Let Y₁, Y₂... be a sequence of random variables obeying the law Y_i = β’_i + ε_i, where β₁, β₂, ... is a sequence of unknown k-dimensional regression vectors; x₁, x₂, ... is a sequence of known k-dimensional regressor vectors; and ε₁ , ε₂, ... is a sequence of independent and identically distributed random variables. Assume that β₁ = ... = β_m = β, m ≥ k, and that β̂₀ is an asymptotically normal estimate of β based on Y₁ , ..., Y_m. This study develops nonparametric procedures for testing H₀: = β = β_m+1 = β_m+2 = …. The proposed tests involve sequences of truncated sequential tests. That is, a function of the residuals Y_m+1 - β̂’₀ x_m+1, …, Y_m+N - β̂’₀ x_m+N is examined for a shift in the model. If no shift is indicated all m+N observations are pooled and a new estimate of β, β̂₁, is formed. The next N residuals are then examined for a shift. The procedure continues until a.shift is indicated. Brownian motion results are used to obtain approximate critical values when the function of the residuals is: the cumulative sum of the signs of the residuals; the sequential Wilcoxon scores; the ordinary cumulative sums of residuals. Exact results are obtained for the cumulative sum of signs procedure when testing for a shift in median. Asymptotic relative efficiency results are also obtained. / Ph. D.

This paper applies and extends Machado and Mata's parametric quantile decomposition method and a similar nonparametric technique to explore changes in welfare in Zimbabwe between 1995 and 2001. These methods allow us to construct a counterfactual distribution in order to decompose the shift into the part due to changes in endowments and that due to changes in returns. We examine two subsets of a nationally representative dataset and find that endowments had a positive effect but that returns account for more of the difference. In communal farming areas, the effect of returns was positive while, in urban Harare, it was negative. / Master of Science

The study seeks to determine the effect upon the Marascuilo Ú₀ statistic of violating the small sample assumption. The study employed a Monte Carlo simulation technique to vary the degree of sample size and unequal sample sizes within experiments to determine the effect of such conditions, Twenty-two simulations, with 1200 trials each, were used. The following conclusion appeared to be appropriate: The Marascuilo Ú₀ statistic should not be used with small sample sizes and it is recommended that the statistic be used only if sample sizes are larger than ten.

The analysis of survival data with a possible cure fraction has attracted much interest in the last two decades. Various models and estimating methods have been proposed for such data and they have been applied in many fields, especially in cancer clinical trials. In the thesis, we consider some new general cure models, which include existing survival models as their special cases. We also consider a nonparametric estimation of cure rate. The estimator is proved consistent and asymptotically normal. We also consider the application of proportional density for cure data and the analysis of length-biased cure data. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2012-01-26 09:53:08.127

This thesis seeks to identify factors affecting the probability of selection of a Surface Warfare Officer (SWO) to Executive Officer (XO) in the U.S. Navy. Selections to XO are made by a board that meets annually. Because a candidate is considered for selection in up to three consecutive boards, the possible outcomes in this process are selection to XO in one of three annual boards, failure to be selected to XO in the third board, or attrition from the process between boards. Using data on the board's selections over a three-year period (2002-2004) a hazards-based logistic regression model is developed to estimate the probabilities associated with a candidate's disposition based on his or her career profile. The model confirms that a candidate's recent fitness and evaluation report (FITREP) is the single-most-important factor affecting selection. Additionally, officers who have completed a tour in Washington D.C. or at the Bureau of Naval Personnel have higher probabilities of selection than do those who have completed other shore tours. But when an officer receives a poor FITREP, the probability of selection is low, regardless of other factors. A nonparametric statistical analysis is used to confirm these findings.

The purpose of this research was to evaluate the effect on parametric and nonparametric tests using ordinal data when the distances between points changed on the measurement scale. The research examined the performance of Type I and Type II error rates using selected parametric and nonparametric tests.

<p>Bayesian nonparametric models, such as the Gaussian process and the Dirichlet process, have been extensively applied for target kinematics modeling in various applications including environmental monitoring, traffic planning, endangered species tracking, dynamic scene analysis, autonomous robot navigation, and human motion modeling. As shown by these successful applications, Bayesian nonparametric models are able to adjust their complexities adaptively from data as necessary, and are resistant to overfitting or underfitting. However, most existing works assume that the sensor measurements used to learn the Bayesian nonparametric target kinematics models are obtained a priori or that the target kinematics can be measured by the sensor at any given time throughout the task. Little work has been done for controlling the sensor with bounded field of view to obtain measurements of mobile targets that are most informative for reducing the uncertainty of the Bayesian nonparametric models. To present the systematic sensor planning approach to leaning Bayesian nonparametric models, the Gaussian process target kinematics model is introduced at first, which is capable of describing time-invariant spatial phenomena, such as ocean currents, temperature distributions and wind velocity fields. The Dirichlet process-Gaussian process target kinematics model is subsequently discussed for modeling mixture of mobile targets, such as pedestrian motion patterns. </p><p>Novel information theoretic functions are developed for these introduced Bayesian nonparametric target kinematics models to represent the expected utility of measurements as a function of sensor control inputs and random environmental variables. A Gaussian process expected Kullback Leibler divergence is developed as the expectation of the KL divergence between the current (prior) and posterior Gaussian process target kinematics models with respect to the future measurements. Then, this approach is extended to develop a new information value function that can be used to estimate target kinematics described by a Dirichlet process-Gaussian process mixture model. A theorem is proposed that shows the novel information theoretic functions are bounded. Based on this theorem, efficient estimators of the new information theoretic functions are designed, which are proved to be unbiased with the variance of the resultant approximation error decreasing linearly as the number of samples increases. Computational complexities for optimizing the novel information theoretic functions under sensor dynamics constraints are studied, and are proved to be NP-hard. A cumulative lower bound is then proposed to reduce the computational complexity to polynomial time.</p><p>Three sensor planning algorithms are developed according to the assumptions on the target kinematics and the sensor dynamics. For problems where the control space of the sensor is discrete, a greedy algorithm is proposed. The efficiency of the greedy algorithm is demonstrated by a numerical experiment with data of ocean currents obtained by moored buoys. A sweep line algorithm is developed for applications where the sensor control space is continuous and unconstrained. Synthetic simulations as well as physical experiments with ground robots and a surveillance camera are conducted to evaluate the performance of the sweep line algorithm. Moreover, a lexicographic algorithm is designed based on the cumulative lower bound of the novel information theoretic functions, for the scenario where the sensor dynamics are constrained. Numerical experiments with real data collected from indoor pedestrians by a commercial pan-tilt camera are performed to examine the lexicographic algorithm. Results from both the numerical simulations and the physical experiments show that the three sensor planning algorithms proposed in this dissertation based on the novel information theoretic functions are superior at learning the target kinematics with</p><p>little or no prior knowledge</p> / Dissertation

A research report submitted to the Faculty of Science, University of the Witwatersrand, for the degree of Master of Science by Coursework and Research Report. / Researchers and data analysts often encounter a problem when analysing data with missing values. Methods for imputing continuous data are well developed in the literature. However, methods for imputing categorical data are not well established. This research report focuses on categorical data imputation using non-parametric and semi-parametric methods. The aims of the study are to compare different imputation methods for categorical data and to assess the quality of the imputation. Three imputation methods are compared namely; multiple imputation, hot deck imputation and random forest imputation. Missing data are created on a complete data set using the missing completely at random mechanism. The imputed data sets are compared with the original complete data set, and the imputed values which are the same as the values in the original data set are counted. The analysis revealed that the hot deck imputation method is more precise, compared to random forest and multiple imputation methods. Logistic regression is fitted on the imputed data sets and the original data set and the resulting models are compared. The analysis shows that the multiple imputation method affects the model fit of the logistic regression negatively.

The main goal of this thesis is to investigate the frequentist asymptotic properties of nonparametric Bayesian procedures in inverse problems and the Gaussian white noise model. In the first part, we study the frequentist posterior contraction rate of nonparametric Bayesian procedures in linear inverse problems in both the mildly and severely ill-posed cases. This rate provides a quantitative measure of the quality of statistical estimation of the procedure. A theorem is proved in a general Hilbert space setting under approximation-theoretic assumptions on the prior. The result is applied to non-conjugate priors, notably sieve and wavelet series priors, as well as in the conjugate setting. In the mildly ill-posed setting, minimax optimal rates are obtained, with sieve priors being rate adaptive over Sobolev classes. In the severely ill-posed setting, oversmoothing the prior yields minimax rates. Previously established results in the conjugate setting are obtained using this method. Examples of applications include deconvolution, recovering the initial condition in the heat equation and the Radon transform. In the second part of this thesis, we investigate Bernstein--von Mises type results for adaptive nonparametric Bayesian procedures in both the Gaussian white noise model and the mildly ill-posed inverse setting. The Bernstein--von Mises theorem details the asymptotic behaviour of the posterior distribution and provides a frequentist justification for the Bayesian approach to uncertainty quantification. We establish weak Bernstein--von Mises theorems in both a Hilbert space and multiscale setting, which have applications in $L^2$ and $L^\infty$ respectively. This provides a theoretical justification for plug-in procedures, for example the use of certain credible sets for sufficiently smooth linear functionals. We use this general approach to construct optimal frequentist confidence sets using a Bayesian approach. We also provide simulations to numerically illustrate our approach and obtain a visual representation of the different geometries involved.

有各式各樣的參數與非參數期貨定價模型被廣泛應用於金融領域。其中一些模型的組合能顯著提升期貨定價的準確性。更具體的說，可以先通過參數模型擬合數據，再使用非參數模型學習並修正誤差估價誤差。本論文作為范和Mancini(2009) 結果的延伸，將市場交易的歐式期權價格作為輸入數據，運用「有參數模型指導的非參數定價方法」對障礙期權進行估價。「自動誤差修正估價法」運用非參數方法對由參數估價法產生的誤差進行修正，使得障礙期權的非參數定價模型可以被視為一系列的歐式期權定價的組合。在整個障礙期權的估價過程中，本論文同時提供了一種分數階快速傅裡葉變換的應用，可通過由非參數方法獲得的標的資產對數的存活函數計算標的資產對數最大值分佈的特徵函數。 / There are a variety of parametric and nonparametric option pricing models commonly used in Finance. A combination of them can enhance the pricing performance significantly. Specifically, one proposes to fit the data with a parametric method and then correct the pricing errors empirically with a nonparametric learning approach. This thesis extends Fan and Mancini's (2009) model-guided nonparametric method to barrier option pricing using market traded European option data. Adopting automatic correction of errors (ACE) method to estimate the risk neutral conditional survivor function, by which the pricing error of the initial parametric estimates is captured nonparametrically, enables the nonparametric pricing procedure to value a barrier option as a sum of sequence of European options. As a byproduct from the valuation process, this thesis also provides a modified fractional fast Fourier transform technique compute the characteristic function of the running maximum log-price of the underlying asset nonparametrically through the calibrated survivor functions. / Detailed summary in vernacular field only. / Chi, Chengzhan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 38-39). / Abstracts also in Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Nonparametric Local Regression Modelling --- p.4 / Chapter 2.1 --- Function Estimation by Local Constant --- p.4 / Chapter 2.2 --- Function Estimation by Local Linear Regression --- p.5 / Chapter 3 --- Nonparametric ACE European Option Pricing --- p.7 / Chapter 3.1 --- European Option Prices and Risk Neutral Survivor Functions --- p.7 / Chapter 3.2 --- Estimation of Risk Neutral Survivor Functions --- p.10 / Chapter 3.2.1 --- Risk Neutral Survivor Functions and Traded Options --- p.10 / Chapter 3.2.2 --- Survivor Function Estimation with Nonparametric ACE Method --- p.11 / Chapter 3.3 --- Representation of European Option Prices at Log-asset Level and Numerical Example --- p.15 / Chapter 4 --- Nonparametric ACE Barrier Option Pricing Framework --- p.20 / Chapter 4.1 --- Continuous-time Barrier Option --- p.20 / Chapter 4.2 --- Discrete Approximation and Backward Induction --- p.21 / Chapter 4.3 --- Decomposed Problems --- p.25 / Chapter 5 --- Nonparametric Estimation of Cumulative Distribution Function of M{U+2C7C}(R{U+209C}) --- p.28 / Chapter 5.1 --- Survivor Functions and Maxima Probabilities --- p.28 / Chapter 5.2 --- Characteristic Functions of Maxima --- p.30 / Chapter 5.2.1 --- Algorithm --- p.30 / Chapter 5.2.2 --- Preparation --- p.31 / Chapter 5.2.3 --- Fast Fourier Transform (FFT) --- p.31 / Chapter 5.2.4 --- Fractional Fast Fourier Transform (FRFT) --- p.33 / Chapter 5.2.5 --- Derivation of ΦR{U+209C} --- p.34 / Chapter 5.3 --- Numerical Experiments --- p.35 / Chapter 6 --- Conclusion --- p.37 / Bibliography --- p.38