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By
He, Hua; Wang, Wenjuan; Tang, Wan
The density function is a fundamental concept in data analysis. When a population consists of heterogeneous subjects, it is often of great interest to estimate the density functions of the subpopulations. Nonparametric methods such as kernel smoothing estimates may be applied to each subpopulation to estimate the density functions if there are no missing values. In situations where the membership for a subpopulation is missing, kernel smoothing estimates using only subjects with membership available are valid only under missing complete at random (MCAR). In this paper, we propose new kernel smoothing methods for density function estimates by applying prediction models of the membership under the missing at random (MAR) assumption. The asymptotic properties of the new estimates are developed, and simulation studies and a real study in mental health are used to illustrate the performance of the new estimates.
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By
Barakat, H. M.; Nigm, E. M.; Khaled, O. M.; Alaswed, H. A.
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It is well known that the maxstable laws under power normalization attract more distributions than that under linear normalization. This fact practically means that the classical linear model (Lmodel) may fail to fit the given extreme data, while the power model (Pmodel) succeeds to do that. The main object of this paper is developing the modeling of extreme values via Pmodel by suggesting a simple technique to obtain a parallel estimator of the extreme value index (EVI) in the Pmodel for every known estimator to the corresponding parameter in Lmode. An application of this technique yields two classes of moment and moment ratio estimators for EVI in the Pmodel. The performances of these estimators are assessed via a simulation study. Moreover, an efficient criterion for comparing the L and P models is proposed to choose the best model when the two models successfully work.
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By
Giraldo, Ramón; Caballero, William; CamachoTamayo, Jesús
2 Citations
Statistics for spatial functional data is an emerging field in statistics which combines methods of spatial statistics and functional data analysis to model spatially correlated functional data. Checking for spatial autocorrelation is an important step in the statistical analysis of spatial data. Several statistics to achieve this goal have been proposed. The test based on the Mantel statistic is widely known and used in this context. This paper proposes an application of this test to the case of spatial functional data. Although we focus particularly on geostatistical functional data, that is functional data observed in a region with spatial continuity, the test proposed can also be applied with functional data which can be measured on a discrete set of areas of a region (areal functional data) by defining properly the distance between the areas. Based on two simulation studies, we show that the proposed test has a good performance. We illustrate the methodology by applying it to an agronomic data set.
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By
McArdle, John J.
8 Citations
The purpose of this paper is to highlight some classic issues in the measurement of change and to show how contemporary solutions can be used to deal with some of these issues. Five classic issues will be raised here: (1) Separating individual changes from group differences; (2) options for incomplete longitudinal data over time, (3) options for nonlinear changes over time; (4) measurement invariance in studies of changes over time; and (5) new opportunities for modeling dynamic changes. For each issue we will describe the problem, and then review some contemporary solutions to these problems base on Structural Equation Models (SEM). We will fit these SEM to using existing panel data from the Health & Retirement Study (HRS) cognitive variables. This is not intended as an overly technical treatment, so only a few basic equations are presented, examples will be displayed graphically, and more complete references to the contemporary solutions will be given throughout.
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By
Janczura, Joanna; Weron, Rafał
9 Citations
This paper complements a recently published study (Janczura and Weron in AStAAdv Stat Anal 96(3):385–407, 2012) on efficient estimation of Markov regimeswitching models. Here, we propose a new goodnessoffit testing scheme for the marginal distribution of such models. We consider models with an observable (like threshold autoregressions) as well as a latent state process (like Markov regimeswitching). The test is based on the Kolmogorov–Smirnov supremumdistance statistic and the concept of the weighted empirical distribution function. The motivation for this research comes from a recent stream of literature in energy economics concerning electricity spot price models. While the existence of distinct regimes in such data is generally unquestionable (due to the supply stack structure), the actual goodnessoffit of the models requires statistical validation. We illustrate the proposed scheme by testing whether commonly used Markov regimeswitching models fit deseasonalized electricity prices from the NEPOOL (US) dayahead market.
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By
AlSharadqah, Ali; Mojirsheibani, Majid
A longstanding problem in the construction of asymptotically correct confidence bands for a regression function
$$m(x)=E[YX=x]$$
, where Y is the response variable influenced by the covariate X, involves the situation where Y values may be missing at random, and where the selection probability, the density function f(x) of X, and the conditional variance of Y given X are all completely unknown. This can be particularly more complicated in nonparametric situations. In this paper, we propose a new kerneltype regression estimator and study the limiting distribution of the properly normalized versions of the maximal deviation of the proposed estimator from the true regression curve. The resulting limiting distribution will be used to construct uniform confidence bands for the underlying regression curve with asymptotically correct coverages. The focus of the current paper is on the case where
$$X\in \mathbb {R}$$
. We also perform numerical studies to assess the finitesample performance of the proposed method. In this paper, both mechanics and the theoretical validity of our methods are discussed.
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By
Fontanella, Lara; Sarra, Annalina; Valentini, Pasquale; Zio, Simone; Fontanella, Sara
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Recent years have seen increased attention paid to monitoring social anomie and its dependency on micro and macrofactors. In this paper, we endorse the theorisation of social anomie as a complex, multidimensional and multilevel phenomenon. To ensure a rigorous measurement of the varying levels of social anomie in the European countries, the current study relies on a multilevel multidimensional item response theory model which explicitly accounts for the presence of a nonignorable missing data mechanism. This unified approach makes it possible to specify an analytical model of links between anomie features and their determinants and to explore how the latent traits of interest are influenced by individuallevel factors, as well as by countrylevel indicators. Additionally, to avoid misleading inferential conclusions, the proposed model takes into account the respondent’s omitting behaviour, assuming that the missingness mechanism is driven by a latent propensity to respond. Data used in this study have been collected in the 2010 wave of the European Social Survey. To reduce the computational complexities, a Bayesian specification of the MIRT model is provided and the parameter model estimates are obtained through MCMC algorithms.
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By
Yang, Yiping; Tong, Tiejun; Li, Gaorong
3 Citations
In this paper, we consider the singleindex measurement error model with mismeasured covariates in the nonparametric part. To solve the problem, we develop a simulationextrapolation (SIMEX) algorithm based on the local linear smoother and the estimating equation. For the proposed SIMEX estimation, it is not needed to assume the distribution of the unobserved covariate. We transform the boundary of a unit ball in
$${\mathbb {R}}^p$$
to the interior of a unit ball in
$${\mathbb {R}}^{p1}$$
by using the constraint
$$\Vert \beta \Vert =1$$
. The proposed SIMEX estimator of the index parameter is shown to be asymptotically normal under some regularity conditions. We also derive the asymptotic bias and variance of the estimator of the unknown link function. Finally, the performance of the proposed method is examined by simulation studies and is illustrated by a real data example.
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