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## Asymptotic Palm likelihood theory for stationary point processes

### Annals of the Institute of Statistical Mathematics (2013-04-01) 65: 387-412 , April 01, 2013

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 second-order 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.

## Second-order least-squares estimation for regression models with autocorrelated errors

### Computational Statistics (2014-10-01) 29: 931-943 , October 01, 2014

In their recent paper, Wang and Leblanc (Ann Inst Stat Math 60:883–900, 2008) have shown that the second-order 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.

## Estimation of the conditional distribution in a conditional Koziol-green model

### Test (2000-06-01) 9: 97-122 , June 01, 2000

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.

## Kernel type smoothed quantile estimation under long memory

### Statistical Papers (2008-01-05) 51: 57-67 , January 05, 2008

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.

## Analysis of rounded data in mixture normal model

### Statistical Papers (2012-11-01) 53: 895-914 , November 01, 2012

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.

## Asymptotic Normality for Inference on Multisample, High-Dimensional Mean Vectors Under Mild Conditions

### Methodology and Computing in Applied Probability (2015-06-01) 17: 419-439 , June 01, 2015

In this paper, we consider the asymptotic normality for various inference problems on multisample and high-dimensional mean vectors. We verify that the asymptotic normality of concerned statistics is proved under mild conditions for high-dimensional data. We show that the asymptotic normality can be justified theoretically and numerically even for non-Gaussian data. We introduce the extended cross-data-matrix (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 high-dimensional mean vectors. We give several applications such as confidence regions for high-dimensional 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.

## Asymptotic normality of estimators in heteroscedastic errors-in-variables model

### AStA Advances in Statistical Analysis (2014-04-01) 98: 165-195 , April 01, 2014

This article is concerned with the estimating problem of heteroscedastic partially linear errors-in-variables 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.

## Asymptotic results of a nonparametric conditional cumulative distribution estimator in the single functional index modeling for time series data with applications

### Metrika (2016-07-01) 79: 485-511 , July 01, 2016

In this paper, we treat nonparametric estimation of the conditional cumulative distribution with a scalar response variable conditioned by a functional Hilbertian regressor. We establish asymptotic normality and uniform almost complete convergence rates of the conditional cumulative distribution estimator for dependent variables, linked semiparametrically by the single index structure. Furthermore, we provide some applications and simulations to illustrate our methodology.

## Adaptive varying-coefficient linear quantile model: a profiled estimating equations approach

### Annals of the Institute of Statistical Mathematics (2017-02-20): 1-30 , February 20, 2017

We consider an estimating equations approach to parameter estimation in adaptive varying-coefficient linear quantile model. We propose estimating equations for the index vector of the model in which the unknown nonparametric functions are estimated by minimizing the check loss function, resulting in a profiled approach. The estimating equations have a bias-corrected form that makes undersmoothing of the nonparametric part unnecessary. The estimating equations approach makes it possible to obtain the estimates using a simple fixed-point algorithm. We establish asymptotic properties of the estimator using empirical process theory, with additional complication due to the nuisance nonparametric part. The finite sample performance of the new model is illustrated using simulation studies and a forest fire dataset.

## Nonlinear wavelet density estimation with data missing at random when covariates are present

### Metrika (2015-11-01) 78: 967-995 , November 01, 2015

In this paper, we construct the nonlinear wavelet estimator of a density with data missing at random when covariables are present, and provide an asymptotic expression for the mean integrated squared error (MISE) of the estimator. Unlike for kernel estimators, the MISE expression of the wavelet-based estimator still holds when the density function is piecewise smooth. Also, the asymptotic normality of the estimator is established.