A consistent parameter estimation in the three-parameter lognormal distribution

In this work, we propose a consistent method of estimation for the parameters of the three-parameter lognormal distribution. We then discuss some properties of these estimators and show by means of a Monte Carlo simulation study that the proposed estimators perform better than some other prominent estimators in terms of bias and root mean squared error. Finally, we present two real-life examples to illustrate the method of estimation proposed.     

Unbiased estimation of the MSE matrices of improved estimators in linear regression

Stein-rule and other improved estimators have scarcely been used in empirical work. One major reason is that it is not easy to obtain precision measures for these estimators. In this paper, we derive unbiased estimators for both the mean squared error (MSE) and the scaled MSE matrices of a class of Stein-type estimators. Our derivation provides the basis for measuring the estimators' precision and constructing confidence bands. Comparisons are made between these MSE estimators and the least squares covariance estimator. For illustration, the methodology is applied to data on energy consumption.     

Robust estimators based on generalization of trimmed mean

In this article, we propose new estimators of location. These estimators select a robust set around the geometric median, enlarge it, and compute the (iterative) weighted mean from it. By doing so, we obtain a robust estimator in the sense of the breakdown point, which uses more observations than standard estimators. We apply our approach on the concepts of boxplot and bagplot. We work in a general normed vector space and allow multi-valued estimators.     

Properties of design-based functional principal components analysis

This work aims at performing functional principal components analysis (FPCA) with Horvitz–Thompson estimators when the observations are curves collected with survey sampling techniques. One important motivation for this study is that FPCA is a dimension reduction tool which is the first step to develop model-assisted approaches that can take auxiliary information into account. FPCA relies on the estimation of the eigenelements of the covariance operator which can be seen as nonlinear functionals. Adapting to our functional context the linearization technique based on the influence function developed by Deville [1999. Variance estimation for complex statistics and estimators: linearization and residual techniques. Survey Methodology 25, 193–203], we prove that these estimators are asymptotically design unbiased and consistent. Under mild assumptions, asymptotic variances are derived for the FPCA’ estimators and consistent estimators of them are proposed. Our approach is illustrated with a simulation study and we check the good properties of the proposed estimators of the eigenelements as well as their variance estimators obtained with the linearization approach.     

Reweighting approximate GM estimators: Asymptotics and residual-based graphics

The iterative weighted least squares algorithm is handy for solving generalized estimating equations. In some situations it may be desirable to limit the number of iterations to a fixed finite number, for instance, to keep the breakdown point under control. Such a scheme is called reweighting. Usually reweighting leads to a different large sample theory than full iteration, and the reweighted estimator may inherit deficiencies of the starting value. When might the reweighting scheme work? To answer this question we define a broad class of estimators, namely, approximate GM estimators, and we show that reweighting leads to the same large sample theory as full iteration within this class. As an example, we provide conditions under which one-step Newton-Raphson estimators are approximate GM estimators. We then use the reweighting to construct residual-based graphics for approximate GM estimates, adapting weighted residual plots that have been proposed previously, and developing new plots to provide complementary views of the data.     

Invariant methods for estimating variance components in mixed linear models 2

The subject of this contribution is to present a survey on new methods for variance component estimation, which appeared in the literature in recent years. Starting from mixed models treated in analysis of variance research work on this field turned over to a more general approach in which the covariance matrix of the vector of observations is assumed to be a unknown linear combination of known symmetric matrices. Much interest has been shown in developing some kinds op optimal estimators for the unknown parameters and most results were obtained for estimators being invariant with respect to a certain group of translations. Therefore we restrict attention to this class of estimates. We will deal with minimum variance unbiased estimators, least squared errors estimators, maximum likelihood estimators. Bayes quadratic estimators and show some relations to the mimimum norm quadratic unbiased estimation principle (MINQUE) introduced by C. R. Rao [20]. We do not mention the original motivation of MINQUE since the otion of minimum norm depends on a measure that is not accepted by all statisticians. Also we do‘nt deal with other approaches like the BAYEsian and fiducial methods which were successfully applied by S. Portnoy [18], P. Rusolph [22], G. C. Tiao, W. Y. Tan [28], M. J. K. Healy [9] and others, although in very special situations, only. Additionally we add some new results and also new insight in the properties of known estimators. We give a new characterization of MINQUE in the class of all estimators, extend explicite expressions for locally optimal quadratic estimators given by C. R. Rao [22] to a slightly more general situation and prove complete class theorems useful for the computation of BAYES quadratic estimators. We also investigate situations in which BAYES quadratic unbiased estimators do'nt change if the distribution of the error terms differ from the normal distribution.     

Non parametric estimation of the structural expectation of a stochastic increasing function

This article introduces a non parametric warping model for functional data. When the outcome of an experiment is a sample of curves, data can be seen as realizations of a stochastic process, which takes into account the variations between the different observed curves. The aim of this work is to define a mean pattern which represents the main behaviour of the set of all the realizations. So, we define the structural expectation of the underlying stochastic function. Then, we provide empirical estimators of this structural expectation and of each individual warping function. Consistency and asymptotic normality for such estimators are proved.     

Estimation of parameters of two-dimensional sinusoidal signal in heavy-tailed errors

In this paper, we consider a two-dimensional sinusoidal model observed in an additive random field. The proposed model has wide applications in statistical signal processing. The additive noise has mean zero but the variance may not be finite. We propose the least squares estimators to estimate the unknown parameters. It is observed that the least squares estimators are strongly consistent. We obtain the asymptotic distribution of the least squares estimators under the assumption that the additive errors are from a symmetric stable distribution. Some numerical experiments are performed to see how the results work for finite samples.     

Optimized estimation for population mean using conventional and non-conventional measures under the joint influence of measurement error and non-response

Most of the research work in the theory of survey sampling only deals with the sampling errors under the assumptions: (i) there is a complete response and (ii) recorded information from individuals is correct but in practice it is not always true. Non-sampling errors like non-response and measurement errors (MEs) mostly creep into the survey and become more influential for estimators than sampling errors. Considering this practical situation of non-response and MEs jointly, we proposed an optimum class of estimators for population mean under simple random sampling using conventional and non-conventional measures. Bias and mean square error of the proposed estimators are derived up to first degree of approximation. Moreover, a simulation study is conducted to assess the performance of new estimators which proves that proposed estimators are more efficient than the traditional Hansen and Hurwitz estimator and other competing estimators.     

Estimation of the Parameters of Type-I Generalized Logistic Distribution Using Order Statistics

In this work, we propose a technique of estimating the location parameter μ and scale parameter σ of Type-I generalized logistic distribution by U-statistics constructed by using best linear functions of order statistics as kernels. The efficiency comparison of the proposed estimators with respect to maximum likelihood estimators is also made.     

Asymptotic Distribution of the Maximum Likelihood Estimators of the Parameters of the Right-Truncated Dagum Distribution

In this work we have determined the asymptotic distribution of the maximum likelihood estimators of the parameters β, λ, and δ for the right-truncated Dagum model. Some numerical comparisons show that, for each combination of the parameters and for each sample size, the variance of maximum likelihood estimators increases as the truncation point decreases, i.e., with the increase in the cut of the right tail of distribution.     

New two-stage sampling designs based on neoteric ranked set sampling

Neoteric ranked set sampling (NRSS) is a recently developed sampling plan, derived from the well-known ranked set sampling (RSS) scheme. It has already been proved that NRSS provides more efficient estimators for population mean and variance compared to RSS and other sampling designs based on ranked sets. In this work, we propose and evaluate the performance of some two-stage sampling designs based on NRSS. Five different sampling schemes are proposed. Through an extensive Monte Carlo simulation study, we verified that all proposed sampling designs outperform RSS, NRSS, and the original double RSS design, producing estimators for the population mean with a lower mean square error. Furthermore, as with NRSS, two-stage NRSS estimators present some bias for asymmetric distributions. We complement the study with a discussion on the relative performance of the proposed estimators. Moreover, an additional simulation based on data of the diameter and height of pine trees is presented.     

Multiple-output quantile regression through optimal quantization

A new nonparametric quantile regression method based on the concept of optimal quantization was developed recently and was showed to provide estimators that often dominate their classical, kernel-type, competitors. In the present work, we extend this method to multiple-output regression problems. We show how quantization allows approximating population multiple-output regression quantiles based on halfspace depth. We prove that this approximation becomes arbitrarily accurate as the size of the quantization grid goes to infinity. We also derive a weak consistency result for a sample version of the proposed regression quantiles. Through simulations, we compare the performances of our estimators with (local constant and local bilinear) kernel competitors. The results reveal that the proposed quantization-based estimators, which are local constant in nature, outperform their kernel counterparts and even often dominate their local bilinear kernel competitors. The various approaches are also compared on artificial and real data.     

Robust estimation in growth curve models

The growth curve model introduced by potthoff and Roy 1964 is a general statistical model which includes as special cases regression models and both univariate and multivariate analysis of variance models. The methods currently available for estimating the parameters of this model assume an underlying multivariate normal distribution of errors. In this paper, we discuss tw robst estimators of the growth curve loction and scatter parameters based upon M-estimation techniques and the work done by maronna 1976. The asymptotic distribution of these robust estimators are discussed and a numerical example given.     

Randomized quantile regression estimation for heteroskedastic non parametric model

In this paper, we propose robust randomized quantile regression estimators for the mean and (condition) variance functions of the popular heteroskedastic non parametric regression model. Unlike classical approaches which consider quantile as a fixed quantity, our method treats quantile as a uniformly distributed random variable. Our proposed method can be employed to estimate the error distribution, which could significantly improve prediction results. An automatic bandwidth selection scheme will be discussed. Asymptotic properties and relative efficiencies of the proposed estimators are investigated. Our empirical results show that the proposed estimators work well even for random errors with infinite variances. Various numerical simulations and two real data examples are used to demonstrate our methodologies.     

Estimating the parameters of the linear compartment model

In this paper we consider the linear compartment model and consider the estimation procedures of the different parameters. We discuss a method to obtain the initial estimators, which can be used for any iterative procedures to obtain the least-squares estimators. Four different types of confidence intervals have been discussed and they have been compared by computer simulations. We propose different methods to estimate the number of components of the linear compartment model. One data set has been used to see how the different methods work in practice.     

Modified skew-slash distribution

Abstract

In this work, we introduce a new skewed slash distribution. This modification of the skew-slash distribution is obtained by the quotient of two independent random variables. That quotient consists on a skew-normal distribution divided by a power of an exponential distribution with scale parameter equal to two. In this way, the new skew distribution has a heavier tail than that of the skew-slash distribution. We give the probability density function expressed by an integral, but we obtain some important properties useful for making inferences, such as moment estimators and maximum likelihood estimators. By way of illustration and by using real data, we provide maximum likelihood estimates for the parameters of the modified skew-slash and the skew-slash distributions. Finally, we introduce a multivariate version of this new distribution.     

Statistical Inference on a Stochastic Epidemic Model

In this work, we develop statistical inference for the parameters of a discrete-time stochastic SIR epidemic model. We use a Markov chain for describing the dynamic behavior of the epidemic. Specifically, we propose estimators for the contact and removal rates based on the maximum likelihood and martingale methods, and establish their asymptotic distributions. The obtained results are applied in the statistical analysis of the basic reproduction number, a quantity that is useful in establishing vaccination policies. In order to evaluate the population size for which the results are useful, a numerical study is carried out. Finally, a comparison of the maximum likelihood and martingale estimators is conducted by means of Monte Carlo simulations.     

A note on efficient density estimators of convolutions

It is already known that the convolution of a bounded density with itself can be estimated at the root-n rate using the two asymptotically equivalent kernel estimators: (i) Frees estimator ( Frees, 1994) and (ii) Saavedra and Cao estimator ( Saavedra and Cao, 2000). In this work, we investigate the efficiency of these estimators of the convolution of a bounded density. The efficiency criterion used in this work is that of a least dispersed regular estimator described in Begun et al. (1983). This concept is based on the Hájek–Le Cam convolution theorem for locally asymptotically normal (LAN) families.     

Binary quantile regression and variable selection: A new approach

In this paper, we propose a new estimation method for binary quantile regression and variable selection which can be implemented by an iteratively reweighted least square approach. In contrast to existing approaches, this method is computationally simple, guaranteed to converge to a unique solution and implemented with standard software packages. We demonstrate our methods using Monte-Carlo experiments and then we apply the proposed method to the widely used work trip mode choice dataset. The results indicate that the proposed estimators work well in finite samples.