In the field of linear regression analysis, a single outlier can dramatically influence ordinary least squares estimation while low-breakdown procedures such as M regression and bounded influence regression may be unable to combat a small percentage of outliers. A high-breakdown procedure such as least trimmed squares (LTS) regression can accommodate up to 50% of the data (in the limit) being outlying with respect to the general trend. Two available one-step improvement procedures based on LTS are Mallows 1-step (M1S) regression and Schweppe 1-step (S1S) regression (the current state-of-the-art method). Issues with these methods include (1) computational approximations and sub-sampling variability, (2) dramatic coefficient sensitivity with respect to very slight differences in initial values, (3) internal instability when determining the general trend and (4) performance in low-breakdown scenarios. A new high-breakdown regression procedure is introduced that addresses these issues, plus offers an insightful summary regarding the presence and structure of multivariate outliers. This proposed method blends a cluster analysis phase with a controlled bounded influence regression phase, thereby referred to as cluster-based bounded influence regression, or CBI. Representing the data space via a special set of anchor points, a collection of point-addition OLS regression estimators forms the basis of a metric used in defining the similarity between any two observations. Cluster analysis then yields a main cluster "halfset" of observations, with the remaining observations becoming one or more minor clusters. An initial regression estimator arises from the main cluster, with a multiple point addition DFFITS argument used to carefully activate the minor clusters through a bounded influence regression framework. CBI achieves a 50% breakdown point, is regression equivariant, scale equivariant and affine equivariant and distributionally is asymptotically normal. Case studies and Monte Carlo studies demonstrate the performance advantage of CBI over S1S and the other high breakdown methods regarding coefficient stability, scale estimation and standard errors. A dendrogram of the clustering process is one graphical display available for multivariate outlier detection. Overall, the proposed methodology represents advancement in the field of robust regression, offering a distinct philosophical viewpoint towards data analysis and the marriage of estimation with diagnostic summary. / Ph. D.

Atkinson 及 Riani 應用前進搜尋演算法來處理百牡利資料中所包含的多重離群值(2001）。在這篇論文中，我們沿用相同的想法來處理在不完整資料下一般線性模型中的多重離群值。這個演算法藉由先填補資料中遺漏的部分，再利用前進搜尋演算法來確認資料中的離群值。我們所提出的方法可以解決處理多重離群值時常會遇到的遮蓋效應。我們應用了一些真實資料來說明這個演算法並得到令人滿意結果。 / Atkinson and Riani (2001) apply the forward search algorithm to deal with the problem of the detection of multiple outliers in binomial data. In this thesis, we extend the similar idea to identify multiple outliers for the generalized linear models when part of data are missing. The algorithm starts with imputation method to fill-in the missing observations in the data, and then use the forward search algorithm to confirm outliers. The proposed method can overcome the masking effect, which commonly occurs when multiple outliers exit in the data. Real data are used to illustrate the procedure, and satisfactory results are obtained.

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The initial portion of this research focuses on appropriate parameter estimators within a general context of multivariate quality control. The goal of Phase I analysis of multivariate quality control data is to identify multivariate outliers and step changes so that the estimated control limits are sufficiently accurate for Phase II monitoring. High breakdown estimation methods based on the minimum volume ellipsoid (MVE) or the minimum covariance determinant (MCD) are well suited to detecting multivariate outliers in data. Because of the inherent difficulties in computation many algorithms have been proposed to obtain them. We consider the subsampling algorithm to obtain the MVE estimators and the FAST-MCD algorithm to obtain the MCD estimators. Previous studies have not clearly determined which of these two estimation methods is best for control chart applications. The comprehensive simulation study here gives guidance for when to use which estimator. Control limits are provided. High breakdown estimation methods such as MCD and MVE can be applied to a wide variety of multivariate quality control data. The final, lengthier portion of this research considers profile monitoring. Profile monitoring is a relatively new technique in quality control used when the product or process quality is best represented by a profile (or a curve) at each time period. The essential idea is often to model the profile via some parametric method and then monitor the estimated parameters over time to determine if there have been changes in the profiles. Because the estimated parameters may be correlated, it is convenient to monitor them using a multivariate control method such as the T-squared statistic. Previous modeling methods have not incorporated the correlation structure within the profiles. We propose the use of mixed models (both linear and nonlinear) to monitor linear and nonlinear profiles in order to account for the correlation structure within a profile. We consider various data scenarios and show using simulation when the mixed model approach is preferable to an approach that ignores the correlation structure. Our focus is on Phase I control chart applications. / Ph. D.

The Square Kilometre Array (SKA) is a multibillion and a multinational science project to build the world’s largest and most sensitive radio telescope. For a very large field of view, the combined collecting area would be one square kilometre (or 1, 000, 000 square metre) and spread over more than 3,000 km wide which will require a massive count of antennas (thousands). Each of the antennas contains hundreds of low noise amplifier (LNA) circuits. The antenna arrays are divided into low, medium and high operational frequencies and located at different positions to boost up the telescope’s scanning sensitivity.The objective of this work was to develop and fabricate fully on-chip LNA circuits to meet the stringent requirements for the mid-frequency array from 0.4 GHz to 1.4 GHz of the SKA radio astronomy telescope using Monolithic Microwave Integrated Circuit technology (MMIC). Due to the number of LNA reaching figures of millions, the fabricated circuits were designed with the consideration for low cost fabrication and high reliability in the receiver chain. Therefore, a relaxed optical lithography with Lg = 1 µm was adopted for a high yield fabrication process.Towards the fulfilment of the device’s low noise characteristics, a large number of device designs, fabrication and characterisation of InGaAs/InAlAs/InP pHEMTs were undertaken. These include optimisations at each critical fabrication steps. The device’s high breakdown and very low gate leakage characteristics were further improved by a combination of judicious epitaxial growth and manipulation of materials’ energy gaps. An attempt to increase the device breakdown voltage was also employed by incorporating Field Plate structure at the gate terminal. This yielded the devices with improvements in the breakdown voltage up to 15 V and very low gate leakage of 1 µA/mm, in addition to high transconductance (gm) characteristic. Fully integrated double stage LNA had measured NF varying from 1.2 dB to 1.6 dB from 0.4 GHz to 1.4 GHz, compared with a slightly lower NF obtained from simulation (0.8 dB to 1.1 dB) across the same frequency band.These are amongst the attractive device properties for the implementation of a fully on-chip MMIC LNA circuits demonstrated in this work. The lower circuit’s low noise characteristic has been demonstrated using large gate width geometry pHEMTs, where the system’s noise resistance (Rn) has successfully reduced to a few ohms. The work reported here should facilitate the successful implementation of rugged low noise amplifiers as required by SKA receivers.