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By
Yamada, Eika
In this study, we derive the asymptotic normality of a class of rank estimators in a simple spatial linear regression model, when errors form a strongly mixing random field and when the spatial data are both on the lattice and on the irregularly spaced spatial sites. This result in turn is used to investigate the asymptotic relative efficiency (ARE) of these estimators relative to the LSE. In addition, we conduct numerical experiments under both the lattice and the irregularly spaced sampling, which lends support to the robustness of these estimators compared to the LSE.
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By
Prokešová, Michaela; Jensen, Eva B. Vedel
11 Citations
In the present paper, we propose a Palm likelihood approach as a general estimating principle for stationary point processes in
$$\mathbf{R}^d$$
for which the density of the secondorder factorial moment measure is available in closed form or in an integral representation. Examples of such point processes include the Neyman–Scott processes and the log Gaussian Cox processes. The computations involved in determining the Palm likelihood estimator are simple. Conditions are provided under which the Palm likelihood estimator is strongly consistent and asymptotically normally distributed.
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By
Rosadi, Dedi; Peiris, Shelton
4 Citations
In their recent paper, Wang and Leblanc (Ann Inst Stat Math 60:883–900, 2008) have shown that the secondorder least squares estimator (SLSE) is more efficient than the ordinary least squares estimator (OLSE) when the errors are independent and identically distributed with non zero third moments. In this paper, we generalize the theory of SLSE to regression models with autocorrelated errors. Under certain regularity conditions, we establish the consistency and asymptotic normality of the proposed estimator and provide a simulation study to compare its performance with the corresponding OLSE and generalized least square estimator (GLSE). It is shown that the SLSE performs well giving relatively small standard error and bias (or the mean square error) in estimating parameters of such regression models with autocorrelated errors. Based on our study, we conjecture that for less correlated data, the standard errors of SLSE lie between those of the OLSE and GLSE which can be interpreted as adding the second moment information can improve the performance of an estimator.
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By
Veraverbeke, Noel; CadarsoSuárez, Carmen
11 Citations
We introduce a new estimator for the conditional distribution functions under the proportional hazards model of random censorship. Such estimator generalizes the one proposed by Abdushkurov, Chen and Lin when covariates are present. Asymptotic theory is given for this estimator. First, we established the strong consistency, and also obtain the rate of this convergence. Then, an asymptotic representation for the conditional distribution function estimator leads us to derive its asymptotic normality. The practical performance of the estimation procedure is illustrated on a real data set. Finally, as a further application of the new estimator, some functionals of interest in survival exploratory analysis are brieflys discussed.
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By
Ahmed, Hanan; Einmahl, John H. J.
Heavy tailed phenomena are naturally analyzed by extreme value statistics. A crucial step in such an analysis is the estimation of the extreme value index, which describes the tail heaviness of the underlying probability distribution. We consider the situation where we have next to the n observations of interest another n + m observations of one or more related variables, like, e.g., financial losses due to earthquakes and the related amounts of energy released, for a longer period than that of the losses. Based on such a data set, we present an adapted version of the Hill estimator. For this adaptation the tail dependence between the variable of interest and the related variable(s) plays an important role. We establish the asymptotic normality of this new estimator. It shows greatly improved behavior relative to the Hill estimator, in particular the asymptotic variance is substantially reduced, whereas we can keep the asymptotic bias the same. A simulation study confirms the substantially improved performance of our adapted estimator. We also present an application to the aforementioned earthquake losses.
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By
Aoshima, Makoto ; Yata, Kazuyoshi
2 Citations
In this paper, we consider highdimensional quadratic classifiers in nonsparse settings. The quadratic classifiers proposed in this paper draw information about heterogeneity effectively through both the differences of growing mean vectors and covariance matrices. We show that they hold a consistency property in which misclassification rates tend to zero as the dimension goes to infinity under nonsparse settings. We also propose a quadratic classifier after feature selection by using both the differences of mean vectors and covariance matrices. We discuss the performance of the classifiers in numerical simulations and actual data analyzes. Finally, we give concluding remarks about the choice of the classifiers for highdimensional, nonsparse data.
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By
Wang, Lihong
3 Citations
This paper studies nonparametric kernel type (smoothed) estimation of quantiles for long memory stationary sequences. The uniform strong consistency and asymptotic normality of the estimates with rates are established. Finite sample behaviors are investigated in a small Monte Carlo simulation study.
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By
Zhao, Ningning; Bai, Zhidong
6 Citations
Rounding errors have a considerable impact on statistical inferences, especially when the data size is large and the finite normal mixture model is very important in many applied statistical problems, such as bioinformatics. In this article, we investigate the statistical impacts of rounding errors to the finite normal mixture model with a known number of components, and develop a new estimation method to obtain consistent and asymptotically normal estimates for the unknown parameters based on rounded data drawn from this kind of models.
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By
Aoshima, Makoto; Yata, Kazuyoshi
10 Citations
In this paper, we consider the asymptotic normality for various inference problems on multisample and highdimensional mean vectors. We verify that the asymptotic normality of concerned statistics is proved under mild conditions for highdimensional data. We show that the asymptotic normality can be justified theoretically and numerically even for nonGaussian data. We introduce the extended crossdatamatrix (ECDM) methodology to construct an unbiased estimator at a reasonable computational cost. With the help of the asymptotic normality, we show that the concerned statistics given by ECDM can ensure consistency properties for inference on multisample and highdimensional mean vectors. We give several applications such as confidence regions for highdimensional mean vectors, confidence intervals for the squared norm and the test of multisample mean vectors. We also provide sample size determination so as to satisfy prespecified accuracy on inference. Finally, we give several examples by using a microarray data set.
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By
Zhang, JingJing; Liang, HanYing; Amei, Amei
This article is concerned with the estimating problem of heteroscedastic partially linear errorsinvariables models. We derive the asymptotic normality for estimators of the slope parameter and the nonparametric component in the case of known error variance with stationary
$$\alpha $$
mixing random errors. Also, when the error variance is unknown, the asymptotic normality for the estimators of the slope parameter and the nonparametric component as well as variance function is considered under independent assumptions. Finite sample behavior of the estimators is investigated via simulations too.
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