Non-Standard Statistical Inference Under Short and Long Range Dependence.

The work discusses different non-standard problems under different types of short and long range dependence. In the first part we introduce new point-wise confidence interval estimates for monotone functions observed with additive and dependent noise. Existence of such monotone trend is quite common in time series data. We study both short- and long-range dependence regimes for the errors. The interval estimates are obtained via the method of inversion of certain discrepancy statistics. This approach avoids the estimation of nuisance parameters such as the derivative of the unknown function, which other methods are forced to deal with. The resulting estimates are therefore more accurate, stable, and widely applicable in practice under mild assumptions on the trend and error structure. While motivated by earlier work in the independent context, the dependence of the errors, especially long-range dependence leads to new phenomena and new universal limits based on convex minorant functionals of drifted fractional Brownian motion. In the second part we investigate the problem of M-estimation, the technique of extracting a parameter estimate by minimizing a loss function is used in almost every statistical problems. We focus on the general theory of such estimators in the presence of dependence in data, a very common feature in time series or econometric applications. Unlike the case of independent and identically distributed observations, there is a lack of an overarching asymptotic theory for M-estimation under dependence. In order to develop a general theory, we have proved a new triangular version of functional central limit theorem for dependent observations, which is useful for broader applications beyond our current paper. We use this general CLT along with standard empirical process techniques to provide the rate and asymptotic distribution of minimizer of a general empirical process. We have used our theory to make inferences for many important problems like change point problems, excess-mass-baseline-inverse problem, different regression settings including maximum score estimator, least absolute deviation regression and censored regression among others.PhDStatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/113564/1/pramita_1.pd

A test for separability in covariance operators of random surfaces

The assumption of separability is a simplifying and very popular assumption in the analysis of spatio-temporal or hypersurface data structures. It is often made in situations where the covariance structure cannot be easily estimated, for example because of a small sample size or because of computational storage problems. In this paper we propose a new and very simple test to validate this assumption. Our approach is based on a measure of separability which is zero in the case of separability and positive otherwise. The measure can be estimated without calculating the full non-separable covariance operator. We prove asymptotic normality of the corresponding statistic with a limiting variance, which can easily be estimated from the available data. As a consequence quantiles of the standard normal distribution can be used to obtain critical values and the new test of separability is very easy to implement. In particular, our approach does neither require projections on subspaces generated by the eigenfunctions of the covariance operator, nor resampling procedures to obtain critical values nor distributional assumptions as recently used by Aston et al. (2017) and Constantinou et al. (2017) to construct tests for separability. We investigate the finite sample performance by means of a simulation study and also provide a comparison with the currently available methodology. Finally, the new procedure is illustrated analyzing wind speed and temperature data

A nonparametric test for stationarity in functional time series

We propose a new measure for stationarity of a functional time series, which is based on an explicit representation of the L2-distance between the spectral density operator of a non-stationary process and its best (L2-)approximation by a spectral density operator corresponding to a stationary process. This distance can easily be estimated by sums of Hilbert-Schmidt inner products of periodogram operators (evaluated at different frequencies), and asymptotic normality of an appropriately standardised version of the estimator can be established for the corresponding estimate under the null hypothesis and alternative. As a result we obtain confidence intervals for the discrepancy of the underlying process from a functional stationary process and a simple asymptotic frequency domain level ® test (using the quantiles of the normal distribution) for the hypothesis of stationarity of functional time series. Moreover, the new methodology allows also to test precise hypotheses of the form “the functional time series is approximately stationarity”, which means that the new measure of stationarity is smaller than a given threshold. Thus in contrast to methods proposed in the literature our approach also allows to test for “relevant” deviations from stationarity. We demonstrate in a small simulation study that the new method has very good finite sample properties and compare it with the currently available alternative procedures. Moreover, we apply our test to annual temperature curves

Social media-based intervention to promote HBV screening and liver cancer prevention among Korean Americans: Results of a pilot study

Objective: In United States, Asian Americans are 10 times more likely to have hepatitis B virus (HBV) infection than Whites. Asian immigrants with limited English proficiency face extra barriers to HBV screening and many are unaware of the infectious status. This study aimed to evaluate a social media-based intervention to promote HBV screening and liver cancer prevention among Korean Americans (KA) with limited English proficiency. Methods: Our community-academia partnership developed the Lets talk about liver cancer mHealth program by adapting a CDC media campaign. The program consisted of culturally tailored short video clips and pictorial messages and was delivered over 4 weeks to the participants via the popular Korean social media app, Kakao Talk. A total 100 KA living in greater Washington DC metropolitan were recruited via social media networks and completed this pre-post pilot study. Results: Out of the 100 participants of KA, 56 were female, mean age was 60, and most have lived in the U.S. for more than 20 years, 84% had limited English proficiency, and 21% had a family history of HBV infection or liver cancer. After 4-week intervention, 95% completed the follow-up survey. Participants reported significant improvements in HBV-related knowledge, liver cancer prevention knowledge, perceived benefits of HBV testing, perceived risks of HBV infection, injunctive norms of HBV testing, and self-efficacy of HBV testing. Conclusions: The Kakao Talk-based liver cancer prevention program for KAs was feasible and effective. We advocate for community-academia partnership to develop and implement culturally appropriate and social media-based interventions for underserved immigrants

A study on the least square estimator of multiple isotonic regression function

Consider the problem of pointwise estimation of f in a multiple isotonic regression model Z = f(X1, ... ,Xd) + ε , where Z is the response variable, f is an unknown non-parametric regression function, which is isotonic with respect to each component, and is the error term. In this article, we investigate the behaviour of the least square estimator of f and establish its asymptotic properties. We generalize the greatest convex minorant characterization of isotonic regression estimator for the multivariate case and use it to establish the asymptotic distribution of properly normalized version of the estimator. Moreover, we test whether the multiple isotonic regression function at a fixed point is larger (or smaller) than a specified value or not based on this estimator, and the consistency of the test is established. The practicability of the estimator and the test are shown on simulated and real data as well

Social media-based intervention to promote HBV screening and liver cancer prevention among Korean Americans: Results of a pilot study

Objective: In United States, Asian Americans are 10 times more likely to have hepatitis B virus (HBV) infection than Whites. Asian immigrants with limited English proficiency face extra barriers to HBV screening and many are unaware of the infectious status. This study aimed to evaluate a social media-based intervention to promote HBV screening and liver cancer prevention among Korean Americans (KA) with limited English proficiency. Methods: Our community-academia partnership developed the Lets talk about liver cancer mHealth program by adapting a CDC media campaign. The program consisted of culturally tailored short video clips and pictorial messages and was delivered over 4 weeks to the participants via the popular Korean social media app, Kakao Talk. A total 100 KA living in greater Washington DC metropolitan were recruited via social media networks and completed this pre-post pilot study. Results: Out of the 100 participants of KA, 56 were female, mean age was 60, and most have lived in the U.S. for more than 20 years, 84% had limited English proficiency, and 21% had a family history of HBV infection or liver cancer. After 4-week intervention, 95% completed the follow-up survey. Participants reported significant improvements in HBV-related knowledge, liver cancer prevention knowledge, perceived benefits of HBV testing, perceived risks of HBV infection, injunctive norms of HBV testing, and self-efficacy of HBV testing. Conclusions: The Kakao Talk-based liver cancer prevention program for KAs was feasible and effective. We advocate for community-academia partnership to develop and implement culturally appropriate and social media-based interventions for underserved immigrants

Acculturation Strategies and Symptoms of Depression: The Mediators of Atherosclerosis in South Asians Living in America (MASALA) Study

Using latent class analysis, we previously identified three acculturation strategies employed by South Asian immigrants in the US. Members of the Separation class showed a preference for South Asian culture over US culture, while members of the Assimilation class showed a preference for US culture, and those in the Integration class showed a similar preference for South Asian and US cultures. The purpose of this study was to examine associations between these acculturation strategies and symptoms of depression, a common yet underdiagnosed and undertreated mental disorder. We used data from the Mediators of Atherosclerosis in South Asians Living in America (MASALA) study (n = 856). Data were collected between October 2010 and March 2013 in the San Francisco Bay Area and Chicago. Depressive symptoms were assessed using the CES-D Scale. Applying a simple new method to account for uncertainty in class assignment when modeling latent classes as an exposure, we found that respondents in the Separation class had more depressive symptoms than those in the Integration class, but only after taking into account self-reported social support (b = 0.11; p = 0.05). There were no differences in depressive symptoms among those in the Assimilation class vs. those in the Integration class (b = -0.06; p = 0.41). Social support may protect against elevated symptoms of depression in South Asian immigrants with lower levels of integration into US culture

Acculturation Strategies Among South Asian Immigrants: The Mediators of Atherosclerosis in South Asians Living in America (MASALA) Study.

In the past, epidemiologic research on acculturation and health has been criticized for its conceptual ambiguity and simplistic measurement approaches. This study applied a widely-used theoretical framework from cross-cultural psychology to identify acculturation strategies among South Asian immigrants in the US and to examine sociodemographic correlates of acculturation strategies. Data were from the Mediators of Atherosclerosis in South Asians Living in America study. We used latent class analysis to identify groups of individuals that were similar based on cultural attitudes and behaviors. We used latent class regression analysis to examine sociodemographic correlates of acculturation strategies. We found that South Asian immigrants employed three acculturation strategies, including separation (characterized by a relatively high degree of preference for South Asian culture over US culture), assimilation (characterized by a relatively high degree of preference for US culture over South Asian culture), and integration (characterized by a similar level of preference for South Asian and US cultures). Respondents with no religious affiliation, those with higher levels of income, those who lived a greater percentage of their lives in the US, and those who spoke English well or very well were less likely to use the separation strategy than the assimilation or integration strategies. Using epidemiologic cohort data, this study illustrated a conceptual and methodological approach that addresses limitations of previous research on acculturation and health. More work is needed to understand how the acculturation strategies identified in this study affect the health of South Asian immigrants in the US