A note on successive comparisons between several ordered variances

ABSTRACT

In this article, a procedure for comparisons between k (k ? 3) successive populations with respect to the variance is proposed when it is reasonable to assume that variances satisfy simple ordering. Critical constants required for the implementation of the proposed procedure are computed numerically and selected values of the computed critical constants are tabulated. The proposed procedure for normal distribution is extended for making comparisons between successive exponential populations with respect to scale parameter. A comparison between the proposed procedure and its existing competitor procedures is carried out, using Monte Carlo simulation. Finally, a numerical example is given to illustrate the proposed procedure.     

A classifier under the strongly spiked eigenvalue model in high-dimension,low-sample-size context

Abstract

We consider the classification of high-dimensional data under the strongly spiked eigenvalue (SSE) model. We create a new classification procedure on the basis of the high-dimensional eigenstructure in high-dimension, low-sample-size context. We propose a distance-based classification procedure by using a data transformation. We also prove that our proposed classification procedure has consistency property for misclassification rates. We discuss performances of our classification procedure in simulations and real data analyses using microarray data sets.     

Empirical likelihood-based serial correlation testing in partially varying coefficient single-index models

ABSTRACT

Partially varying coefficient single-index models (PVCSIM) are a class of semiparametric regression models. One important assumption is that the model error is independently and identically distributed, which may contradict with the reality in many applications. For example, in the economical and financial applications, the observations may be serially correlated over time. Based on the empirical likelihood technique, we propose a procedure for testing the serial correlation of random error in PVCSIM. Under some regular conditions, we show that the proposed empirical likelihood ratio statistic asymptotically follows a standard χ² distribution. We also present some numerical studies to illustrate the performance of our proposed testing procedure.     

On the estimation of non linear functions in stochastic volatility models

Abstract

This paper focuses on the inference of suitable generally non linear functions in stochastic volatility models. In this context, in order to estimate the variance of the proposed estimators, a moving block bootstrap (MBB) approach is suggested and discussed. Under mild assumptions, we show that the MBB procedure is weakly consistent. Moreover, a methodology to choose the optimal length block in the MBB is proposed. Some examples and simulations on the model are also made to show the performance of the proposed procedure.     

B-spline estimation for partially linear varying coefficient composite quantile regression models

Abstract

In this article, a new composite quantile regression estimation (CQR) approach is proposed for partially linear varying coefficient models (PLVCM) under composite quantile loss function with B-spline approximations. The major advantage of the proposed procedures over the existing ones is easy to implement using existing software, and it requires no specification of the error distributions. Under the regularity conditions, the consistency and asymptotic normality of the estimators are also derived. Finally, a simulation study and a real data application are undertaken to assess the finite sample performance of the proposed estimation procedure.     

Asymptotic results in gamma kernel regression

Abstract

Based on the Gamma kernel density estimation procedure, this article constructs a nonparametric kernel estimate for the regression functions when the covariate are nonnegative. Asymptotic normality and uniform almost sure convergence results for the new estimator are systematically studied, and the finite performance of the proposed estimate is discussed via a simulation study and a comparison study with an existing method. Finally, the proposed estimation procedure is applied to the Geyser data set.     

Information approach for a lifetime change-point model based on the exponential-logarithmic distribution

ABSTRACT

The exponential-logarithmic distribution is a distribution which has a decreasing failure function and various applications such as in biological and engineering fields. In this paper, we study a change-point problem of this distribution. A procedure based on Schwarz information criterion is proposed to detect changes in parameters of this distribution. Simulations are conducted to indicate the performance of the proposed procedure under different scenarios. Applications on two real data are provided to illustrate the detection procedure.     

Sequential Procedures for Selecting the Most Probable Multinomial Cell When a Nuisance Cell Is Present

Abstract

This article considers the problem of selecting the most probable cell in a multinomial distribution in the presence of a nuisance cell. Two open sequential procedures are proposed and studied. One is a two-stage procedure and the other a multistage procedure.     

A simple solution for spurious regressions

ABSTRACT

The literature on spurious regressions has found that the t-statistic for testing the null of no relationship between two independent variables diverges asymptotically under a wide variety of non stationary data-generating processes for the dependent and explanatory variables. This paper introduces a simple method which guarantees convergence of this t-statistic to a pivotal limit distribution, thus allowing asymptotic inference. This method can be used to distinguish a genuine relationship from a spurious one among integrated processes. We apply the proposed procedure to several pairs of apparently independent integrated variables, and find that our procedure does not find (spurious) significant relationships.     

MOSUM monitoring for variance change in nonparametric regression models

ABSTRACT

This article considers the monitoring for variance change in nonparametric regression models. First, the local linear estimator of the regression function is given. A moving square cumulative sum procedure is proposed based on residuals of the estimator. And the asymptotic results of the statistic under the null hypothesis and the alternative hypothesis are obtained. Simulations and Application support our procedure.     

Variable selection for semiparametric varying coefficient partially linear model based on modal regression with missing data

Abstract

In this article, we focus on the variable selection for semiparametric varying coefficient partially linear model with response missing at random. Variable selection is proposed based on modal regression, where the non parametric functions are approximated by B-spline basis. The proposed procedure uses SCAD penalty to realize variable selection of parametric and nonparametric components simultaneously. Furthermore, we establish the consistency, the sparse property and asymptotic normality of the resulting estimators. The penalty estimation parameters value of the proposed method is calculated by EM algorithm. Simulation studies are carried out to assess the finite sample performance of the proposed variable selection procedure.     

A goodness-of-fit test for the stratified proportional hazards model for survival data

Abstract

Goodness-of-fit testing is addressed in the stratified proportional hazards model for survival data. A test statistic based on within-strata cumulative sums of martingale residuals over covariates is proposed and its asymptotic distribution is derived under the null hypothesis of model adequacy. A Monte Carlo procedure is proposed to approximate the critical value of the test. Simulation studies are conducted to examine finite-sample performance of the proposed statistic.     

Robust estimation and variable selection for varying-coefficient single-index models based on modal regression

ABSTRACT

In this paper, we propose a new efficient and robust penalized estimating procedure for varying-coefficient single-index models based on modal regression and basis function approximations. The proposed procedure simultaneously solves two types of problems: separation of varying and constant effects and selection of variables with non zero coefficients for both non parametric and index components using three smoothly clipped absolute deviation (SCAD) penalties. With appropriate selection of the tuning parameters, the new method possesses the consistency in variable selection and the separation of varying and constant coefficients. In addition, the estimators of varying coefficients possess the optimal convergence rate and the estimators of constant coefficients and index parameters have the oracle property. Finally, we investigate the finite sample performance of the proposed method through a simulation study and real data analysis.     

Smoothed detrended fluctuation analysis

ABSTRACT

The method of detrended fluctuation analysis (DFA) is useful in revealing the extent of long-range dependence, it has successfully been applied to different fields of interest. In this paper we proposed a smoothed detrended fluctuation analysis method based on the principle of wavelet shrinkage. The procedure is illustrated and compared with the DFA method by Monte Carlo simulations on fractional Gaussian noise models.     

Robust variable selection and parametric component identification in varying coefficient models

ABSTRACT

In this paper, we study a novelly robust variable selection and parametric component identification simultaneously in varying coefficient models. The proposed estimator is based on spline approximation and two smoothly clipped absolute deviation (SCAD) penalties through rank regression, which is robust with respect to heavy-tailed errors or outliers in the response. Furthermore, when the tuning parameter is chosen by modified BIC criterion, we show that the proposed procedure is consistent both in variable selection and the separation of varying and constant coefficients. In addition, the estimators of varying coefficients possess the optimal convergence rate under some assumptions, and the estimators of constant coefficients have the same asymptotic distribution as their counterparts obtained when the true model is known. Simulation studies and a real data example are undertaken to assess the finite sample performance of the proposed variable selection procedure.     

A new nonlinear unit root test with Fourier function

Abstract

Traditional unit root tests display a tendency to be nonstationary in the case of structural breaks and nonlinearity. To eliminate this problem this paper proposes a new flexible Fourier form nonlinear unit root test. This test eliminates this problem to add structural breaks and nonlinearity together to the test procedure. In this test procedure, structural breaks are modeled by means of a Fourier function and nonlinear adjustment is modeled by means of an exponential smooth threshold autoregressive (ESTAR) model. The simulation results indicate that the proposed unit root test is more powerful than the Kruse and KSS tests.     

Ma system identification using higher order cumulants application to modelling solar radiation

The main goal of this investigation is to elaborate an accurate and efficient algorithm able to estimate the moving average (MA) parameters in noisy environment. So, we address the problem of estimating the parameters of a MA--non-minimum phase (NMP)-system from the output observation when the system is excited by an unobservable independent identically distributed (i.i.d.) sequence. A new procedure, based on third and fourth order cumulants, to estimate the parameters of MA process when the order is known, is presented. This procedure was tested for various examples of MA (NMP) system, and for different order and different signal-to-noise-ratio (SNR). A comparison with some existing methods was also performed and the result shows the efficiency of the proposed algorithm. For validation purpose this method is used to search for a model able to describe and to predict the data set representing the daily solar radiation.     

High breakdown point robust estimators with missing data

In this paper, we propose a new procedure to estimate the distribution of a variable y when there are missing data. To compensate the presence of missing responses, it is assumed that a covariate vector x is observed and that y and x are related by means of a semi-parametric regression model. Observed residuals are combined with predicted values to estimate the missing response distribution. Once the responses distribution is consistently estimated, we can estimate any parameter defined through a continuous functional T using a plug in procedure. We prove that the proposed estimators have high breakdown point.     

Use of several auxiliary variables in estimating the population mean in a two-occasion rotation pattern

ABSTRACT

This paper addresses the problem of estimation of the population mean on the current (second) occasion in two-occasion successive sampling. Utilizing the readily available information on several auxiliary variables on both occasions and the information on the study variable from the previous occasion, an estimation procedure of the population mean on the current occasion has been proposed. Theoretical properties of the proposed estimator have been investigated. Optimum replacement policy to the proposed estimator has been discussed. The proposed estimator has been compared empirically with the sample mean estimator, when there is no matching and the optimum estimator which is a linear combination of the means of the matched and unmatched portions of the sample at the current occasion. Appropriate recommendations have been made for practical applications.     

Extending the inference function for augmented margins method to implement trivariate Clayton copula-based SUR Tobit models

Abstract

In this paper, we perform the analysis of the SUR Tobit model for three left-censored dependent variables by modeling its nonlinear dependence structure through the one-parameter Clayton copula. For unbiased parameter estimation, we propose an extension of the Inference Function for Augmented Margins (IFAM) method to the trivariate case. The interval estimation for the model parameters using resampling procedures is also discussed. We perform simulation and empirical studies, whose satisfactory results indicate the good performance of the proposed model and methods. Our procedure is illustrated using real data on consumption of food items (salad dressings, lettuce, tomato) by Americans.