Browsing by Subject "Nonparametric Estimation"
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Item Inference and Visualization of Periodic Sequences(2011-10-21) Sun, YingThis dissertation is composed of four articles describing inference and visualization of periodic sequences. In the first article, a nonparametric method is proposed for estimating the period and values of a periodic sequence when the data are evenly spaced in time. The period is estimated by a "leave-out-one-cycle" version of cross-validation (CV) and complements the periodogram, a widely used tool for period estimation. The CV method is computationally simple and implicitly penalizes multiples of the smallest period, leading to a "virtually" consistent estimator. The second article is the multivariate extension, where we present a CV method of estimating the periods of multiple periodic sequences when data are observed at evenly spaced time points. The basic idea is to borrow information from other correlated sequences to improve estimation of the period of interest. We show that the asymptotic behavior of the bivariate CV is the same as the CV for one sequence, however, for finite samples, the better the periods of the other correlated sequences are estimated, the more substantial improvements can be obtained. The third article proposes an informative exploratory tool, the functional boxplot, for visualizing functional data, as well as its generalization, the enhanced functional boxplot. Based on the center outwards ordering induced by band depth for functional data, the descriptive statistics of a functional boxplot are: the envelope of the 50 percent central region, the median curve and the maximum non-outlying envelope. In addition, outliers can be detected by the 1.5 times the 50 percent central region empirical rule. The last article proposes a simulation-based method to adjust functional boxplots for correlations when visualizing functional and spatio-temporal data, as well as detecting outliers. We start by investigating the relationship between the spatiotemporal dependence and the 1.5 times the 50 percent central region empirical outlier detection rule. Then, we propose to simulate observations without outliers based on a robust estimator of the covariance function of the data. We select the constant factor in the functional boxplot to control the probability of correctly detecting no outliers. Finally, we apply the selected factor to the functional boxplot of the original data.Item Three Essays on Microfoundations of Economics(2012-10-19) Ju, GaoshengThis dissertation, which consists of three essays, studies three applications. Each of them emphasizes the microfoundations of economic models. The first essay proposes a nonparametric estimation of structural labor supply and exact welfare change under nonconvex piecewise-linear budget sets. Different from previous literature, my method focuses on a nonparametric specification of an indirect utility function. I find that working with the indirect utility function is very useful in simultaneously addressing the labor supply problems with individual heterogeneity, nonconvex budget sets, labor nonparticipation, and measurement errors in working hours that previous literature was unable to. Further, the estimated indirect utility function proves to be convenient and efficient in calculating exact welfare change and deadweight loss under general piecewise-linear budget sets. In the second essay, I solve the equity premium, risk-free rate, and capital structure puzzles by laying a more solid microfoundation for consumption-based asset pricing models. I argue that the above two asset pricing puzzles arise from the aggregation of hump-shaped life-cycle consumption into per capita consumption, which accounts for the unanimous rejections of Euler equations in the literature. As for the third puzzle, I show that a firm's capital structure can be determined by heterogenous investors maximizing life-time utility even though the capital structure is irrelevant on the firm side. The endogenously determined leverage generates an even larger equity premium than a fixed one. The third essay studies the solution concepts of coalition equilibrium. Traditional solution concepts such as Strong Nash Equilibrium, Coalition-proof Nash Equilibrium, Largest Consistent Set, and Coalition Equilibrium violate the fundamental principles of individual rationality. I define a new solution concept, Weak Coalition Equilibrium, which requires each coalitional deviation to be within-coalition self-enforceable and cross-coalition self-enforceable. The cross-coalition self-enforceability endows coalitions with farsightedness. Weak Coalition Equilibrium is a generalization of Coalition-proof Nash Equilibrium and a re nement of the concept Nash Equilibrium. It exists under a weak condition. Most importantly, it is in line with the principle of individual rationality.