Thesis (Ph. D.)--Oregon State University, 1969. / Typescript. Includes bibliographical references (leaves 76-79). Also available on the World Wide Web.

Thesis (Ph. D.)--Ohio State University, 2004. / Title from first page of PDF file. Document formatted into pages; contains xii, 119 p.; also includes graphics (some col.). Includes bibliographical references (p. 106-109). Available online via OhioLINK's ETD Center

Thesis (Ph.D.)--University of Delaware, 2009. / Principal faculty advisor: Wenbo Li, Dept. of Mathematical Sciences. Includes bibliographical references.

Thesis (M.S.)--Oregon State University, 2011. / Printout. Includes bibliographical references (leaves 57-59). Also available on the World Wide Web.

Thesis (M.Phil.)--Hong Kong University of Science and Technology, 2008. / Includes bibliographical references (p. 114).

Much work has been done on design of efficient coded modulation schemes since the publication of [Ungerboeck, 1982] for trellis coded modulation and [Imai & Hirakawa, 1977] for block coded modulation. Recently, increasing interest in digital mobile radio and indoor wireless systems has led to the consideration of coded modulation designs for combating fading channels. In this research, it is intended to present results of an investigation of the construction of Reed Solomon coded MPSK modulation which is robust for the Gaussian channel and a Rayleigh fading channel. Two approaches have been applied to Reed Solomon coded modulation. First, a Reed Solomon code was combined with MPSK signal set using Gray code mapping; this was called Reed Solomon coded modulation not based on set partitioning. This approach was the baseline scheme which would be compared with the proposed approach, namely Reed Solomon coded modulation based on set partitioning. The second approach to coded MPSK with M = 2m was multilevel Reed Solomon coding. In this case, each of the m bits defining an MPSK symbol was coded and decoded by different Reed Solomon codecs. The set partitioning principle was applied to define subsets with distances Deltai,-, (i = 1 to m) that were nondecreasing with i. Each of the m bits defined a subset and was decoded in multistage decoding schemes. The novel idea here was that in the receiver, we used a rotated 2m+1-PSK detector if the transmitter used a 2m-PSK modulator. The designs of Reed Solomon coded modulation schemes for the Gaussian channel and a Rayleigh fading channel (i.e. choice of the code configurations which were suitable for this channel) have been studied. The performance of Reed Solomon coded modulation based on set partitioning was compared with Reed Solomon coded modulation not based on set-partitioning, then with multilevel Reed Solomon coded modulation using Gray mapping and finally with coded modulation schemes using binary codes, Reed Muller codes. It has been shown that over the Gaussian channel and a Rayleigh fading channel, Reed Solomon coded modulation based on set partitioning is better than several alternatives, such as schemes not based on set partitioning, multistage Reed Solomon coded modulation based on Gray mapping and Reed Muller coded modulation. It was found that good codes for a Rayleigh fading channel have configurations in which all component codes have the same minimum Hamming distance because the fading phase is uniformly distributed random process. Therefore, by matching configurations of component codes with the channel characteristics, it was shown that Reed Solomon coded modulation based on set partitioning was robust for the Gaussian and a Rayleigh fading channel. Reed Solomon coded modulation schemes were applied to Orthogonal Frequency Division Multiplexing (OFDM) transmissions. The main disadvantage of OFDM systems is that they have high Peak-to-Mean Envelope Power Ratio (PMEPR). A scheme for reducing the PMEPR of OFDM systems was investigated. Multiphase complementary code pairs of length 2 are proposed to reduce the PMEPR of MPSK and QAM OFDM. Concatenated codes with Reed Solomon coded modulation as an inner code and an RS(511, 443) code as an outer code are proposed as coding schemes for OFDM systems.

Kernel embedding methods have witnessed a great deal of practical success in the area of nonparametric hypothesis testing in recent years. But ever since its first proposal, there exists an inevitable problem that researchers in this area have been trying to answer--what kernel should be selected, because the performance of the associated nonparametric tests can vary dramatically with different kernels. While the way of kernel selection is usually ad hoc, we wonder if there exists a principled way of kernel selection so as to ensure that the associated nonparametric tests have good performance. As consistency results against fixed alternatives do not tell the full story about the power of the associated tests, we study their statistical performance within the minimax framework. First, focusing on the case of goodness-of-fit tests, our analyses show that a vanilla version of the kernel embedding based test could be suboptimal, and suggest a simple remedy by moderating the kernel. We prove that the moderated approach provides optimal tests for a wide range of deviations from the null and can also be made adaptive over a large collection of interpolation spaces. Then, we study the asymptotic properties of goodness-of-fit, homogeneity and independence tests using Gaussian kernels, arguably the most popular and successful among such tests. Our results provide theoretical justifications for this common practice by showing that tests using a Gaussian kernel with an appropriately chosen scaling parameter are minimax optimal against smooth alternatives in all three settings. In addition, our analysis also pinpoints the importance of choosing a diverging scaling parameter when using Gaussian kernels and suggests a data-driven choice of the scaling parameter that yields tests optimal, up to an iterated logarithmic factor, over a wide range of smooth alternatives. Numerical experiments are presented to further demonstrate the practical merits of our methodology.

Cross-validation is a widely used technique in statistics and machine learning for predictive performance assessment and model selection. It involves dividing the available data into multiple sets, training the model on some of the data and testing it on the rest, and repeating this process multiple times. The goal of cross-validation is to assess the model’s predictive performance on unseen data. Two standard methods for cross-validation are leave-one-out cross-validation and K-fold cross-validation. However, these methods may not be suitable for structured models with many potential prediction tasks, as they do not take into account the structure of the data. As a solution, leave-group-out cross-validation is an extension of cross-validation that allows the left-out groups to make training sets and testing points to adapt to different prediction tasks. In this dissertation, we propose an automatic group construction procedure for leave-group-out cross-validation to estimate the predictive performance of the model when the prediction task is not specified. We also propose an efficient approximation of leave-group-out cross-validation for latent Gaussian models. Both of these procedures are implemented in the R-INLA software. We demonstrate the usefulness of our proposed leave-group-out cross-validation method through its application in the joint modeling of survival data and longitudinal data. The example shows the effectiveness of this method in real-world scenarios.

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