Statistics

We propose a method of constructing a network, in which its time structure is directly incorporated, based on a deterministic model from a time series. To construct such a network, we transform a linear model containing terms with different time delays into network topology. The terms in the model are translated into temporal nodes of the network. On each link connecting these nodes, we assign a positive real number representing the strength of relationship, or the "distance," between nodes specified by the parameters of the model. The method is demonstrated by a known system and applied to two actual time series.

We give a geometrically motivated measure of skewness, define a mean value triangle number, and dispersion (in that order) of a fuzzy number without reference or seeking analogy to the namesake but parallel concepts in probability theory. These measures come about by way of a new representation of fuzzy numbers as parameterized curves respectively their associated tangent bundle. Importantly skewness and dispersion are given as functions of α (the degree of membership) and such may be given separately and pointwise at each α -level, as well as overall. This allows for e.g., when a mathematical model is formulated in fuzzy numbers, to run optimization programs level-wise thereby encapsuling with deliberate accuracy the involved membership functions' characteristics while increasing the computational complexity by only a multiplicative factor compared to the same program formulated in real variables and parameters. As an example the work offers a contribution to the recently very popular fuzzy mean-variance-skewness portfolio optimization.

In the present paper we construct plans orthogonal through the block factor (POTBs). We describe procedures for adding blocks as well as factors to an initial plan and thus generate a bigger plan. Using these procedures we construct POTBs for symmetrical experiments with factors having three or more levels. We also construct a series of plans inter-class orthogonal through the block factor for two-level factors.

In this paper after a brief revision of VW-means, which are extrinsic means on real and complex projective spaces, relative to the Veronese-Whitney embeddings, we give two examples of sample VW means computations on planar Kendall shape spaces. Here we derive large sample and pivotal nonparametric bootstrap confidence regions for VW-antimeans, using VW-anti-covariance matrices, and their sample counterparts

Spherical regression explores relationships between variables on spherical domains. We develop a nonparametric model that uses a diffeomorphic map from a sphere to itself. The restriction of this mapping to diffeomorphisms is natural in several settings. The model is estimated in a penalized maximum-likelihood framework using gradient-based optimization. Towards that goal, we specify a first-order roughness penalty using the Jacobian of diffeomorphisms. We compare the prediction performance of the proposed model with state-of-the-art methods using simulated and real data involving cloud deformations, wind directions, and vector-cardiograms. This model is found to outperform others in capturing relationships between spherical variables.

Nonparametric regression is a standard statistical tool with increased importance in the Big Data era. Boundary points pose additional difficulties but local polynomial regression can be used to alleviate them. Local linear regression, for example, is easy to implement and performs quite well both at interior as well as boundary points. Estimating the conditional distribution function and/or the quantile function at a given regressor point is immediate via standard kernel methods but problems ensue if local linear methods are to be used. In particular, the distribution function estimator is not guaranteed to be monotone increasing, and the quantile curves can "cross". In the paper at hand, a simple method of correcting the local linear distribution estimator for monotonicity is proposed, and its good performance is demonstrated via simulations and real data examples.

We study the nonparametric estimation of the branching rate B(x) of a supercritical Bellman-Harris population: a particle with age x has a random lifetime governed by B(x) ; at its death time, it gives rise to k≥2 children with lifetimes governed by the same division rate and so on. We observe in continuous time the process over [0,T] . Asymptotics are taken as T→∞ ; the data are stochastically dependent and one has to face simultaneously censoring, bias selection and non-ancillarity of the number of observations. In this setting, under appropriate ergodicity properties, we construct a kernel-based estimator of B(x) that achieves the rate of convergence exp(− λ B β 2β+1 T) , where λ B is the Malthus parameter and β>0 is the smoothness of the function B(x) in a vicinity of x . We prove that this rate is optimal in a minimax sense and we relate it explicitly to classical nonparametric models such as density estimation observed on an appropriate (parameter dependent) scale. We also shed some light on the fact that estimation with kernel estimators based on data alive at time T only is not sufficient to obtain optimal rates of convergence, a phenomenon which is specific to nonparametric estimation and that has been observed in other related growth-fragmentation models.

Recently Kim and Kvam (2004) and Singh, Sharma, Kumar (2008) proposed different load-sharing models and developed parametric inference for the these models. However, their parametric estimates are calculated using iterative numerical methods. In this note, we provide the general closed-form MLEs for the two load-sharing models provided by them.

Null hypothesis statistical significance tests (NHST) are widely used in quantitative research in the empirical sciences including scientometrics. Nevertheless, since their introduction nearly a century ago significance tests have been controversial. Many researchers are not aware of the numerous criticisms raised against NHST. As practiced, NHST has been characterized as a null ritual that is overused and too often misapplied and misinterpreted. NHST is in fact a patchwork of two fundamentally different classical statistical testing models, often blended with some wishful quasi-Bayesian interpretations. This is undoubtedly a major reason why NHST is very often misunderstood. But NHST also has intrinsic logical problems and the epistemic range of the information provided by such tests is much more limited than most researchers recognize. In this article we introduce to the scientometric community the theoretical origins of NHST, which is mostly absent from standard statistical textbooks, and we discuss some of the most prevalent problems relating to the practice of NHST and trace these problems back to the mixup of the two different theoretical origins. Finally, we illustrate some of the misunderstandings with examples from the scientometric literature and bring forward some modest recommendations for a more sound practice in quantitative data analysis.

Models are consistently treated as approximations and all procedures are consistent with this. They do not treat the model as being true. In this context p -values are one measure of approximation, a small p -value indicating a poor approximation. Approximation regions are defined and distinguished from confidence regions.