This dissertation contains two essays studying panel data econometric models. First, we consider the problem of estimating a nonparametric panel data models with fixed effects. We propose using the profile least squares method to concentrate out the fixed effects and then estimate the unknown function by the kernel method. We show that our proposed estimator is consistent and has an asymptotically normal distribution. Monte Carlo simulations show that our proposed estimator performs well compared with several existing estimators. Second, we study the effects of Hong Kong’s fixed exchange rate against U.S. dollar using a novel panel data method. After the 1997 Asian Financial Crisis, many of the Asia countries adopted flexible exchange rate policies while Hong Kong still keeps its fixed exchange rate. By comparing Hong Kong versus its major trading partners, we show that if, like other Asian countries, Hong Kong had adopted a float exchange rate policy in October 1998, Hong Kong’s (counterfactual) total value of exports would increase by 14.65 %. Similarly, Hong Kong’s total value of imports would increase about 31%. We conclude that Hong Kong dollar is overvalued by 9.34% due to its fixed exchange rate policy.

This thesis is about some issues in system modeling: The first is a parsimonious representation of MISO Hammerstein system, which is by projecting the multivariate linear function into a univariate input function space. This leads to the so-called semiparamtric Hammerstein model, which overcomes the commonly known “Curse of dimensionality” for nonparametric estimation on MISO systems. The second issue discussed in this thesis is orthogonal expansion analysis on a univariate Hammerstein model and hypothesis testing for the structure of the nonlinear subsystem. The generalization of this technique can be used to test the validity for parametric assumptions of the nonlinear function in Hammersteim models. It can also be applied to approximate a general nonlinear function by a certain class of parametric function in the Hammerstein models. These techniques can also be extended to other block-oriented systems, e.g, Wiener systems, with slight modification. The third issue in this thesis is applying machine learning and system modeling techniques to transient stability studies in power engineering. The simultaneous variable section and estimation lead to a substantially reduced complexity and yet possesses a stronger prediction power than techniques known in the power engineering literature so far.

<p>This dissertation develops new econometric techniques for use in estimating and conducting inference on parameters that can be identified from option prices. The techniques in question extend the existing literature in financial econometrics along several directions.</p><p>The first essay considers the problem of estimating and conducting inference on the term structures of a class of economically interesting option portfolios. The option portfolios of interest play the role of functionals on an infinite-dimensional parameter (the option surface indexed by the term structure of state-price densities) that is well-known to be identified from option prices. Admissible functionals in the essay are generalizations of the VIX volatility index, which represent weighted integrals of options prices at a fixed maturity. By forming portfolios for various maturities, one can study their term structure. However, an important econometric difficulty that must be addressed is the illiquidity of options at longer maturities, which the essay overcomes by proposing a new nonparametric framework that takes advantage of asset pricing restrictions to estimate a shape-conforming option surface. In a second stage, the option portfolios of interest are cast as functionals of the estimated option surface, which then gives rise to a new, asymptotic distribution theory for option portfolios. The distribution theory is used to quantify the estimation error induced by computing integrated option portfolios from a sample of noisy option data. Moreover, by relying on the method of sieves, the framework is nonparametric, adheres to economic shape restrictions for arbitrary maturities, yields closed-form option prices, and is easy to compute. The framework also permits the extraction of the entire term structure of risk-neutral distributions in closed-form. Monte Carlo simulations confirm the framework's performance in finite samples. An application to the term structure of the synthetic variance swap portfolio finds sizeable uncertainty around the swap's true fair value, particularly when the variance swap is synthesized from noisy long-maturity options. A nonparametric investigation into the term structure of the variance risk premium finds growing compensation for variance risk at long maturities.</p><p>The second essay, which represents joint work with Jia Li, proposes an econometric framework for inference on parametric option pricing models with two novel features. First, point identification is not assumed. The lack of identification arises naturally when a researcher only has interval observations on option quotes rather than on the efficient option price itself, which implies that the parameters of interest are only partially identified by observed option prices. This issue is solved by adopting a moment inequality approach. Second, the essay imposes no-arbitrage restrictions between the risk-neutral and the physical measures by nonparametrically estimating quantities that are invariant to changes of measures using high-frequency returns data. Theoretical justification for this framework is provided and is based on an asymptotic setting in which the sampling interval of high frequency returns goes to zero as the sampling span goes to infinity. Empirically, the essay shows that inference on risk-neutral parameters becomes much more conservative once the assumption of identification is relaxed. At the same time, however, the conservative inference approach yields new and interesting insights into how option model parameters are related. Finally, the essay shows how the informativeness of the inference can be restored with the use of high frequency observations on the underlying.</p><p>The third essay applies the sieve estimation framework developed in this dissertation to estimate a weekly time series of the risk-neutral return distribution's quantiles. Analogous quantiles for the objective-measure distribution are estimated using available methods in the literature for forecasting conditional quantiles from historical data. The essay documents the time-series properties for a range of return quantiles under each measure and further compares the difference between matching return quantiles. This difference is shown to correspond to a risk premium on binary options that pay off when the underlying asset moves below a given quantile. A brief empirical study shows asymmetric compensation for these return risk premia across different quantiles of the conditional return distribution.</p> / Dissertation

<p>Two-sample comparison is a fundamental problem in statistics. Given two samples of data, the interest lies in understanding whether the two samples were generated by the same distribution or not. Traditional two-sample comparison methods are not suitable for modern data where the underlying distributions are multivariate and highly multi-modal, and the differences across the distributions are often locally concentrated. The focus of this thesis is to develop novel statistical methodology for two-sample comparison which is effective in such scenarios. Tools from the nonparametric Bayesian literature are used to flexibly describe the distributions. Additionally, the two-sample comparison problem is decomposed into a collection of local tests on individual parameters describing the distributions. This strategy not only yields high statistical power, but also allows one to identify the nature of the distributional difference. In many real-world applications, detecting the nature of the difference is as important as the existence of the difference itself. Generalizations to multi-sample comparison and more complex statistical problems, such as multi-way analysis of variance, are also discussed.</p> / Dissertation

Charnigo and Srinivasan originally developed compound estimators to nonparametrically estimate mean response functions and their derivatives simultaneously when there is one response variable and one covariate. The compound estimator maintains self consistency and almost optimal convergence rate. This dissertation studies, in part, compound estimation with multiple responses and/or covariates. An empirical comparison of compound estimation, local regression and spline smoothing is included, and near optimal convergence rates are established in the presence of multiple covariates. James and Stein proposed an estimator of the mean vector of a p dimensional multivariate normal distribution, which produces a smaller risk than the maximum likelihood estimator if p is at least 3. In this dissertation, we also extend their idea to a nonparametric regression setting. More specifically, we present Steinized local regression estimators of p mean response functions and their derivatives. We consider different covariance structures for the error terms, and whether or not a known upper bound for the estimation bias is assumed. We also apply Steinization to compound estimation, considering the application of Steinization to both pointwise estimators (for example, as obtained through local regression) and weight functions. Finally, the new methodology introduced in this dissertation will be demonstrated on numerical data illustrating the outcomes of a laboratory experiment in which radiation induces nanoparticles to scatter evanescent waves. The patterns of scattering, as represented by derivatives of multiple mean response functions, may be used to classify nanoparticles on their sizes and structures.

Even a modest positive autocorrelation results in a considerable increase in the number of false alarms that are produced when applying a CUSUM chart. Knowledge of the process to be controlled allows for suitable adaptation of the CUSUM procedure. If one has to suspect the normality assumption, nonparametric control procedures such as the rank-based CUSUM chart are a practical alternative. The paper reports the results of a simulation study on the robustness (in terms of sensitivity of the ARL) of the rank-based CUSUM chart against serial correlation of the control variable. The results indicate that the rank-based CUSUM chart is less affected by correlation than the observation-based chart: The rank-based CUSUM chart shows a smaller increase in the number of false alarms and a higher decrease in the ARL in the out-of-control case than the the observation-based chart. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

This thesis is about some issues in system modeling: The first is a parsimonious representation of MISO Hammerstein system, which is by projecting the multivariate linear function into a univariate input function space. This leads to the so-called semiparamtric Hammerstein model, which overcomes the commonly known “Curse of dimensionality” for nonparametric estimation on MISO systems. The second issue discussed in this thesis is orthogonal expansion analysis on a univariate Hammerstein model and hypothesis testing for the structure of the nonlinear subsystem. The generalization of this technique can be used to test the validity for parametric assumptions of the nonlinear function in Hammersteim models. It can also be applied to approximate a general nonlinear function by a certain class of parametric function in the Hammerstein models. These techniques can also be extended to other block-oriented systems, e.g, Wiener systems, with slight modification. The third issue in this thesis is applying machine learning and system modeling techniques to transient stability studies in power engineering. The simultaneous variable section and estimation lead to a substantially reduced complexity and yet possesses a stronger prediction power than techniques known in the power engineering literature so far.

Background: The overall quality of care has been defined in terms of a set of seven core attributes taken from contemporary conceptual frameworks for assessing primary healthcare systems. Attributes are assessed using sub-attribute questions picked from previously developed and validated national level survey instruments. Data has been collected through structured questionnaire survey utilizing Likert items and scale to capture respondents’ perceptions of care. Both descriptive and nonparametric statistical methods have been used for data analysis. Information on demographic factors helped to understand the response patterns across different cohort groups. Key objectives: 1) To determine the perception of patients and physicians regarding the overall quality of care and its constituent elements delivered through the primary healthcare clinics in Winnipeg. 2) To compare the perceptions about different quality of care attributes as expressed by participating patients and physicians. Results: Both patients and physicians have positive views about the overall quality of care (median score >=4 on a 1-6 scale). Regarding individual attributes, “Interpersonal communication” and “Respectfulness” received the highest average score (5) and long-term health management received the lowest score (2). Patient and physician responses were found to be statistically different for access, comprehensiveness and long-term health management. The long wait time for seeing a doctor appeared to be a widely shared concern – only 43% of the patients urgently needing to see a doctor could get a same-day appointment; for non-urgent cases, less than 3% got a same-day appointment. Patients with higher educational levels appeared to be more critical about the quality of care; conversely, patients in good health rated the quality of care attributes more favourably. Conclusion: Patients and physicians are generally satisfied with the overall quality of care. However, patients have identified issues related to access, comprehensiveness of care and long-term health management. Patients concerns were found to be consistent with national level results. Long wait time was also flagged as a key concern. Primary healthcare clinics should proactively seek patient feedback to identify issues and improve their quality of service.

There is significant interest in using gene expression measurements to aid in the personalization of medical treatment. The presence of significant normal tissue contamination in tumor samples makes it difficult to use tumor expression measurements to predict clinical variables and treatment response. I present a probabilistic method, TMMpure, to infer the expression profile of the cancerous tissue using a modified topic model that contains a hierarchical Dirichlet process prior on the cancer profiles. I demonstrate that TMMpure is able to infer the expression profile of cancerous tissue and improves the power of predictive models for clinical variables using expression profiles.

There is significant interest in using gene expression measurements to aid in the personalization of medical treatment. The presence of significant normal tissue contamination in tumor samples makes it difficult to use tumor expression measurements to predict clinical variables and treatment response. I present a probabilistic method, TMMpure, to infer the expression profile of the cancerous tissue using a modified topic model that contains a hierarchical Dirichlet process prior on the cancer profiles. I demonstrate that TMMpure is able to infer the expression profile of cancerous tissue and improves the power of predictive models for clinical variables using expression profiles.