Higher-order moments in the theory of diversifying and portfolio composition

This paper examines the role of higher-order moments in portfolio choice within an expected-utility framework. We consider two-, three-, four- and five-parameter density functions for portfolio returns and derive exact conditions under which investors would all be optimally plungers rather than diversifiers. Through comparative statics we show the importance of higher-order risk preference properties, such as riskiness, prudence and temperance, in determining plunging behaviour. Empirical estimates for the S&P500 provide evidence for the optimality of diversification.

Pure higher-order effects in the portfolio choice model

This paper examines the effects of higher-order risk attitudes and statistical moments on the optimal allocation of risky assets within the standard portfolio choice model. We derive the expressions for the optimal proportion of wealth invested in the risky asset to show they are functions of portfolio returns third- and fourth-order moments as well as on the investor’s risk preferences of prudence and temperance. We illustrate the relative importance that the introduction of those higher-order effects have in the decision of expected utility maximizers using data for the US.

Design, analysis and evaluation of sigma-delta based beamformers for medical ultrasound imaging applications

The inherent analogue nature of medical ultrasound signals in conjunction with the abundant merits provided by digital image acquisition, together with the increasing use of relatively simple front-end circuitries, have created considerable demand for single-bit  beamformers in digital ultrasound imaging systems. Furthermore, the increasing need to design lightweight ultrasound systems with low power consumption and low noise, provide ample justification for development and innovation in the use of single-bit  beamformers in ultrasound imaging systems. The overall aim of this research program is to investigate, establish, develop and confirm through a combination of theoretical analysis and detailed simulations, that utilize raw phantom data sets, suitable techniques for the design of simple-to-implement hardware efficient  digital ultrasound beamformers to address the requirements for 3D scanners with large channel counts, as well as portable and lightweight ultrasound scanners for point-of-care applications and intravascular imaging systems. In addition, the stability boundaries of higher-order High-Pass (HP) and Band-Pass (BP) Σ−Δ modulators for single- and dual- sinusoidal inputs are determined using quasi-linear modeling together with the describing-function method, to more accurately model the  modulator quantizer. The theoretical results are shown to be in good agreement with the simulation results for a variety of input amplitudes, bandwidths, and modulator orders. The proposed mathematical models of the quantizer will immensely help speed up the design of higher order HP and BP Σ−Δ modulators to be applicable for digital ultrasound beamformers. Finally, a user friendly design and performance evaluation tool for LP, BP and HP  modulators is developed. This toolbox, which uses various design methodologies and covers an assortment of  modulators topologies, is intended to accelerate the design process and evaluation of  modulators. This design tool is further developed to enable the design, analysis and evaluation of  beamformer structures including the noise analyses of the final B-scan images. Thus, this tool will allow researchers and practitioners to design and verify different reconstruction filters and analyze the results directly on the B-scan ultrasound images thereby saving considerable time and effort.

Design and implementation of generalized topologies of time-interleaved variable bandpass Σ−Δ modulators

In this thesis, novel analog-to-digital and digital-to-analog generalized time-interleaved variable bandpass sigma-delta modulators are designed, analysed, evaluated and implemented that are suitable for high performance data conversion for a broad-spectrum of applications. These generalized time-interleaved variable bandpass sigma-delta modulators can perform noise-shaping for any centre frequency from DC to Nyquist. The proposed topologies are well-suited for Butterworth, Chebyshev, inverse-Chebyshev and elliptical filters, where designers have the flexibility of specifying the centre frequency, bandwidth as well as the passband and stopband attenuation parameters. The application of the time-interleaving approach, in combination with these bandpass loop-filters, not only overcomes the limitations that are associated with conventional and mid-band resonator-based bandpass sigma-delta modulators, but also offers an elegant means to increase the conversion bandwidth, thereby relaxing the need to use faster or higher-order sigma-delta modulators. A step-by-step design technique has been developed for the design of time-interleaved variable bandpass sigma-delta modulators. Using this technique, an assortment of lower- and higher-order single- and multi-path generalized A/D variable bandpass sigma-delta modulators were designed, evaluated and compared in terms of their signal-to-noise ratios, hardware complexity, stability, tonality and sensitivity for ideal and non-ideal topologies. Extensive behavioural-level simulations verified that one of the proposed topologies not only used fewer coefficients but also exhibited greater robustness to non-idealties. Furthermore, second-, fourth- and sixth-order single- and multi-path digital variable bandpass digital sigma-delta modulators are designed using this technique. The mathematical modelling and evaluation of tones caused by the finite wordlengths of these digital multi-path sigmadelta modulators, when excited by sinusoidal input signals, are also derived from first principles and verified using simulation and experimental results. The fourth-order digital variable-band sigma-delta modulator topologies are implemented in VHDL and synthesized on Xilinx® SpartanTM-3 Development Kit using fixed-point arithmetic. Circuit outputs were taken via RS232 connection provided on the FPGA board and evaluated using MATLAB routines developed by the author. These routines included the decimation process as well. The experiments undertaken by the author further validated the design methodology presented in the work. In addition, a novel tunable and reconfigurable second-order variable bandpass sigma-delta modulator has been designed and evaluated at the behavioural-level. This topology offers a flexible set of choices for designers and can operate either in single- or dual-mode enabling multi-band implementations on a single digital variable bandpass sigma-delta modulator. This work is also supported by a novel user-friendly design and evaluation tool that has been developed in MATLAB/Simulink that can speed-up the design, evaluation and comparison of analog and digital single-stage and time-interleaved variable bandpass sigma-delta modulators. This tool enables the user to specify the conversion type, topology, loop-filter type, path number and oversampling ratio.

Examination of the factor structure of the Schizotypal Personality Questionnaire (SPQ) among British and Trinidadian adults

Much debate in schizotypal research has centred on the factor structure of the Schizotypal Personality Questionnaire (SPQ), with research variously showing higher-order dimensionality consisting of two to seven dimensions. In addition, cross-cultural support for the stability of those factors remains limited. Here, we examined the factor structure of the SPQ among British and Trinidadian adults. Participants from a White British sub-sample (n = 351) resident in the UK and from an African Caribbean sub-sample (n = 284) resident in Trinidad completed the SPQ. The higher-order factor structure of the SPQ was analysed through confirmatory factor analysis, followed by multiple-group analysis for the model of best-fit. Between-group differences for sex and ethnicity were investigated using multivariate analysis of variance in relation to the higher-order domains. The model of best-fit was the four-factor structure, which demonstrated measurement invariance across groups. Additionally, these data had an adequate fit for two alternative models: a) 3 factors and b) a modified 4-factor. The British sub-sample had significantly higher scores across all domains than the Trinidadian group, and men scored significantly higher on the disorganised domain than women. The four-factor structure received confirmatory support and, importantly, support for use with populations varying in ethnicity and culture.

Psychometric properties of the Drive for Muscularity Scale in Malay men

The Drive for Muscularity Scale (DMS) is a widely used measure in studies of men’s body image, but few studies have examined its psychometric properties outside English-speaking samples. Here, we assessed the factor structure of a Malay translation of the DMS. A community sample of 159 Malay men from Kuala Lumpur, Malaysia, completed the DMS, along with measures of self-esteem, body appreciation, and muscle discrepancy. Exploratory factor analysis led to the extraction of two factors, differentiating attitudes from behaviours, which mirrors the parent scale. Both factors also loaded on to a higher-order drive for muscularity factor. The subscales of the Malay DMS had adequate internal consistencies and good convergent validity, insofar as significant relationships were reported with self-esteem, body appreciation,muscle discrepancy, and body mass index. These results indicate that the Malay DMS has acceptable psychometric properties and can be used to assess body image concerns in Malay men.