Spatial Regression Models Using Inter-Region Distances in a Non-Random Context

This article considers spatial data z( s ₁), z( s ₂),…, z( s _n ) collected at n locations, with the objective of predicting z( s ₀) at another location. The usual method of analysis for this problem is kriging, but here we introduce a new signal-plus-noise model whose essential feature is the identification of hot spots. The signal decays in relation to distance from hot spots. We show that hot spots can be located with high accuracy and that the decay parameter can be estimated accurately. This new model compares well to kriging in simulations.     

MODELING AND ESTIMATING VARIANCES IN REGRESSION

ABSTRACT

It is well known that ignoring heteroscedasticity in regression analysis adversely affects the efficiency of estimation and renders the usual procedure for constructing prediction intervals inappropriate. In some applications, such as off-line quality control, knowledge of the variance function is also of considerable interest in its own right. Thus the modeling of variance constitutes an important part of regression analysis. A common practice in modeling variance is to assume that a certain function of the variance can be closely approximated by a function of a known parametric form. The logarithm link function is often used even if it does not fit the observed variation satisfactorily, as other alternatives may yield negative estimated variances. In this paper we propose a rich class of link functions for more flexible variance modeling which alleviates the major difficulty of negative variances. We suggest also an alternative analysis for heteroscedastic regression models that exploits the principle of “separation” discussed in Box (Signal-to-Noise Ratios, Performance Criteria and Transformation. Technometrics 1988, 30, 1–31). The proposed method does not require any distributional assumptions once an appropriate link function for modeling variance has been chosen. Unlike the analysis in Box (Signal-to-Noise Ratios, Performance Criteria and Transformation. Technometrics 1988, 30, 1–31), the estimated variances and their associated asymptotic variances are found in the original metric (although a transformation has been applied to achieve separation in a different scale), making interpretation of results considerably easier.     

Discussion on “ Transparency in Structural Research” by I. Andrews,M. Gentkow and J. Shapiro

Abstract

We provide a complementary approach to global sensitivity analysis that should be useful for empirical work in economics.     

Generalized Sobol sensitivity indices for dependent variables: numerical methods

The hierarchically orthogonal functional decomposition of any measurable function η of a random vector X=(X₁,?…?, X_p) consists in decomposing η(X) into a sum of increasing dimension functions depending only on a subvector of X. Even when X₁,?…?, X_p are assumed to be dependent, this decomposition is unique if the components are hierarchically orthogonal. That is, two of the components are orthogonal whenever all the variables involved in one of the summands are a subset of the variables involved in the other. Setting Y=η(X), this decomposition leads to the definition of generalized sensitivity indices able to quantify the uncertainty of Y due to each dependent input in X [Chastaing G, Gamboa F, Prieur C. Generalized Hoeffding–Sobol decomposition for dependent variables – application to sensitivity analysis. Electron J Statist. 2012;6:2420–2448]. In this paper, a numerical method is developed to identify the component functions of the decomposition using the hierarchical orthogonality property. Furthermore, the asymptotic properties of the components estimation is studied, as well as the numerical estimation of the generalized sensitivity indices of a toy model. Lastly, the method is applied to a model arising from a real-world problem.     

Expedient universal robust likelihood method for general dispersed count data

ABSTRACT

We introduce a universal robust likelihood approach for regression analysis of general count data. The robust likelihood function is able to accommodate a wide range of dispersion and is insensitive to model failures. We use simulations and real data analysis to demonstrate the merit of the robust procedure.     

On the Computation of the Distribution for the Analysis of Means

Abstract

We discuss the accuracy of the computation and present a fortran program to compute the cumulative distribution function (CDF) for the analysis of means (ANOM).     

A superiority problem in misspecified restricted linear models

Abstract

In this article we study the relationship between principal component analysis and a multivariate dependency measure. It is shown, via simulated examples and real data, that the information provided by principal components is compatible with that obtained via the dependency measure δ. Furthermore, we show that in some instances in which principal component analysis fails to give reasonable results due to nonlinearity among the random variables, the dependency statistic δ still provides good results. Finally, we give some ideas about using the statistic δ in order to reduce the dimensionality of a given data set.     

A MATRIX VARIATE GENERALIZATION OF THE POWER EXPONENTIAL FAMILY OF DISTRIBUTIONS

ABSTRACT

This paper proposes a matrix variate generalization of the power exponential distribution family, which can be useful in generalizing statistical procedures in multivariate analysis and in designing robust alternatives to them. An example is added to show an application of the generalization.     

Bayesian quantile inference

The paper proposes a Bayesian interpretation of quantile regression that is shown to be equivalent to scale mixtures of normals leading to a skewed Laplace distribution. This representation of the model facilitates Bayesian analysis by means of Gibbs sampling with data augmentation, and nests regression in the L₁ norm as a special case. The new methods are applied to an analysis of the patents - R&D relationship for U.S. firms and unit root inference for the dollar-deutschemark exchange rate.     

A Bayesian Analysis of Directional Data Using the von Mises–Fisher Distribution

ABSTRACT

This article presents a Bayesian analysis of the von Mises–Fisher distribution, which is the most important distribution in the analysis of directional data. We obtain samples from the posterior distribution using a sampling-importance-resampling method. The procedure is illustrated using simulated data as well as real data sets previously analyzed in the literature.     

Some Observations on Copula Regression Functions

ABSTRACT

The main objective of this article is to introduce an alternative way of looking at regression analysis by using copulas. To achieve our objective we work on copula regression function, study its properties, and discuss advantages that will come out from our approach.     

Improved ridge estimators in a linear regression model

In this paper, the notion of the improved ridge estimator (IRE) is put forward in the linear regression model y=X β+e. The problem arises if augmenting the equation 0=c′α+ε instead of 0=C α+? to the model. Three special IREs are considered and studied under the mean-squared error criterion and the prediction error sum of squares criterion. The simulations demonstrate that the proposed estimators are effective and recommendable, especially when multicollinearity is severe.     

Comparing the BLUEs Under Two Linear Models

In this article, we consider two linear models, ?₁ = {y, X β, V ₁} and ?₂ = {y, X β, V ₂}, which differ only in their covariance matrices. Our main focus lies on the difference of the best linear unbiased estimators, BLUEs, of X β under these models. The corresponding problems between the models {y, X β, I _n } and {y, X β, V}, i.e., between the OLSE (ordinary least squares estimator) and BLUE, are pretty well studied. Our purpose is to review the corresponding considerations between the BLUEs of X β under ?₁ and ?₂. This article is an expository one presenting also new results.     

A study of generalized skew-normal distribution

Following the paper by Genton and Loperfido [Generalized skew-elliptical distributions and their quadratic forms, Ann. Inst. Statist. Math. 57 (2005), pp. 389–401], we say that Z has a generalized skew-normal distribution, if its probability density function (p.d.f.) is given by f(z)=2φ _p (z; ξ, Ω)π (z?ξ), z∈? ^p , where φ _p (·; ξ, Ω) is the p-dimensional normal p.d.f. with location vector ξ and scale matrix Ω, ξ∈? ^p , Ω>0, and π is a skewing function from ? ^p to ?, that is 0≤π (z)≤1 and π (?z)=1?π (z), ? z∈? ^p . First the distribution of linear transformations of Z are studied, and some moments of Z and its quadratic forms are derived. Next we obtain the joint moment-generating functions (m.g.f.’s) of linear and quadratic forms of Z and then investigate conditions for their independence. Finally explicit forms for the above distributions, m.g.f.’s and moments are derived when π (z)=κ (α′z), where α∈? ^p and κ is the normal, Laplace, logistic or uniform distribution function.     

An Algorithm Based on Singular Spectrum Analysis for Change-Point Detection

Abstract

This paper is devoted to application of the singular-spectrum analysis to sequential detection of changes in time series. An algorithm of change-point detection in time series, based on sequential application of the singular-spectrum analysis is developed and studied. The algorithm is applied to different data sets and extensively studied numerically. For specific models, several numerical approximations to the error probabilities and the power function of the algorithm are obtained. Numerical comparisons with other methods are given.     

Compliance of the Token-Bucket Model with Markovian Traffic

Abstract

Recently, risk processes have been analyzed as fluid queues. That approach is adapted here to the analysis of the token bucket model for Markovian traffic patterns. This paper presents the Laplace transform of the time until a given traffic pattern is not compliant anymore with a particular token bucket model.     

Using Lasso RCCA for cross-language information retrieval

ABSTRACT

Restricted canonical correlation analysis and the lasso shrinkage method were paired together for canonical correlation analysis with non-negativity restrictions on datasets, where a sample size is much smaller than the number of variables. The method was implemented in an alternating least-squares algorithm and applied to cross-language information retrieval on a dataset with aligned documents in eight languages. A set of experiments was ran to evaluate the method and compare it to other methods in the field.     

Identification of technical analysis patterns with smoothing splines for bitcoin prices

ABSTRACT

This research studies automatic price pattern search procedure for bitcoin cryptocurrency based on 1-min price data. To achieve this, search algorithm is proposed based on nonparametric regression method of smoothing splines. We investigate some well-known technical analysis patterns and construct algorithmic trading strategy to evaluate the effectiveness of the patterns. We found that method of smoothing splines for identifying the technical analysis patterns and that strategies based on certain technical analysis patterns yield returns that significantly exceed results of unconditional trading strategies.     

Questions & Answers: The Role of Mathematical Models in Clinical Research

Given any generalized inverse (X'X)^? appropriate to normal equations X'Xb ⁰ = X'y for the linear model y = Xb + e, a procedure is given for obtaining from it a generalized inverse appropriate to a restricted model having restrictions P'b = 0 for P'b nonestimable.