A flexible generalization of the skew normal distribution based on a weighted normal distribution

The skew normal distribution of Azzalini (Scand J Stat 12:171–178, 1985) has been found suitable for unimodal density but with some skewness present. Through this article, we introduce a flexible extension of the Azzalini (Scand J Stat 12:171–178, 1985) skew normal distribution based on a symmetric component normal distribution (Gui et al. in J Stat Theory Appl 12(1):55–66, 2013). The proposed model can efficiently capture the bimodality, skewness and kurtosis criteria and heavy-tail property. The paper presents various basic properties of this family of distributions and provides two stochastic representations which are useful for obtaining theoretical properties and to simulate from the distribution. Further, maximum likelihood estimation of the parameters is studied numerically by simulation and the distribution is investigated by carrying out comparative fitting of three real datasets.     

Calibration estimation in dual-frame surveys

Survey statisticians make use of auxiliary information to improve estimates. One important example is calibration estimation, which constructs new weights that match benchmark constraints on auxiliary variables while remaining “close” to the design weights. Multiple-frame surveys are increasingly used by statistical agencies and private organizations to reduce sampling costs and/or avoid frame undercoverage errors. Several ways of combining estimates derived from such frames have been proposed elsewhere; in this paper, we extend the calibration paradigm, previously used for single-frame surveys, to calculate the total value of a variable of interest in a dual-frame survey. Calibration is a general tool that allows to include auxiliary information from two frames. It also incorporates, as a special case, certain dual-frame estimators that have been proposed previously. The theoretical properties of our class of estimators are derived and discussed, and simulation studies conducted to compare the efficiency of the procedure, using different sets of auxiliary variables. Finally, the proposed methodology is applied to real data obtained from the Barometer of Culture of Andalusia survey.     

Maximal autocorrelation functions in functional data analysis

This paper proposes a new factor rotation for the context of functional principal components analysis. This rotation seeks to re-express a functional subspace in terms of directions of decreasing smoothness as represented by a generalized smoothing metric. The rotation can be implemented simply and we show on two examples that this rotation can improve the interpretability of the leading components.     

On the robustness of the generalized fused lasso to prior specifications

Using networks as prior knowledge to guide model selection is a way to reach structured sparsity. In particular, the fused lasso that was originally designed to penalize differences of coefficients corresponding to successive features has been generalized to handle features whose effects are structured according to a given network. As any prior information, the network provided in the penalty may contain misleading edges that connect coefficients whose difference is not zero, and the extent to which the performance of the method depend on the suitability of the graph has never been clearly assessed. In this work we investigate the theoretical and empirical properties of the adaptive generalized fused lasso in the context of generalized linear models. In the fixed \(p\) setting, we show that, asymptotically, adding misleading edges in the graph does not prevent the adaptive generalized fused lasso from enjoying asymptotic oracle properties, while forgetting suitable edges can be more problematic. These theoretical results are complemented by an extensive simulation study that assesses the robustness of the adaptive generalized fused lasso against misspecification of the network as well as its applicability when theoretical coefficients are not exactly equal. Our contribution is also to evaluate the applicability of the generalized fused lasso for the joint modeling of multiple sparse regression functions. Illustrations are provided on two real data examples.     

Finie mixures of canonical fundamenal skew $$$$-disribuions

This paper introduces a finite mixture of canonical fundamental skew \(t\) (CFUST) distributions for a model-based approach to clustering where the clusters are asymmetric and possibly long-tailed (in: Lee and McLachlan, arXiv:1401.8182 [statME], 2014b). The family of CFUST distributions includes the restricted multivariate skew \(t\) and unrestricted multivariate skew \(t\) distributions as special cases. In recent years, a few versions of the multivariate skew \(t\) (MST) mixture model have been put forward, together with various EM-type algorithms for parameter estimation. These formulations adopted either a restricted or unrestricted characterization for their MST densities. In this paper, we examine a natural generalization of these developments, employing the CFUST distribution as the parametric family for the component distributions, and point out that the restricted and unrestricted characterizations can be unified under this general formulation. We show that an exact implementation of the EM algorithm can be achieved for the CFUST distribution and mixtures of this distribution, and present some new analytical results for a conditional expectation involved in the E-step.     

New recursive estimators of the time-average variance constant

Estimation of the time-average variance constant (TAVC) of a stationary process plays a fundamental role in statistical inference for the mean of a stochastic process. Wu (2009) proposed an efficient algorithm to recursively compute the TAVC with \(O(1)\) memory and computational complexity. In this paper, we propose two new recursive TAVC estimators that can compute TAVC estimate with \(O(1)\) computational complexity. One of them is uniformly better than Wu’s estimator in terms of asymptotic mean squared error (MSE) at a cost of slightly higher memory complexity. The other preserves the \(O(1)\) memory complexity and is better then Wu’s estimator in most situations. Moreover, the first estimator is nearly optimal in the sense that its asymptotic MSE is \(2^{10/3}3^{-2} \fallingdotseq 1.12\) times that of the optimal off-line TAVC estimator.     

Approximate Bayesian computation with composite score functions

Both approximate Bayesian computation (ABC) and composite likelihood methods are useful for Bayesian and frequentist inference, respectively, when the likelihood function is intractable. We propose to use composite likelihood score functions as summary statistics in ABC in order to obtain accurate approximations to the posterior distribution. This is motivated by the use of the score function of the full likelihood, and extended to general unbiased estimating functions in complex models. Moreover, we show that if the composite score is suitably standardised, the resulting ABC procedure is invariant to reparameterisations and automatically adjusts the curvature of the composite likelihood, and of the corresponding posterior distribution. The method is illustrated through examples with simulated data, and an application to modelling of spatial extreme rainfall data is discussed.     

Computing the log concave NPMLE for interval censored data

In analyzing interval censored data, a non-parametric estimator is often desired due to difficulties in assessing model fits. Because of this, the non-parametric maximum likelihood estimator (NPMLE) is often the default estimator. However, the estimates for values of interest of the survival function, such as the quantiles, have very large standard errors due to the jagged form of the estimator. By forcing the estimator to be constrained to the class of log concave functions, the estimator is ensured to have a smooth survival estimate which has much better operating characteristics than the unconstrained NPMLE, without needing to specify a parametric family or smoothing parameter. In this paper, we first prove that the likelihood can be maximized under a finite set of parameters under mild conditions, although the log likelihood function is not strictly concave. We then present an efficient algorithm for computing a local maximum of the likelihood function. Using our fast new algorithm, we present evidence from simulated current status data suggesting that the rate of convergence of the log-concave estimator is faster (between \(n^{2/5}\) and \(n^{1/2}\)) than the unconstrained NPMLE (between \(n^{1/3}\) and \(n^{1/2}\)).     

Variable selection for survival data with a class of adaptive elastic net techniques

The accelerated failure time (AFT) models have proved useful in many contexts, though heavy censoring (as for example in cancer survival) and high dimensionality (as for example in microarray data) cause difficulties for model fitting and model selection. We propose new approaches to variable selection for censored data, based on AFT models optimized using regularized weighted least squares. The regularized technique uses a mixture of \(\ell _1\) and \(\ell _2\) norm penalties under two proposed elastic net type approaches. One is the adaptive elastic net and the other is weighted elastic net. The approaches extend the original approaches proposed by Ghosh (Adaptive elastic net: an improvement of elastic net to achieve oracle properties, Technical Reports 2007) and Hong and Zhang (Math Model Nat Phenom 5(3):115–133 2010), respectively. We also extend the two proposed approaches by adding censoring observations as constraints into their model optimization frameworks. The approaches are evaluated on microarray and by simulation. We compare the performance of these approaches with six other variable selection techniques-three are generally used for censored data and the other three are correlation-based greedy methods used for high-dimensional data.