Asymptotic theory of least squares estimators for nearly unstable processes under strong dependence

This paper considers the effect of least squares procedures for nearly unstable linear time series with strongly dependent innovations. Under a general framework and appropriate scaling, it is shown that ordinary least squares procedures converge to functionals of fractional Ornstein--Uhlenbeck processes. We use fractional integrated noise as an example to illustrate the important ideas. In this case, the functionals bear only formal analogy to those in the classical framework with uncorrelated innovations, with Wiener processes being replaced by fractional Brownian motions. It is also shown that limit theorems for the functionals involve nonstandard scaling and nonstandard limiting distributions. Results of this paper shed light on the asymptotic behavior of nearly unstable long-memory processes.Comment: Published in at http://dx.doi.org/10.1214/009053607000000136 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Fractional constant elasticity of variance model

This paper develops a European option pricing formula for fractional market models. Although there exist option pricing results for a fractional Black-Scholes model, they are established without accounting for stochastic volatility. In this paper, a fractional version of the Constant Elasticity of Variance (CEV) model is developed. European option pricing formula similar to that of the classical CEV model is obtained and a volatility skew pattern is revealed.Comment: Published at http://dx.doi.org/10.1214/074921706000001012 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

The Clinical Utility of Zinc Transporter 8 Autoantibody Measurement in Diabetes

Maturity onset diabetes of the young (MODY) is caused by single gene mutations that are of autosomal dominant inheritance. Mutations are highly penetrant, and patients often develop a phenotype similar to type 1 or type 2 diabetes. Glucokinase, Hepatic nuclear factor 1a and 4a mutations consists of 80% of MODY cases. Approximately 1% of patients with diabetes have MODY, and it is often misdiagnosed. Diagnosis is important as patients with MODY often have a good prognosis and glycaemic control if they are treated appropriately. The aim of this thesis was to explore the use of islet autoantibodies, in particular a new autoantibody against Zinc Transporter 8, as biomarkers to identify MODY. A literature review of MODY and its important subtypes are discussed. It highlights the major mutation that cause MODY and the management of patients with MODY is also explored. Islet autoantibodies will also be reviewed in the same chapter, with a discussion on established autoantibodies and ZnT8 autoantibodies in relation to type 1 diabetes. Chapter 1 aims to investigate whether ZnT8 autoantibodies are similar to established autoantibodies against GAD and IA-2 as a biomarker in differentiating T1D patients from MODY patients. The prevalence of ZnT8 autoantibodies in MODY patients and the effect of disease duration on antibody prevalence and discriminative power would also be investigated. In Chapter 2, a study was performed to investigate whether islet autoantibodies are useful in the MODY referral setting in ruling out patients for genetic testing. This is a way to rationalise genetic testing at the Exeter molecular genetics referral service. Additionally, other biomarkers will also be investigated, namely C-peptide levels and Type 1 Diabetes Genetic Risk score. Results from the study will have implications to how MODY is diagnosed at the referral service. A discussion of the findings of each chapter, implications and plans for future research will be explored in chapter 3

Decoding the consumer’s brain: Neural representations of consumer experience

Understanding consumer experience – what consumers think about brands, how they feel about services, whether they like certain products – is crucial to marketing practitioners. ‘Neuromarketing’, as the application of neuroscience in marketing research is called, has generated excitement with the promise of understanding consumers’ minds by probing their brains directly. Recent advances in neuroimaging analysis leverage machine learning and pattern classification techniques to uncover patterns from neuroimaging data that can be associated with thoughts and feelings. In this dissertation, I measure brain responses of consumers by functional magnetic resonance imaging (fMRI) in order to ‘decode’ their mind. In three different studies, I have demonstrated how different aspects of consumer experience can be studied with fMRI recordings. First, I study how consumers think about brand image by comparing their brain responses during passive viewing of visual templates (photos depicting various social scenarios) to those during active visualizing of a brand’s image. Second, I use brain responses during viewing of affective pictures to decode emotional responses during watching of movie-trailers. Lastly, I examine whether marketing videos that evoke s

Integrated functionals of normal and fractional processes

Consider $Z^f_t(u)=\int_0^{tu}f(N_s) ds$, $t>0$, $u\in[0,1]$, where $N=(N_t)_{t\in\mathbb{R}}$ is a normal process and $f$ is a measurable real-valued function satisfying $Ef(N_0)^2<\infty$ and $Ef(N_0)=0$. If the dependence is sufficiently weak Hariz [J. Multivariate Anal. 80 (2002) 191--216] showed that $Z_t^f/t^{1/2}$ converges in distribution to a multiple of standard Brownian motion as $t\to\infty$. If the dependence is sufficiently strong, then $Z_t/(EZ_t(1)^2)^{1/2}$ converges in distribution to a higher order Hermite process as $t\to\infty$ by a result by Taqqu [Wahrsch. Verw. Gebiete 50 (1979) 53--83]. When passing from weak to strong dependence, a unique situation encompassed by neither results is encountered. In this paper, we investigate this situation in detail and show that the limiting process is still a Brownian motion, but a nonstandard norming is required. We apply our result to some functionals of fractional Brownian motion which arise in time series. For all Hurst indices $H\in(0,1)$, we give their limiting distributions. In this context, we show that the known results are only applicable to $H3/4$, respectively, whereas our result covers $H=3/4$.Comment: Published in at http://dx.doi.org/10.1214/08-AAP531 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Residual empirical processes for long and short memory time series

This paper studies the residual empirical process of long- and short-memory time series regression models and establishes its uniform expansion under a general framework. The results are applied to the stochastic regression models and unstable autoregressive models. For the long-memory noise, it is shown that the limit distribution of the Kolmogorov-Smirnov test statistic studied in Ho and Hsing [Ann. Statist. 24 (1996) 992-1024] does not hold when the stochastic regression model includes an unknown intercept or when the characteristic polynomial of the unstable autoregressive model has a unit root. To this end, two new statistics are proposed to test for the distribution of the long-memory noises of stochastic regression models and unstable autoregressive models. (With Correction.)Comment: Published in at http://dx.doi.org/10.1214/07-AOS543 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Identifying items for assessing the expressive vocabulary of 4-year-old Cantonese-speaking children

Thesis (B.Sc)--University of Hong Kong, 2010."A dissertation submitted in partial fulfillment of the requirements for the Bachelor of Science (Speech and Hearing Sciences), The University of Hong Kong, June 30, 2010."Includes bibliographical references (p. 27-30).This study aimed at identifying items for assessing the expressive vocabulary of 4-year-old Cantonese-speaking children in Hong Kong using a dynamic elicitation method. In phase 1, 214 words were selected from various language sources and their levels of difficulty were rated by 10 experienced preschool teachers. A revised list of 99 words, which consisted of different difficulty levels and word types, were chosen. A PowerPoint file was then made to present the pictures and video clips for eliciting these words. In phase 2, the 99 words were tested on 32 4-year-old children recruited from two local preschools. Forty-seven words met the required item statistics for inclusion in the final word list for further development of an expressive vocabulary test. Characteristics of the final word list and the children’s performance were discussed. This study also provided some preliminary data on 4-year-old Hong Kong Cantonese children’s understanding of English vocabulary.published_or_final_versionSpeech and Hearing SciencesBachelorBachelor of Science in Speech and Hearing Science