Journal of Data Science

Abstract: It is always useful to have a confidence interval, along with a single estimate of the parameter of interest. We propose a new algorithm for kernel based interval estimation of a density, with an aim to minimize the coverage error. The bandwidth used in the estimator is chosen by minimizing a bootstrap estimate of the absolute value of the coverage error. The resulting confidence interval seems to perform well, in terms of coverage accuracy and length, especially for large sample size. We illustrate our methodology with data on the eruption durations for the Old Faithful geyser in USA. It seems to be the first bandwidth selector in the literature for kernel based interval estimation of a density.

Abstract: Various statistical models have been proposed to analyze fMRI data. The usual goal is to make inferences about the effects that are related to an external stimulus. The primary focus of this paper is on those statistical methods that enable one to detect ‘significantly activated’ regions of the brain due to event-related stimuli. Most of these methods share a common property, requiring estimation of the hemodynamic response function (HRF) as part of the deterministic component of the statistical model. We propose and investigate a new approach that does not require HRF fits to detect ‘activated’ voxels. We argue that the method not only avoids fitting a specific HRF, but still takes into account that the unknown response is delayed and smeared in time. This method also adapts to differential responses of the BOLD response across different brain regions and experimental sessions. The maximum cross-correlation between the kernel-smoothed stimulus sequence and shifted (lagged) values of the observed response is the proposed test statistic. Using our recommended approach we show through realistic simulations and with real data that we obtain better sensitivity than simple correlation methods using default values of SPM2. The simulation experiment incorporates different HRFs empirically determined from real data. The noise models are also different AR(3) fits and fractional Gaussians estimated from real data. We conclude that our proposed method is more powerful than simple correlation procedures, because of its robustness to variation in the HRF.

Abstract: Forecasting incidence and/or mortality rates of cancer is of special inter est to epidemiologists, health researchers and other planners in predicting the demand for health care. This paper proposes a methodology for devel oping prediction intervals using forecasts from Poisson APC models. The annual Canadian age-specific prostate cancer mortality rates among males aged 45 years or older for the period between 1950 and 1990 are calculated using 5-year intervals. The data were analyzed by fitting an APC model to the logarithm of the mortality rate. Based on the fit of the 1950 to 1979 data, the known prostate mortality in 1980 to 1990 is estimated. The period effects, for 1970-1979, are extended linearly to estimate the next ten period effects. With the aims of parsimony, scientific validity, and a reasonable fit to existing data two different possible forms are evaluated namely, the age period and the age-period-cohort models. The asymptotic 95% prediction intervals are based on the standard errors using an assumption of normality (estimate ±1.96× standard error of the estimate)

Abstract: The Weibull distribution has received much interest in reliability theory. The well-known maximum likelihood estimators (MLE) of this fam ily are not available in closed form expression. In this work, we propose a consistent and closed form estimator for shape parameter of three-parameter Weibull distribution. Apart from high degree of performance, the derived estimator is location and scale-invariant.

Abstract: A new set of methods are developed to perform cluster analysis of functions, motivated by a data set consisting of hydraulic gradients at several locations distributed across a wetland complex. The methods build on previous work on clustering of functions, such as Tarpey and Kinateder (2003) and Hitchcock et al. (2007), but explore functions generated from an additive model decomposition (Wood, 2006) of the original time series. Our decomposition targets two aspects of the series, using an adaptive smoother for the trend and circular spline for the diurnal variation in the series. Different measures for comparing locations are discussed, including a method for efficiently clustering time series that are of different lengths using a functional data approach. The complicated nature of these wetlands are highlighted by the shifting group memberships depending on which scale of variation and year of the study are considered.

Abstract: Progress towards government health targets for health areas may be assessed by short term extrapolation of recent trends. Often the observed longitudinal series for a set of health areas is relatively short and a parsimonious model is needed that is adapted to varying observed trajectories between areas. A forecasting model should also include spatial dependence between areas both in representing stable cross-sectional differences and in terms of changing incidence. A fully Bayesian spatio-temporal forecasting model is developed incorporating flexible but parsimonious time dependence while allowing spatial dependencies. An application involves conception rates to women aged under 18 in the 32 boroughs of London.

In this paper, we introduce a new four-parameter distribution called the transmuted Weibull power function (TWPF) distribution which e5xtends the transmuted family proposed by Shaw and Buckley [1]. The hazard rate function of the TWPF distribution can be constant, increasing, decreasing, unimodal, upside down bathtub shaped or bathtub shape. Some mathematical properties are derived including quantile functions, expansion of density function, moments, moment generating function, residual life function, reversed residual life function, mean deviation, inequality measures. The estimation of the model parameters is carried out using the maximum likelihood method. The importance and flexibility of the proposed model are proved empirically using real data sets.

Abstract: It is important to examine the symmetry of an underlying distribution before applying some statistical procedures to a data set. For example, in the Zuni School District case, a formula originally developed by the Department of Education trimmed 5% of the data symmetrically from each end. The validity of this procedure was questioned at the hearing by Chief Justice Roberts. Most tests of symmetry (even nonparametric ones) are not distribution free in finite sample sizes. Hence, using asymptotic distribution may not yield an accurate type I error rate or/and loss of power in small samples. Bootstrap resampling from a symmetric empirical distribution function fitted to the data is proposed to improve the accuracy of the calculated p-value of several tests of symmetry. The results show that the bootstrap method is superior to previously used approaches relying on the asymptotic distribution of the tests that assumed the data come from a normal distribution. Incorporating the bootstrap estimate in a recently proposed test due to Miao, Gel and Gastwirth (2006) preserved its level and shows it has reasonable power properties on the family of distribution evaluated.