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1.
Many research fields increasingly involve analyzing data of a complex structure. Models investigating the dependence of a response on a predictor have moved beyond the ordinary scalar-on-vector regression. We propose a regression model for a scalar response and a surface (or a bivariate function) predictor. The predictor has a random component and the regression model falls in the framework of linear random effects models. We estimate the model parameters via maximizing the log-likelihood with the ECME (Expectation/Conditional Maximization Either) algorithm. We use the approach to analyze a data set where the response is the neuroticism score and the predictor is the resting-state brain function image. In the simulations we tried, the approach has better performance than two other approaches, a functional principal component regression approach and a smooth scalar-on-image regression approach.  相似文献   
2.
In this paper, we investigate the k-nearest neighbours (kNN) estimation of nonparametric regression model for strong mixing functional time series data. More precisely, we establish the uniform almost complete convergence rate of the kNN estimator under some mild conditions. Furthermore, a simulation study and an empirical application to the real data analysis of sea surface temperature (SST) are carried out to illustrate the finite sample performances and the usefulness of the kNN approach.  相似文献   
3.
The hierarchically orthogonal functional decomposition of any measurable function η of a random vector X=(X1,?…?, Xp) consists in decomposing η(X) into a sum of increasing dimension functions depending only on a subvector of X. Even when X1,?…?, Xp 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.  相似文献   
4.
G. Aneiros  F. Ferraty  P. Vieu 《Statistics》2015,49(6):1322-1347
The problem of variable selection is considered in high-dimensional partial linear regression under some model allowing for possibly functional variable. The procedure studied is that of nonconcave-penalized least squares. It is shown the existence of a √n/sn-consistent estimator for the vector of pn linear parameters in the model, even when pn tends to ∞ as the sample size n increases (sn denotes the number of influential variables). An oracle property is also obtained for the variable selection method, and the nonparametric rate of convergence is stated for the estimator of the nonlinear functional component of the model. Finally, a simulation study illustrates the finite sample size performance of our procedure.  相似文献   
5.
E. Brunel  A. Roche 《Statistics》2015,49(6):1298-1321
Our aim is to estimate the unknown slope function in the functional linear model when the response Y is real and the random function X is a second-order stationary and periodic process. We obtain our estimator by minimizing a standard (and very simple) mean-square contrast on linear finite dimensional spaces spanned by trigonometric bases. Our approach provides a penalization procedure which allows to automatically select the adequate dimension, in a non-asymptotic point of view. In fact, we can show that our penalized estimator reaches the optimal (minimax) rate of convergence in the sense of the prediction error. We complete the theoretical results by a simulation study and a real example that illustrates how the procedure works in practice.  相似文献   
6.
Max Boholm 《Risk analysis》2019,39(6):1243-1261
In risk analysis and research, the concept of risk is often understood quantitatively. For example, risk is commonly defined as the probability of an unwanted event or as its probability multiplied by its consequences. This article addresses (1) to what extent and (2) how the noun risk is actually used quantitatively. Uses of the noun risk are analyzed in four linguistic corpora, both Swedish and English (mostly American English). In total, over 16,000 uses of the noun risk are studied in 14 random (n = 500) or complete samples (where n ranges from 173 to 5,144) of, for example, news and magazine articles, fiction, and websites of government agencies. In contrast to the widespread definition of risk as a quantity, a main finding is that the noun risk is mostly used nonquantitatively. Furthermore, when used quantitatively, the quantification is seldom numerical, instead relying on less precise expressions of quantification, such as high risk and increased risk. The relatively low frequency of quantification in a wide range of language material suggests a quantification bias in many areas of risk theory, that is, overestimation of the importance of quantification in defining the concept of risk. The findings are also discussed in relation to fuzzy‐trace theory. Findings of this study confirm, as suggested by fuzzy‐trace theory, that vague representations are prominent in quantification of risk. The application of the terminology of fuzzy‐trace theory for explaining the patterns of language use are discussed.  相似文献   
7.
Functional logistic regression is becoming more popular as there are many situations where we are interested in the relation between functional covariates (as input) and a binary response (as output). Several approaches have been advocated, and this paper goes into detail about three of them: dimension reduction via functional principal component analysis, penalized functional regression, and wavelet expansions in combination with Least Absolute Shrinking and Selection Operator penalization. We discuss the performance of the three methods on simulated data and also apply the methods to data regarding lameness detection for horses. Emphasis is on classification performance, but we also discuss estimation of the unknown parameter function.  相似文献   
8.
We discuss some analogues of the lack of memory property, the strong lack of memory property and the almost lack of memory properties for the Gompertz distribution as applications of the integrated Cauchy functional equation.  相似文献   
9.
We consider the estimation of the conditional hazard function of a scalar response variable Y given a Hilbertian random variable X when the observations are linked via a single-index structure in the quasi-associated framework. We establish the pointwise almost complete convergence and the uniform almost complete convergence (with the rate) of the estimate of this model. A simulation is given to illustrate the good behavior in the practice of our methodology.  相似文献   
10.
In this article, we develop a series estimation method for unknown time-inhomogeneous functionals of Lévy processes involved in econometric time series models. To obtain an asymptotic distribution for the proposed estimators, we establish a general asymptotic theory for partial sums of bivariate functionals of time and nonstationary variables. These results show that the proposed estimators in different situations converge to quite different random variables. In addition, the rates of convergence depend on various factors rather than just the sample size. Finite sample simulations are provided to evaluate the finite sample performance of the proposed model and estimation method.  相似文献   
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