Global kernel estimator and test of varying‐coefficient autoregressive model

We propose a varying‐coefficient autoregressive model that contains additive models, varying‐ coefficient models, partially linear models and low‐dimensional interaction models as special cases. A global kernel backfitting method is proposed for the estimation and inference of parameters and unknown functions in this model. Key large‐sample results are established, including estimation consistency, asymptotic normality and the generalized likelihood ratio test for parameters and non‐parametric functions. The proposed methodology is examined by simulation studies and applied to examine the relationship between suicide news reports in the three leading newspapers and the daily number of suicides in Taiwan. The relationship between the media reporting and suicide incidence has been established and explored. The Canadian Journal of Statistics 47: 487–519; 2019 © 2019 Statistical Society of Canada     

Efficiency Measure from Dynamic Stochastic Production Frontier: Application to Tunisian Textile, Clothing, and Leather Industries

This paper adresses the measurement of technical efficiency of textile, clothing, and leather (TCL) industries in Tunisia through a panel data estimation of a dynamic translog production frontier. It provides a perspective on productivity and efficiency that should be instructive to a developing economy which will face substantial competitive pressure along the gradual economic liberalisation process. The importance of TCL industries in Tunisian manufacturing sector is a reason for obtaining more knowledge of productivity and efficiency for this key industry. Dynamic is introduced to reflect the production consequences of the adjustment costs, which are associated with changes in factor inputs. Estimation of a dynamic error components model is considered using the system generalized method of moments (GMM) estimator suggested by Arellano and Bover (1995), Another look at the instrumental-variable estimation of error-components models, J. Econometrics68:29-51) and Blundell and Bond (Blundell, R., Bond, S. (1998a), Initial conditions and moment restrictions in dynamic panel data models. J. Econometrics87:115-143; Blundell, R., Bond, S. (1998b), GMM estimation with persistent panel data: an application to production functions, Paper presented at the Eighth International Conference on Panel Data, Goteborg University). Our study evaluates the sensitivity of the results, particularly of the efficiency measures, to different specifications. Firm-specific time-invariant technical efficiency is obtained using the Schmidt and Sickles (Schmidt, P., Sickles, R. C. (1984). Production frontiers and panel data. J. Bus. Econ. Stat.2:367-374) approach after estimating the dynamic frontier. We stress the importance of allowing for lags in adjustment of output to inputs and of controlling for time-invariant variables when estimating firm-specific efficiency. The results suggest that the system GMM estimation of the dynamic specification produces the most accurate parameter estimates and technical efficiency measure. Mean efficiency scores is of 68%. Policy implications of the results are outlined.     

Local Linear Additive Quantile Regression

Abstract.  We consider non-parametric additive quantile regression estimation by kernel-weighted local linear fitting. The estimator is based on localizing the characterization of quantile regression as the minimizer of the appropriate 'check function'. A backfitting algorithm and a heuristic rule for selecting the smoothing parameter are explored. We also study the estimation of average-derivative quantile regression under the additive model. The techniques are illustrated by a simulated example and a real data set.     

On Mixture Double Autoregressive Time Series Models

This article proposes a mixture double autoregressive model by introducing the flexibility of mixture models to the double autoregressive model, a novel conditional heteroscedastic model recently proposed in the literature. To make it more flexible, the mixing proportions are further assumed to be time varying, and probabilistic properties including strict stationarity and higher order moments are derived. Inference tools including the maximum likelihood estimation, an expectation–maximization (EM) algorithm for searching the estimator and an information criterion for model selection are carefully studied for the logistic mixture double autoregressive model, which has two components and is encountered more frequently in practice. Monte Carlo experiments give further support to the new models, and the analysis of an empirical example is also reported.     

Estimation in second order branching processes with application to swine flu data

Abstract

This paper discusses inferential issues related to estimation of offspring mean and variance in a second order branching process, when both the offspring distributions are assumed to have identical mean and variance. Estimating equation approach is used to find the estimator of the offspring mean and the fact that a second order branching process model can be modeled as an autoregressive process is utilized to obtain the estimator of the offspring variance. Both the estimators are shown to be consistent and asymptotically normal. The second order branching process model is applied to H1N1 data for Pune, India, and Mexico and is found to be a suitable model. The estimates obtained from this model are used to compute the proportion of vaccination required for elimination of the disease.     

Generalized partially linear varying coefficient models with multiple smoothing variables

This paper is concerned with semiparametric efficient estimation of a generalized partially linear varying coefficient model. The model studied in this paper is very flexible, accommodating various nonlinear relations between the response variable and a set of predictor variables. It is a structured regression model and is particularly useful in dealing with a discrete response variable. We apply the smooth backfitting technique to estimate the nonparametric part of the model and employ the profiling approach to obtain a semiparametric efficient estimator of the parametric part.     

Robust estimation for zero-inflated poisson autoregressive models based on density power divergence

In this study, we consider a robust estimation for zero-inflated Poisson autoregressive models using the minimum density power divergence estimator designed by Basu et al. [Robust and efficient estimation by minimising a density power divergence. Biometrika. 1998;85:549–559]. We show that under some regularity conditions, the proposed estimator is strongly consistent and asymptotically normal. The performance of the estimator is evaluated through Monte Carlo simulations. A real data analysis using New South Wales crime data is also provided for illustration.     

Modelling functional additive quantile regression using support vector machines approach

This work deals with conditional quantiles estimation when several functional covariates are involved, via a support vector machines nonparametric methodology. We establish weak consistency of this estimator. To fit the additive components, we use an ordinary backfitting procedure combined with an iterative reweighted least-squares procedure to solve the penalised minimisation problem. This procedure makes it possible to derive a split sample method for choosing the hyper-parameters of the model. The performances of the proposed technique, in terms of forecast accuracy, are evaluated through simulation and a real dataset study.     

Maximum likelihood estimation with missing spatial data and with an application to remotely sensed data

The paper examines the small and large lattice properties of the exact maximum likelihood estimator for a spatial model where parameter estimation and missing data estimation are tackled simultaneously, A first order conditional autoregressive model is examined in detail. The paper concludes with an empirical analysis of remotely sensed data.     

Nonlinear semiparametric autoregressive model with finite mixtures of scale mixtures of skew normal innovations

We propose data generating structures which can be represented as the nonlinear autoregressive models with single and finite mixtures of scale mixtures of skew normal innovations. This class of models covers symmetric/asymmetric and light/heavy-tailed distributions, so provide a useful generalization of the symmetrical nonlinear autoregressive models. As semiparametric and nonparametric curve estimation are the approaches for exploring the structure of a nonlinear time series data set, in this article the semiparametric estimator for estimating the nonlinear function of the model is investigated based on the conditional least square method and nonparametric kernel approach. Also, an Expectation–Maximization-type algorithm to perform the maximum likelihood (ML) inference of unknown parameters of the model is proposed. Furthermore, some strong and weak consistency of the semiparametric estimator in this class of models are presented. Finally, to illustrate the usefulness of the proposed model, some simulation studies and an application to real data set are considered.     

Non parametric regression analysis for longitudinal data with time-depending autoregressive error process

This paper considers a non parametric longitudinal model, where the within-subject correlation structure is represented by a time-depending autoregressive error process. An initial estimator without taking into account the within-subject correlation is obtained to fit the time-depending autoregressive error process. With the initial estimator, we construct a two-stage local linear estimator of the mean function. According to the asymptotic normality of the initial and two-stage estimators, it is discovered that the two-stage estimator has a smaller asymptotic variance. The simulation results show us that the two-stage estimation has some good properties. The analysis of a data set demonstrates its application.     

A new algorithm for maximum likelihood estimation in normal scale-mixture generalized autoregressive conditional heteroskedastic models

In this paper, we propose a new generalized autoregressive conditional heteroskedastic (GARCH) model using infinite normal scale-mixtures which can suitably avoid order selection problems in the application of finite normal scale-mixtures. We discuss its theoretical properties and develop a two-stage algorithm for the maximum likelihood estimator to estimate the mixing distribution non-parametric maximum likelihood estimator (NPMLE) as well as GARCH parameters (two-stage MLE). For the estimation of a mixing distribution, we employ a fast computational algorithm proposed by Wang [On fast computation of the non-parametric maximum likelihood estimate of a mixing distribution. J R Stat Soc Ser B. 2007;69:185–198] under the gradient characterization of the non-parametric mixture likelihood. The GARCH parameters are then estimated either using the expectation-mazimization algorithm or general optimization scheme. In addition, we propose a new forecasting algorithm of value-at-risk (VaR) using the two-stage MLE and the NPMLE. Through a simulation study and real data analysis, we compare the performance of the two-stage MLE with the existing ones including quasi-maximum likelihood estimator based on the standard normal density and the finite normal mixture quasi maximum estimated-likelihood estimator (cf. Lee S, Lee T. Inference for Box–Cox transformed threshold GARCH models with nuisance parameters. Scand J Stat. 2012;39:568–589) in terms of the relative efficiency and accuracy of VaR forecasting.     

Efficient Estimation of the Partly Linear Additive Hazards Model with Current Status Data

This paper focuses on efficient estimation, optimal rates of convergence and effective algorithms in the partly linear additive hazards regression model with current status data. We use polynomial splines to estimate both cumulative baseline hazard function with monotonicity constraint and nonparametric regression functions with no such constraint. We propose a simultaneous sieve maximum likelihood estimation for regression parameters and nuisance parameters and show that the resultant estimator of regression parameter vector is asymptotically normal and achieves the semiparametric information bound. In addition, we show that rates of convergence for the estimators of nonparametric functions are optimal. We implement the proposed estimation through a backfitting algorithm on generalized linear models. We conduct simulation studies to examine the finite‐sample performance of the proposed estimation method and present an analysis of renal function recovery data for illustration.     

Penalized weighted composite quantile regression in the linear regression model with heavy-tailed autocorrelated errors

In this paper, a penalized weighted composite quantile regression estimation procedure is proposed to estimate unknown regression parameters and autoregression coefficients in the linear regression model with heavy-tailed autoregressive errors. Under some conditions, we show that the proposed estimator possesses the oracle properties. In addition, we introduce an iterative algorithm to achieve the proposed optimization problem, and use a data-driven method to choose the tuning parameters. Simulation studies demonstrate that the proposed new estimation method is robust and works much better than the least squares based method when there are outliers in the dataset or the autoregressive error distribution follows heavy-tailed distributions. Moreover, the proposed estimator works comparably to the least squares based estimator when there are no outliers and the error is normal. Finally, we apply the proposed methodology to analyze the electricity demand dataset.     

Risk efficient estimation of fully dependent random coefficient autoregressive models of general order

We consider a stochastic dynamic model with autoregressive progression. The drift coefficients of the autoregressive model are random where the randomness in the coefficients can have any dependence structure. We propose a two-step sequential estimator and study the asymptotic behavior of few important properties. Paradigm of sequential estimation has its own advantage in reducing sample size and plugging estimates of nuisance parameters while inferring about the main parameters. Our proposed estimator is asymptotically optimal as the predictive risk of the proposed estimator attains the risk of the oracle that assumes known nuisance parameters. Extensive simulation confirms our results.     

Improved estimation for Poisson INAR(1) models

We consider the first-order Poisson autoregressive model proposed by McKenzie [Some simple models for discrete variate time series. Water Resour Bull. 1985;21:645–650] and Al-Osh and Alzaid [First-order integer valued autoregressive (INAR(1)) process. J Time Ser Anal. 1987;8:261–275], which may be suitable in situations where the time series data are non-negative and integer valued. We derive the second-order bias of the squared difference estimator [Weiß. Process capability analysis for serially dependent processes of Poisson counts. J Stat Comput Simul. 2012;82:383–404] for one of the parameters and show that this bias can be used to define a bias-reduced estimator. The behaviour of a modified conditional least-squares estimator is also studied. Furthermore, we access the asymptotic properties of the estimators here discussed. We present numerical evidence, based upon Monte Carlo simulation studies, showing that the here proposed bias-adjusted estimator outperforms the other estimators in small samples. We also present an application to a real data set.     

Isotone additive latent variable models

For manifest variables with additive noise and for a given number of latent variables with an assumed distribution, we propose to nonparametrically estimate the association between latent and manifest variables. Our estimation is a two step procedure: first it employs standard factor analysis to estimate the latent variables as theoretical quantiles of the assumed distribution; second, it employs the additive models’ backfitting procedure to estimate the monotone nonlinear associations between latent and manifest variables. The estimated fit may suggest a different latent distribution or point to nonlinear associations. We show on simulated data how, based on mean squared errors, the nonparametric estimation improves on factor analysis. We then employ the new estimator on real data to illustrate its use for exploratory data analysis.     

Implementing unit roost tests in ARMA models of unknow order

This paper compares the performance of classical and recent unit root tests based on different estimation procedures, including fitting ARMA models of unknown orders. The article also introduces an estimator of the spectral density function that is based on the estimation of an ARMA model with data previously detrended by GLS. The Monte Carlo experiment shows that tests improve their performance if an ARMA model is estimated, instead of an autoregressive approximation. The best results are obtained by tests based on the estimation of the spectral density function.     

动态面板阈模型的一种序贯两步估计

动态面板阈模型可以刻画经济变量动态调整过程的非对称性,在实证分析中有广泛的运用,但阈值参数的引入同时增加了参数估计的困难,理论上尚有许多问题没有解决。针对此类模型,本文提出了一种简单而实用的序贯两步估计方法,首先利用格点搜索获得阈值参数的一致估计,基于该参数对数据结构进行合理划分并引入不同类型的矩条件,然后利用广义矩方法获得自回归参数的估计。理论研究与模拟结果表明,序贯两步估计具有良好的大样本性质和有限样本表现;与现有文献的方法相比,序贯两步估计能够有效避免不同类型参数估计偏差的相互影响,减小估计量的偏差与均方根误差。     

A Seemingly Unrelated Nonparametric Additive Model with Autoregressive Errors

This article considers a nonparametric additive seemingly unrelated regression model with autoregressive errors, and develops estimation and inference procedures for this model. Our proposed method first estimates the unknown functions by combining polynomial spline series approximations with least squares, and then uses the fitted residuals together with the smoothly clipped absolute deviation (SCAD) penalty to identify the error structure and estimate the unknown autoregressive coefficients. Based on the polynomial spline series estimator and the fitted error structure, a two-stage local polynomial improved estimator for the unknown functions of the mean is further developed. Our procedure applies a prewhitening transformation of the dependent variable, and also takes into account the contemporaneous correlations across equations. We show that the resulting estimator possesses an oracle property, and is asymptotically more efficient than estimators that neglect the autocorrelation and/or contemporaneous correlations of errors. We investigate the small sample properties of the proposed procedure in a simulation study.