Model Assisted Statistics and Applications

Markov regime switching models remain enormously popular in speech recognition, economics, finance, etc. Nonparametric segmentation in switching models without probability assignment of jump moments is in many papers by Brodsky and Darkhovsky. We model all regimes as long SCOT strings. Stochastic COntext Tree (abbreviated as SCOT) is m -Markov Chain ( m -MC) with every state of a string independent of the symbols in its more remote past than the context of length determined by the preceding symbols of this state. A parallel super-fast fitting and asymptotically optimal inference in a sparse SCOT model including the nonparametric homogeneity test are described in our previous papers. Our segmentation method is a combination of preliminary online change point detection with its subsequent offline Maximal Likelihood update.

In this paper, we present a new continuous time model for nonstationary correlation structures for longitudinal data. This model, which provides a continuous time analogue to the antedependence model and is thus referred to as the continuous antedependence (CAD) model, is intended to provide more refined correlation models for longitudinal data and to better accommodate sparse (or highly unbalanced) data. A key component of this model is the ‘nonstationarity function’ which describes nonstationarity as a unidimensional function of time and has an interesting time expansion/contraction interpretation. Focusing on a Markovian version of the model, we develop a novel nonlinear regression model providing nonlinear least square estimators of model parameters. Both unstructured (for nonparametric estimation) and structured versions of the model are presented. We apply the proposed approach to data from the Multicenter AIDS Clinical Study (MACS), with a focus on inference for the nonstationarity function. In simulation studies, we show good properties (low finite sample bias, and high convergence rates and efficiency) of the proposed unstructured model estimator, which compare favorably to those of an alternative maximum likelihood estimator, particularly in sparse data situations.

The α -stable distribution can describe a degree of concentration of the observations around the mean as well as their asymmetry, regardless of sample size. As the α stability index is the most interesting parameter in the applications, several estimators have been proposed for α . Here we develop an estimator for α (called STNRW-ECF) based on the empirical characteristic function and the Seismic Trace Noise Reduction by Wavelets and Double Threshold Estimation method (STNRW). We analyze the proposed estimator using Monte Carlo simulations and prove its asymptotic Gaussian distribution. Electrocardiography (ECG) is the process of recording the electrical activity of the heart over a period of time using electrodes placed on the skin. The time intervals between its various peaks, may contain useful information about the nature of disease afflicting the heart. To analyze this kind of data can be tiring and more prone to errors when interpreted by human beings, since there is a huge amount information to be processed. Here we propose the STNRW-ECF estimator to be an additional diagnostic tool that may provide an indication of cardiac arrhythmia, and we also propose a test based on the principal wavelet shrinkage to confirm whether or not the STNRW-ECF estimator should be used for this purpose.

One of the main characteristics of data from survival analysis is that the random variable of interest is not always observed, so that some observations are censored. The usual methods consider that these observations do not carry information about the distribution of the response variable (non-informative censoring). In other words, it is considered that an observation is censored simply by the fact that the event of interest (failure or death) did not occur during the period of study. However, in many situations, the survival time is clearly perturbed by the censoring mechanism, so the effect produced must be included in the analysis. The question is that once informative censoring is assumed to be non-informative, the results of the analysis can mask biases and thus weakening the model’s predictive power. Therefore, we consider the informative censoring mechanism in the odd-logistic Weibull regression model, based on the method described in Huang and Wolfe (2002), to analyze the variations which occur for estimating the model parameters. We obtain maximum likelihood estimates of the parameters by considering censored data and evaluate local influence on the estimates for different perturbation schemes. In addition, we define martingale and deviance residuals to detect outliers and evaluate the model assumptions. We show that the proposed regression model is useful to the analysis of real data and may give more realistic fits than other special regression models.

In this paper it is introduced a new two-parameter discrete distribution derived from the continuous Sushila distribution (Shanker et al., 2013). Its mathematical properties and estimation procedures for the parameters of the proposed model are presented assuming complete and right-censored data. This new model, in the same way as the continuous Sushila distribution, has the discrete Lindley distribution as a special case. An extensive simulation study is carried out to examine the bias and the roots of the mean squared errors for the maximum likelihood estimators as well the moments and Bayesian estimators of the proposed model parameters. Some examples using simulated data and real datasets are considered to show that the new proposed model performs at least as good as its particular case and some other traditional discrete models as the Poisson and geometric distributions.

In sampling from finite populations to estimate the finite population mean/total of the study variable, one often observes available information on an associated auxiliary variable along with study variable to obtain an estimator, which is more efficient than the simple mean per unit estimator based on observations on study variable only. The classical ratio estimator is one such estimator, which is simple to compute and is more efficient than the simple mean per unit estimator under certain conditions. However, the ratio estimator in spite of its simplicity is a biased estimator having bias of O ⁢ ( 1 / n ) , n being the sample size. The bias may be negligible when the sample size is very large. For small sample size the bias may be substantially large so as to make the estimate unreliable to be used in practice. Beale (1962) and Tin (1965) have suggested some modified forms of ratio estimator which remove the first order bias, thus reducing the biases to O ⁢ ( 1 / n 2 ) . Such modified ratio estimators are called Almost Unbiased Ratio estimators. This paper deals with construction of Generalized class of Almost unbiased ratio estimators using Srivastava’s (1971) generalized class of estimators and finds their expected values and variances in a generalized form. Further, as special cases Bahl-Tuteja’s (1991) ratio type exponential estimator and Swain’s (2014) square root transformation ratio type estimator are compared with regard to bias and efficiency along with numerical illustrations.