Search results for "multivariate"
showing 10 items of 1520 documents
On the convenience of heteroscedasticity in highly multivariate disease mapping
2019
Highly multivariate disease mapping has recently been proposed as an enhancement of traditional multivariate studies, making it possible to perform the joint analysis of a large number of diseases. This line of research has an important potential since it integrates the information of many diseases into a single model yielding richer and more accurate risk maps. In this paper we show how some of the proposals already put forward in this area display some particular problems when applied to small regions of study. Specifically, the homoscedasticity of these proposals may produce evident misfits and distorted risk maps. In this paper we propose two new models to deal with the variance-adaptiv…
Statistically validated hierarchical clustering: Nested partitions in hierarchical trees
2022
We develop an algorithm that is fast and scalable in the detection of a nested partition extracted from a dendrogram that is obtained from hierarchical clustering of a multivariate series. Our algorithm provides a -value for each clade observed in the hierarchical tree. The -value is obtained by computing many bootstrap replicas of the dissimilarity matrix and by performing a statistical test on each difference between the dissimilarity associated with a given clade and the dissimilarity of the clade of its parent node. We prove the efficacy of our algorithm with a set of benchmarks generated by a hierarchically nested factor model. We compare results obtained by our algorithm with those of…
Multitype spatial point patterns with hierarchical interactions.
2001
Multitype spatial point patterns with hierarchical interactions are considered. Here hierarchical interaction means directionality: points on a higher level of hierarchy affect the locations of points on the lower levels, but not vice versa. Such relations are common, for example, in ecological communities. Interacting point patterns are often modeled by Gibbs processes with pairwise interactions. However, these models are inherently symmetric, and the hierarchy can be acknowledged only when interpreting the results. We suggest the following in allowing the inclusion of the hierarchical structure in the model. Instead of regarding the pattern as a realization of a stationary multivariate po…
Central Limit Theorem for Linear Eigenvalue Statistics for a Tensor Product Version of Sample Covariance Matrices
2017
For $$k,m,n\in {\mathbb {N}}$$ , we consider $$n^k\times n^k$$ random matrices of the form $$\begin{aligned} {\mathcal {M}}_{n,m,k}({\mathbf {y}})=\sum _{\alpha =1}^m\tau _\alpha {Y_\alpha }Y_\alpha ^T,\quad {Y}_\alpha ={\mathbf {y}}_\alpha ^{(1)}\otimes \cdots \otimes {\mathbf {y}}_\alpha ^{(k)}, \end{aligned}$$ where $$\tau _{\alpha }$$ , $$\alpha \in [m]$$ , are real numbers and $${\mathbf {y}}_\alpha ^{(j)}$$ , $$\alpha \in [m]$$ , $$j\in [k]$$ , are i.i.d. copies of a normalized isotropic random vector $${\mathbf {y}}\in {\mathbb {R}}^n$$ . For every fixed $$k\ge 1$$ , if the Normalized Counting Measures of $$\{\tau _{\alpha }\}_{\alpha }$$ converge weakly as $$m,n\rightarrow \infty $$…
Fractional calculus approach to the statistical characterization of random variables and vectors
2009
Fractional moments have been investigated by many authors to represent the density of univariate and bivariate random variables in different contexts. Fractional moments are indeed important when the density of the random variable has inverse power-law tails and, consequently, it lacks integer order moments. In this paper, starting from the Mellin transform of the characteristic function and by fractional calculus method we present a new perspective on the statistics of random variables. Introducing the class of complex moments, that include both integer and fractional moments, we show that every random variable can be represented within this approach, even if its integer moments diverge. A…
Comparison between splines and fractional polynomials for multivariable model building with continuous covariates: a simulation study with continuous…
2012
In observational studies, many continuous or categorical covariates may be related to an outcome. Various spline-based procedures or the multivariable fractional polynomial (MFP) procedure can be used to identify important variables and functional forms for continuous covariates. This is the main aim of an explanatory model, as opposed to a model only for prediction. The type of analysis often guides the complexity of the final model. Spline-based procedures and MFP have tuning parameters for choosing the required complexity. To compare model selection approaches, we perform a simulation study in the linear regression context based on a data structure intended to reflect realistic biomedica…
Power and Type I Error of the Mean and Covariance Structure Analysis Model for Detecting Differential Item Functioning in Graded Response Items.
2016
In this simulation study, we investigate the power and Type I error rate of a procedure based on the mean and covariance structure analysis (MACS) model in detecting differential item functioning (DIF) of graded response items with five response categories. The following factors were manipulated: type of DIF (uniform and non-uniform), DIF magnitude (low, medium and large), equality/inequality of latent trait distributions, sample size (100, 200, 400, and 800) and equality or inequality of the sample sizes across groups. The simulated test was made up of 10 items, of which only 1 contained DIF. One hundred replications were generated for each simulated condition. Results indicate that the MA…
Multiple Comparisons of Treatments with Stable Multivariate Tests in a Two‐Stage Adaptive Design, Including a Test for Non‐Inferiority
2000
The application of stabilized multivariate tests is demonstrated in the analysis of a two-stage adaptive clinical trial with three treatment arms. Due to the clinical problem, the multiple comparisons include tests of superiority as well as a test for non-inferiority, where non-inferiority is (because of missing absolute tolerance limits) expressed as linear contrast of the three treatments. Special emphasis is paid to the combination of the three sources of multiplicity - multiple endpoints, multiple treatments, and two stages of the adaptive design. Particularly, the adaptation after the first stage comprises a change of the a-priori order of hypotheses.
Some extensions of multivariate sliced inverse regression
2007
Multivariate sliced inverse regression (SIR) is a method for achieving dimension reduction in regression problems when the outcome variable y and the regressor x are both assumed to be multidimensional. In this paper, we extend the existing approaches, based on the usual SIR I which only uses the inverse regression curve, to methods using properties of the inverse conditional variance. Contrary to the existing ones, these new methods are not blind for symmetric dependencies and rely on the SIR II or SIRα. We also propose their corresponding pooled slicing versions. We illustrate the usefulness of these approaches on simulation studies.
Gaussian component mixtures and CAR models in Bayesian disease mapping
2012
Hierarchical Bayesian models involving conditional autoregression (CAR) components are commonly used in disease mapping. An alternative model to the proper or improper CAR is the Gaussian component mixture (GCM) model. A review of CAR and GCM models is provided in univariate settings where only one disease is considered, and also in multivariate situations where in addition to the spatial dependence between regions, the dependence among multiple diseases is analyzed. A performance comparison between models using a set of simulated data to help illustrate their respective properties is reported. The results show that both in univariate and multivariate settings, both models perform in a comp…