical studies, econometricians often have little information on the functional form of the structural model, regardless of whether covariates in model are exogenous or endogenous. In this chapter, I propose tests for restricted structural model specifications with endogenous covariates against the fully nonparametric alternative. The restricted model specifications include the nonparametric specification with a restricted set of covariates, the semiparametric single index specification and the parametric linear specification. Test statistics are “leave-one-out” type kernel U-statistic as used in Fan and Lee (1996). They are constructed using the idea of the control function approach. Monte Carlo results are provided and tests are shown to have reasonable small sample behavior. / text

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A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Master of Science. Johannesburg, 2014. / This dissertation considers the pricing of European and American options. European option prices are determined by the market and can be veri ed by a closed-form solution to the Black-Scholes model. These options can only be exercised at the maturity date. American option prices are not derived from the market and cannot be priced using the same closed-form solution as in the case of the European options because American options can be exercised at any time on or before the maturity date. An initial method was investigated in pricing a European option but could not price American options. Improvements were made producing two robust option pricing models. The results of which were compared to the closed-form solution in the case of European options and a numerical approximation solution in the case of American options. The improved models showed two signi cant bene ts. The rst bene t is the ability to price both European and American options and the second is the ability to calibrate the models to market prices using market data. Changes to the parameters of the models showed the limitations of each improved model. In conclusion, the improved methods are e ective procedures for solving the European and American option pricing problem. Keywords: European options, American options, Markov Decision Processes, Kernel-Based Reinforcement Learning, Calibration.

In this thesis, we introduce a novel model based on the idea of autoencoders. Different from a classic autoencoder which reconstructs its own inputs through a neural network, our model is closer to Kernel Canonical Correlation Analysis (KCCA) and reconstructs input data from another data set, where these two data sets should have some, perhaps non-linear, dependence. Our model extends traditional KCCA in a way that the non-linearity of the data is learned through optimizing a kernel function by a neural network. In one of the novelties of this thesis, we do not optimize our kernel based upon some prediction error metric, as is classical in autoencoders. Rather, we optimize our kernel to maximize the "coherence" of the underlying low-dimensional hidden layers. This idea makes our method faithful to the classic interpretation of linear Canonical Correlation Analysis (CCA). As far we are aware, our method, which we call a Kernel Coherence Encoder (KCE), is the only extent approach that uses the flexibility of a neural network while maintaining the theoretical properties of classic KCCA. In another one of the novelties of our approach, we leverage a modified version of classic coherence which is far more stable in the presence of high-dimensional data to address computational and robustness issues in the implementation of a coherence based deep learning KCCA.

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In this paper, we purpose a kernel-based fuzzy clustering algorithm to cluster data patterns in the feature space. Our method uses kernel functions to project data from the original space into a high dimensional feature space, and data are divided into groups though their similarities in the feature space with an incremental clustering approach. After clustering, data patterns of the same cluster in the feature space are then grouped with an arbitrarily shaped boundary in the original space. As a result, clusters with arbitrary shapes are discovered in the original space. Clustering, which can be taken as unsupervised classification, has also been utilized in resolving classification problems. So, we extend our method to process the classification problems. By working in the high dimensional feature space where the data are expected to more separable, we can discover the inner structure of the data distribution. Therefore, our method has the advantage of dealing with new incoming data pattern efficiently. The effectiveness of our method is demonstrated in the experiment.

Thesis (M. S.)--Computing, Georgia Institute of Technology, 2009. / Committee Chair: Vuduc, Richard; Committee Member: Kim, Hyesoon; Committee Member: Vetter, Jeffrey. Part of the SMARTech Electronic Thesis and Dissertation Collection.

A technique for establishing L1 asymptotic unbiasedness of a kernel density estimator in Rd that does not depend on the form of the kernel function will be demonstrated. We will introduce the concept of a region sequence of a sequence of kernel functions and show how this can be used to give necessary and sufficient conditions for L1 asymptotic unbiasedness. These results are then applied to kernel density estimators whose form is given and a number of known and novel results are obtained.

A technique for establishing L1 asymptotic unbiasedness of a kernel density estimator in Rd that does not depend on the form of the kernel function will be demonstrated. We will introduce the concept of a region sequence of a sequence of kernel functions and show how this can be used to give necessary and sufficient conditions for L1 asymptotic unbiasedness. These results are then applied to kernel density estimators whose form is given and a number of known and novel results are obtained.

&amp / #728 / G Sniffing is computer-network equivalent of telephone tapping. A Sniffer is simply any software tool used for sniffing. Needs of modern networks today are much more than a sniffer can meet, because of high network traffic and load. Some efforts are shown to overcome this problem. Although successful approaches exist, problem is not completely solved. Efforts mainly includes producing faster hardware, modifying NICs (Network Interface Card), modifying kernel, or some combinations of them. Most efforts are either costly or no know-how exists. In this thesis, problem is attacked via modifying kernel and NIC with aim of transferring the data captured from the network to the application as fast as possible. Snort [1], running on Linux, is used as a case study for performance comparison with the original system. A significant amount of decrease in packet lost ratios is observed at resultant system.