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京都大学 / 新制・課程博士 / 博士(医学) / 甲第23798号 / 医博第4844号 / 新制||医||1058(附属図書館) / 京都大学大学院医学研究科医学専攻 / (主査)教授 佐藤 俊哉, 教授 黒田 知宏, 教授 永井 洋士 / 学位規則第4条第1項該当 / Doctor of Medical Science / Kyoto University / DFAM

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Existing sufficient dimension reduction (SDR) methods typically consider cases with no missing data. The dissertation aims to propose methods to facilitate the SDR methods when the response can be missing. The first part of the dissertation focuses on the seminal sliced inverse regression (SIR) approach proposed by Li (1991). We show that missing responses generally affect the validity of the inverse regressions under the mechanism of missing at random. We then propose a simple and effective adjustment with inverse probability weighting that guarantees the validity of SIR. Furthermore, a marginal coordinate test is introduced for this adjusted estimator. The proposed method share the simplicity of SIR and requires the linear conditional mean assumption. The second part of the dissertation proposes two new estimating equation procedures: the complete case estimating equation approach and the inverse probability weighted estimating equation approach. The two approaches are applied to a family of dimension reduction methods, which includes ordinary least squares, principal Hessian directions, and SIR. By solving the estimating equations, the two approaches are able to avoid the common assumptions in the SDR literature, the linear conditional mean assumption, and the constant conditional variance assumption. For all the aforementioned methods, the asymptotic properties are established, and their superb finite sample performances are demonstrated through extensive numerical studies as well as a real data analysis. In addition, existing estimators of the central mean space have uneven performances across different types of link functions. To address this limitation, a new hybrid SDR estimator is proposed that successfully recovers the central mean space for a wide range of link functions. Based on the new hybrid estimator, we further study the order determination procedure and the marginal coordinate test. The superior performance of the hybrid estimator over existing methods is demonstrated in simulation studies. Note that the proposed procedures dealing with the missing response at random can be simply adapted to this hybrid method. / Statistics

<p> Solving the integer least squares problem min ||Hs- x|| 2 , where the unknown vector s is comprised of integers, the coefficient matrix H and given vector x are comprised of real numbers arises in many applications and is equivalent to find the closest lattice point to a given one known as NP-hard. In multiple antenna systems, the received signal represented by vector xis not arbitrary, but an lattice point perturbed by an additive noise vector whose statistical properties are known. It has been shown the Sphere Decoding, in which the lattice points inside a hyper-sphere are generated and the closest lattice point to the received signal is determined, together with Maximum Likelihood (ML) method often yields a near-optimal performance on average (cubic) while the worst case complexity is still exponential. By using lattice basis reduction as pre-processing step in the sub-optimum decoding algorithms, we can show that the lattice reduction aided sphere decoding (LRSD) achieves a better performance than the maximum likelihood sphere decoding (MLSD) in terms of symbol error rate (SER) and average algorithm running time. In the FIR (Finite Impulse Response) MIMO channel, the channel matrix is Toeplitz and thus gives us the leverage to use the fact that all its column vectors all linearly independent and the matrix itself is often well-conditioned. </p> <p> In this thesis, we will develop a lattice reduction added sphere decoding algorithm along with an improved LLL algorithm, and provide the simulations to show that this new algorithm achieves a better performance than the maximum likelihood sphere decoding. </p> <p> In chapter 1, we define our system model and establish the foundations for understanding of mathematical model - namly the integer least squares problem, and thus the choice of the simulation data. In chapter 2, we explain the integer least squares problems and exploit serveral ways for solving the problems, then we introduce the sphere decoding and maximum likelihood at the end. In chapter 3, we explore the famous LLL reduction algorithm named after Lenstra, Lenstra and Lovasz in details and show an example how to break Merkle-Hellman code using the LLL reduction algorithm. Finally, in chapter 4 we give the LLL reduction aided sphere decoding algorithm and the experiment setup as well as the simulation results against the MLSD and conclusions, further research directions. </p> / Thesis / Master of Science (MSc)

<p>The overall focus of this thesis is the implementation of a process monitoring system in a real manufacturing environment that utilizes multivariate analysis techniques to assess the state of the process. The process in question was the medium-high volume manufacturing of discrete aluminum parts using relatively simple machining processes involving the use of two tools. This work can be broken down into three main sections.</p><p>The first section involved the modeling of temperatures and thermal expansion measurements for real-time thermal error compensation. Thermal expansion of the Z-axis was measured indirectly through measurement of the two quality parameters related to this axis with a custom gage that was designed for this part. A compensation strategy is proposed which is able to hold the variation of the parts to ±0.02mm, where the tolerance is ±0.05mm.</p><p>The second section involved the modeling of the process data from the parts that included vibration, current, and temperature signals from the machine. The modeling of the process data using Principal Component Analysis (PCA), while unsuccessful in detecting minor simulated process faults, was successful in detecting a miss-loaded part during regular production. Simple control charts using Hotelling's T^2 statistic and Squared Prediction Error are illustrated. The modeling of quality data from the process data of good parts using Projection to Latent Structures by Partial Least Squares (PLS) data did not provide very accurate fits to the data; however, all of the predictions are within the tolerance specifications.</p><p>The final section discusses the implementation of a process monitoring system in both manual and automatic production environments. A method for the integration and storage of process data with Mitutoyo software MCOSMOS and MeasurLink® is described. All of the codes to perform multivariate analysis and process monitoring were written using Matlab.</p> / Thesis / Master of Applied Science (MASc)