Depth Measures for Multivariate Functional Data

In this article, we address the problem of mining and analyzing multivariate functional data. That is, data where each observation is a set of possibly correlated functions. Complex data of this kind is more and more common in many research fields, particularly in the biomedical context. In this work, we propose and apply a new concept of depth measure for multivariate functional data. With this new depth measure it is possible to generalize robust statistics, such as the median, to the multivariate functional framework, which in turn allows the application of outlier detection, boxplots construction, and nonparametric tests also in this more general framework. We present an application to Electrocardiographic (ECG) signals.     

The estimation of treatment effect for the censored bivariate data under the univariate censoring

This paper establishes a nonparametric estimator for the treatment effect on censored bivariate data under unvariate censoring. This proposed estimator is based on the one from Lin and Ying(1993)'s nonparametric bivariate survival function estimator, which is itself a generalized version of Park and Park(1995)' quantile estimator. A Bahadur type representation of quantile functions were obtained from the marginal survival distribution estimator of Lin and Ying' model. The asymptotic property of this estimator is shown below and the simulation studies are also given     

Unbiased estimation of a nonlinear function a normal mean with application to measurement err oorf models

Let W be a normal random variable with mean μand known variance σ². Conditions on the function f(·) are given under which there exists an unbiased estimator, f(W), of f(μ) for all real μ. In particular it is shown that f(·) must be an entire function over the complex plane. Infinite series solutions for F(·) are obtained which are shown to be valid under growth conditions of the derivatives, f^k( ·), of f(·). Approximate solutions are given for the cases in which no exact solution exists. The theory is applied to nonlinear measurement-error models as a means of finding unbiased score functions when measurement error is normally distributed. Relative efficiencies comparing the proposed method to the use of conditional scores (Stefanski and Carroll, 1987) are given for the Poisson regression model with canonical link.     

Financial-Firm Production of Monetary Services: A Generalized Symmetric Baroett Variable-Profit-Function Approach

An alternative monetary-production model of financial firms is employed to investigate supply-side monetary aggregation. Financial firms are conceived to produce monetary services as outputs through financial intermediation. A new method for testing the existence of consistent monetary-output aggregates in financial firms' production technology is developed in terms of a multiproduct firm's variable profit function, and the method does not require homotheticity of the aggregator function. We use a generalized symmetric Barnett flexible functional form. That specification satisfies global curvature conditions and retains its flexibility under the null hypothesis of weak separability. Neither of those properties is possessed by other flexible functional forms.     

Semiparametric Additive Accelerated Life Models

In this paper we investigate the asymptotic properties of estimators obtained for the semiparametric additive accelerated life model proposed by Bagdonavicius & Nikulin (1995). This model generalizes the well known additive hazards model of survival analysis and is close to the general transformation model (see Dabrowska & Doksum, 1988). Asymptotic properties of the estimator of the regression parameter and the estimator of the reliability function are given in the case of right censoring for discretized data and a numerical example illustrates these results.     

Imposing and Testing for Shape Restrictions in Flexible Parametric Models

In many economic models, theory restricts the shape of functions, such as monotonicity or curvature conditions. This article reviews and presents a framework for constrained estimation and inference to test for shape conditions in parametric models. We show that “regional” shape-restricting estimators have important advantages in terms of model fit and flexibility (as opposed to standard “local” or “global” shape-restricting estimators). In our empirical illustration, this is the first article to impose and test for all shape restrictions required by economic theory simultaneously in the “Berndt and Wood” data. We find that this dataset is consistent with “duality theory,” whereas previous studies have found violations of economic theory. We discuss policy consequences for key parameters, such as whether energy and capital are complements or substitutes.     

On asymptotic distribution of prediction in functional linear regression

There has been substantial recent attention on problems involving a functional linear regression model with scalar response. Among them, there have been few works dealing with asymptotic distribution of prediction in functional linear regression models. In recent literature, the centeral limit theorem for prediction has been discussed, but the proof and conditions under which the random bias terms for a fixed predictor converge to zero have been ignored so that the impact of these terms on the convergence of the prediction has not been well understood. Clarifying the proof and conditions under which the bias terms converge to zero, we show that the asymptotic distribution of the prediction is normal. Furthermore, we have derived those results related to other terms that already obtained by others, under milder conditions. Finally, we conduct a simulation study to investigate performance of the asymptotic distribution under various parameter settings.     

Functional Partial Linear Single‐index Model

This paper deals with the problem of predicting the real‐valued response variable using explanatory variables containing both multivariate random variable and random curve. The proposed functional partial linear single‐index model treats the multivariate random variable as linear part and the random curve as functional single‐index part, respectively. To estimate the non‐parametric link function, the functional single‐index and the parameters in the linear part, a two‐stage estimation procedure is proposed. Compared with existing semi‐parametric methods, the proposed approach requires no initial estimation and iteration. Asymptotical properties are established for both the parameters in the linear part and the functional single‐index. The convergence rate for the non‐parametric link function is also given. In addition, asymptotical normality of the error variance is obtained that facilitates the construction of confidence region and hypothesis testing for the unknown parameter. Numerical experiments including simulation studies and a real‐data analysis are conducted to evaluate the empirical performance of the proposed method.     

An F-type test for detecting departure from monotonicity in a functional linear model

When studying associations between a functional covariate and scalar response using a functional linear model (FLM), scientific knowledge may indicate possible monotonicity of the unknown parameter curve. In this context, we propose an F-type test of monotonicity, based on a full versus reduced nested model structure, where the reduced model with monotonically constrained parameter curve is nested within an unconstrained FLM. For estimation under the unconstrained FLM, we consider two approaches: penalised least-squares and linear mixed model effects estimation. We use a smooth then monotonise approach to estimate the reduced model, within the null space of monotone parameter curves. A bootstrap procedure is used to simulate the null distribution of the test statistic. We present a simulation study of the power of the proposed test, and illustrate the test using data from a head and neck cancer study.