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Electrothermal energy conversion provides attractive solutions for global energy management, such as energy harvesting from waste heat using pyroelectric energy conversion (PEC) and efficient cooling of portable electronics or data servers using the electrocaloric effect. Relaxor ferroelectrics are attractive for electrothermal energy conversion because of their large pyroelectric coefficients over a wide temperature range. Although Pb-based relaxors are well-known, toxicity concerns have mandated the intense search for Pb-free alternatives. Here, we engineered (Ba,Ca)TiO3-based relaxors based on a multisite doping strategy, which show promising electrothermal performance, viz. a maximum PEC efficiency of 14% and electrocaloric refrigeration capacity of 115 J/kg. Using local-scale structural analysis, we provide an atomistic model for large electrothermal properties in the newly designed Pb-free ferroelectrics, whereby a temperature-independent continuous distribution of cation displacement directions creates easy pathways for microscopic polarization reorientation. This research provides key structural insight for future atomic-scale engineering of environmentally sustainable ferroelectrics in energy applications.

This paper proposes a three-step method for detecting multiple structural breaks for piecewise stationary vector autoregressive processes. The number of structural breaks can be large and unknown with the locations of the breaks being different among different components. The proposed method is established via a link between a structural break problem and a high-dimensional regression problem. By means of this connection, a group orthogonal greedy algorithm, originated from the high-dimensional variable selection context, is developed for efficiently screening out potential break-points in the first step. A high-dimensional information criterion is proposed for consistent structural breaks estimation in the second step. In the third step, the information criterion further determines the specific components in which structural breaks occur. Monte Carlo experiments are conducted to demonstrate the finite sample performance, and applications to stock data are provided to illustrate the proposed method.

Recently, Cavaliere, Georgiev, and Taylor (2018, Econometric Theory 34, 302–348) (CGT) considered the augmented Dickey–Fuller (ADF) test for a unit-root model with linear noise driven by i.i.d. infinite variance innovations and showed that ordinary least squares (OLS)-based ADF statistics have the same distribution as in Chan and Tran (1989, Econometric Theory 5, 354–362) for i.i.d. infinite variance noise. They also proposed an interesting question to extend their results to the case with infinite variance GARCH innovations as considered in Zhang, Sin, and Ling (2015, Stochastic Processes and their Applications 125, 482–512). This paper addresses this question. In particular, the limit distributions of the ADF for random walk models with short-memory linear noise driven by infinite variance GARCH innovations are studied. We show that when the tail index $\alpha , the limit distributions are completely different from that of CGT and the estimator of the parameters of the lag terms used in the ADF regression is not consistent. This paper provides a broad treatment of unit-root models with linear GARCH noises, which encompasses the commonly entertained unit-root IGARCH model as a special case.

The tail of the logarithmic degree distribution of networks decays linearly with respect to the logarithmic degree is known as the power law and is ubiquitous in daily lives. A commonly used technique in modeling the power law is preferential attachment (PA), which sequentially joins each new node to the existing nodes according to the conditional probability law proportional to a linear function of their degrees. Although effective, it is tricky to apply PA to real networks because the number of nodes and that of edges have to satisfy a linear constraint. This paper enables real application of PA by making each new node as an isolated node that attaches to other nodes according to PA scheme in some later epochs. This simple and novel strategy provides an additional degree of freedom to relax the aforementioned constraint to the observed data and uses the PA scheme to compute the implied proportion of the unobserved zero-degree nodes. By using martingale convergence theory, the degree distribution of the proposed model is shown to follow the power law and its asymptotic variance is proved to be the solution of a Sylvester matrix equation, a class of equations frequently found in the control theory (see Hansen and Sargent (2008, 2014)). These results give a strongly consistent estimator for the power-law parameter and its asymptotic normality. Note that this statistical inference procedure is non-iterative and is particularly applicable for big networks such as the World Wide Web presented in Section 6 . Moreover, the proposed model offers a theoretically coherent framework that can be used to study other network features, such as clustering and connectedness, as given in Cheung (2016).

A new time‐frequency model and a method to classify time series data are proposed in this article. By viewing the observed signals as realizations of locally dyadic stationary (LDS) processes, a LDS model can be used to provide a time‐frequency decomposition of the signals, under which the evolutionary Walsh spectrum and related statistics can be defined and estimated. The classification procedure is as follows. First choose a training data set that comprises two groups of time series with a known group. Then compute the time frequency feature (the energy) using the training data set, and use a best tree method to maximize the discrepancy of this feature between the two groups. Finally, choose the testing data set with the unknown group as validation data, and use a discriminant statistic to classify the validation data to one of the groups. The classification method is illustrated via an electroencephalographic dataset and the Ericsson B transaction time dataset. The proposed classification method performs better for integer‐valued time series in terms of classification error rates in both simulations and real‐life applications.

This paper studies the maximum likelihood estimation of nonlinear state space models. Particle Markov chain Monte Carlo method is introduced to implement the Monte Carlo expectation maximization algorithm for more accurate and robust estimation. Under this framework, an automated sample size selection criterion is constructed via renewal theory. This criterion would increase the sample size when the relative likelihood indicates that the parameters are close to each other. The proposed methodology is applied to the stochastic volatility model and another nonlinear state space model for illustration, where the results show better estimation performance.

The Bartlett correction is a desirable feature of the likelihood inference, which yields the confidence region for parameters with improved coverage probability. This study examines the Bartlett correction for the frequency domain empirical likelihood (FDEL), based on the Whittle likelihood of linear time series models. Nordman and Lahiri (Ann Stat 34:3019–3050, 2006) showed that the FDEL does not have an ordinary Chi-squared limit when the innovation is non-Gaussian with unknown variance, which restricts the use of the FDEL inference in time series. We show that, by profiling the innovation variance out of the Whittle likelihood function, the FDEL is Chi-squared-distributed and Bartlett correctable. In particular, the order of the coverage error of the confidence region can be reduced from $$O(n^{-1})$$ to $$O(n^{-2})$$ .

ENTHIS LINK GOES TO A ENGLISH SECTIONFRTHIS LINK GOES TO A FRENCH SECTION Bartlett correction constitutes one of the attractive features of empirical likelihood because it enables the construction of confidence regions for parameters with improved coverage probabilities. We study the Bartlett correction of spatial frequency domain empirical likelihood (SFDEL) based on general spectral estimating functions for regularly spaced spatial data. This general formulation can be applied to testing and estimation problems in spatial analysis, for example testing covariance isotropy, testing covariance separability as well as estimating the parameters of spatial covariance models. We show that the SFDEL is Bartlett correctable. In particular, the improvement in coverage accuracies of the Bartlett‐corrected confidence regions depends on the underlying spatial structures. The Canadian Journal of Statistics 47: 455–472; 2019 © 2019 Statistical Society of Canada

Customized personal rate offering is of growing importance in the insurance industry. To achieve this, an important step is to identify subgroups of insureds from the corresponding heterogeneous claim frequency data. In this paper, a penalized Poisson regression approach for subgroup analysis in claim frequency data is proposed. Subjects are assumed to follow a zero-inflated Poisson regression model with group-specific intercepts, which capture group characteristics of claim frequency. A penalized likelihood function is derived and optimized to identify the group-specific intercepts and effects of individual covariates. To handle the challenges arising from the optimization of the penalized likelihood function, an alternating direction method of multipliers algorithm is developed and its convergence is established. Simulation studies and real applications are provided for illustrations.

This paper establishes asymptotic theory for optimal estimation of change points in general time series models under α-mixing conditions. We show that the Bayes-type estimator is asymptotically minimax for change-point estimation under squared error loss. Two bootstrap procedures are developed to construct confidence intervals for the change points. An approximate limiting distribution of the change-point estimator under small change is also derived. Simulations and real data applications are presented to investigate the finite sample performance of the Bayes-type estimator and the bootstrap procedures.

This paper proposes a new portmanteau-type statistic by combining several lags of the sample autocorrelations to test for the presence of a unit-root of an autoregressive model. The proposed method is nonparametric in nature, which is model free and easy to implement. It avoids modeling the fitted residuals and does not require estimation of nuisance parameters, as commonly done in the augmented Dickey–Fuller or Phillips–Perron procedure. Asymptotic properties of the test are established under general stationary conditions on the noises. Finite sample studies are also reported to illustrate the superior power of the proposed method. Applications to test for cointegration are also given.

In this paper, the limit distribution of the least squares estimator for mildly explosive autoregressive models with strong mixing innovations is established, which is shown to be Cauchy as in the iid case. The result is applied to identify the onset and the end of an explosive period of an econometric time series. Simulations and data analysis are also conducted to demonstrate the usefulness of the result.

Interaction of capital market participants is a complicated dynamic process. A stochastic model is proposed to describe the dynamics to predict short-term stock price behaviors. Independent compound Poisson processes are introduced to describe the occurrences of market orders, limit orders and cancellations of limit orders, respectively. Based on high-frequency observations of the limit order book, the maximum empirical likelihood estimator (MELE) is applied to estimate the parameters of the compound Poisson processes. Moreover, an analytical formula is derived to compute the probability distribution of the first-passage time of a compound Poisson process. Based on this formula, the conditional probability of a price increase and the conditional distribution of the duration until the first change in mid-price are obtained. A novel approach of short-term stock price prediction is proposed and this methodology works reasonably well in the data analysis. Copyright © 2016 John Wiley & Sons, Ltd.

An effective model for time-varying quantiles of a time series is of considerable practical importance across various disciplines. In particular, in financial risk management, computation of Value-at-risk (VaR), one of the most popular risk measures, involves knowledge of quantiles of portfolio returns. This paper examines the random walk behavior of VaRs constructed under two most common approaches, viz. historical simulation and the parametric approach using GARCH models. We find that sequences of historical VaRs appear to follow a unit root model, which can be an artifact under some settings, whereas its counterpart constructed via the parametric approach does not follow a random walk model by default.

Analysis of high-dimensional time series data is of increasing interest among different fields. This article studies high-dimensional time series from a dimension reduction perspective using factor modelling. Statistical inference is conducted using eigen-analysis of a certain non-negative definite matrix related to autocovariance matrices of the time series, which is applicable to fixed or increasing dimension. When the dimension goes to infinity, the rate of convergence and limiting distributions of estimated factors are established. Using the limiting distributions of estimated factors, a high-dimensional final prediction error criterion is proposed to select the number of factors. Asymptotic properties of the criterion are illustrated by simulation studies and real applications.

Interest in online auctions has been growing in recent years. There is an extensive literature on this topic, whereas modeling online auction price process constitutes one of the most active research areas. Most of the research, however, only focuses on modeling price curves, ignoring the bidding process. In this paper, a semiparametric regression model is proposed to model the online auction process. This model captures two main features of online auction data: changing arrival rates of bidding processes and changing dynamics of prices. A new inference procedure using B-splines is also established for parameter estimation. The proposed model is used to forecast the price of an online auction. The advantage of this proposed approach is that the price can be forecast dynamically and the prediction can be updated according to newly arriving information. The model is applied to Xbox data with satisfactory forecasting properties. Copyright © 2016 John Wiley & Sons, Ltd.

It is shown in this paper that when the true mean return vector is replaced by the inferred mean vector obtained indirectly from factor model and arbitrage pricing theory, its impact on the resulting optimal portfolio is insignificant. To achieve this goal, several assumptions are imposed: (i) the asset returns are generated from a factor model, (ii) the number of assets goes to infinity, and (iii) there is no asymptotic arbitrage opportunities. Issues related to the efficiency of the estimated optimal portfolio for high-frequency data are discussed. The portfolio constructed using the sample mean vector and using the inferred mean vector from arbitrage pricing theory are compared.

Bartlett correction, which improves the coverage accuracies of confidence regions, is one of the desirable features of empirical likelihood. For empirical likelihood with dependent data, previous studies on the Bartlett correction are mainly concerned with Gaussian processes. By establishing the validity of Edgeworth expansion for the signed root empirical log-likelihood ratio statistics, we show that the Bartlett correction is applicable to empirical likelihood for short-memory time series with possibly non-Gaussian innovations. The Bartlett correction is established under the assumptions that the variance of the innovation is known and the mean of the underlying process is zero for a single parameter model. In particular, the order of the coverage errors of Bartlett-corrected confidence regions can be reduced from O(n−1) to O(n−2).

This paper develops a novel approach for estimating a threshold autoregressive (TAR) model with multiple-regimes and establishes its large sample properties. By reframing the problem in a regression variable selection context, a least absolute shrinkage and selection operator (LASSO) procedure is proposed to estimate a TAR model with an unknown number of thresholds, where the computation can be performed efficiently. It is further shown that the number and the location of the thresholds can be consistently estimated. A near optimal convergence rate of the threshold parameters is also established. Simulation studies are conducted to assess the performance in finite samples. The results are illustrated with an application to the quarterly US real GNP data over the period 1947–2009.

This article investigates likelihood inferences for high-dimensional factor analysis of time series data. We develop a matrix decomposition technique to obtain expressions of the likelihood functions and its derivatives. With such expressions, the traditional delta method that relies heavily on score function and Hessian matrix can be extended to high-dimensional cases. We establish asymptotic theories, including consistency and asymptotic normality. Moreover, fast computational algorithms are developed for estimation. Applications to high-dimensional stock price data and portfolio analysis are discussed. The technical proofs of the asymptotic results and the computer codes are available online.

By allowing deviations from equilibrium to follow a fractionally integrated process, the notion of fractional cointegration analysis encompasses a wide range of mean-reverting behaviors. For fractional cointegrations, asymptotic theories have been extensively studied, and numerous empirical studies have been conducted in finance and economics. But as far as testing for fractional cointegration is concerned, most of the testing procedures have restrictions on the integration orders of observed time series or integrating error and some tests involve determination of bandwidth. In this paper, a general fractional cointegration model with the observed series and the cointegrating error being fractional processes is considered, and a residual-based testing procedure for fractional cointegration is proposed. Under some regularity conditions, the test statistic has an asymptotic standard normal distribution under the null hypothesis of no fractional cointegration and diverges under the alternatives. This test procedure is easy to implement and works well in finite samples, as reported in a Monte Carlo experiment.

Modeling online auction prices is a popular research topic among statisticians and marketing analysts. Recent research mainly focuses on two directions: one is the functional data analysis (FDA) approach, in which the price–time relationship is modeled by a smooth curve, and the other is the point process approach, which directly models the arrival process of bidders and bids. In this paper, a novel model for the bid arrival process using a self-exciting point process (SEPP) is proposed and applied to forecast auction prices. The FDA and point process approaches are linked together by using functional data analysis technique to describe the intensity of the bid arrival point process. Using the SEPP to model the bid arrival process, many stylized facts in online auction data can be captured. We also develop a simulation-based forecasting procedure using the estimated SEPP intensity and historical bidding increment. In particular, prediction interval for the terminal price of merchandise can be constructed. Applications to eBay auction data of Harry Potter books and Microsoft Xbox show that the SEPP model provides more accurate and more informative forecasting results than traditional methods. Copyright © 2014 John Wiley & Sons, Ltd.

Consider a structural break autoregressive (SBAR) process where j = 1, …, m + 1, {t1, …, tm} are change-points, 1 = t0 < t1 < ⋅⋅⋅ < tm + 1 = n + 1, σ( · ) is a measurable function on , and {ϵt} are white noise with unit variance. In practice, the number of change-points m is usually assumed to be known and small, because a large m would involve a huge amount of computational burden for parameters estimation. By reformulating the problem in a variable selection context, the group least absolute shrinkage and selection operator (LASSO) is proposed to estimate an SBAR model when m is unknown. It is shown that both m and the locations of the change-points {t1, …, tm} can be consistently estimated from the data, and the computation can be efficiently performed. An improved practical version that incorporates group LASSO and the stepwise regression variable selection technique are discussed. Simulation studies are conducted to assess the finite sample performance. Supplementary materials for this article are av...

Testing for causality is of critical importance for many econometric applications. For bivariate AR(1) processes, the limit distributions of causality tests based on least squares estimation depend on the presence of nonstationary processes. When nonstationary processes are present, the limit distributions of such tests are usually very complicated, and the full-sample bootstrap method becomes inconsistent as pointed out in Choi (2005, Statistics and Probability Letters 75, 39–48). In this paper, a profile empirical likelihood method is proposed to test for causality. The proposed test statistic is robust against the presence of nonstationary processes in the sense that one does not have to determine the existence of nonstationary processes a priori. Simulation studies confirm that the proposed test statistic works well.

Let X"t=@?"j"="0^~c"j@e"t"-"j be a moving average process with GARCH (1, 1) innovations {@e"t}. In this paper, the asymptotic behavior of the quadratic form Q"n=@?"j"="1^n@?"s"="1^nb(t-s)X"tX"s is derived when the innovation {@e"t} is a long-memory and heavy-tailed process with tail index @a, where {b(i)} is a sequence of constants. In particular, it is shown that when 1 =4, Q"n has an asymptotic normal distribution. These results not only shed light on the singular behavior of the quadratic forms when both long-memory and heavy-tailed properties are present, but also have applications in the inference for general linear processes driven by heavy-tailed GARCH innovations.

A unified asymptotic theory for nearly unstable higher order autoregressive processes and their least squares estimates is established. A novel version of Jordan’s canonical decomposition with perturbations together with a suitable plug-in principle is proposed to develop the underlying theories. Assumptions are stated in terms of the domain of attraction of partial Fourier transforms. The machinery is applied to recapture some of the classical results with the driving noise being martingale differences. Further, we show how to extend the results to higher order fractional ARIMA models in nearly unstable settings, thereby offering a comprehensive theory to analyse nearly unstable time series.

Credit migrations constitute the building blocks of modern risk management. A firm-specific structural model of credit migration that incorporates the firm's capital structure and the risk perception of rating agencies is proposed. The proposed model employs the notion of distance-to-default, which quantifies default probability. The properties of Brownian excursions play an essential role in the analysis. The proposed model not only allows the derivation of closed-form credit transition probability, but also provides plausible explanations for certain empirical evidence, such as the default probability overlaps in ratings and the slow-to-respond feature of rating agencies. The proposed model is calibrated through simulations and applied to empirical data, which show rating agencies' risk perceptions to be significant. The calibrated model allows calculation of the firm-specific transition probabilities of rated companies.

A primary motivation of higher-order asymptotic statistical analysis is to improve the first-order limiting result in accordance with the celebrated Central Limit Theorem in the sense that a better approximation with higher order accuracy can be attained. In this article, several important tools in asymptotic analysis for obtaining higher-order approximations, including Edgeworth expansions, saddle-point approximations and Laplace integral method, will be revisited together with an introduction of some of their applications in finance. A new result on bounds for the difference between American and European calls on small dividend paying stock is also provided. WIREs Comput Stat 2012, 4:571-587. doi: 10.1002/wics.1234

Consider an AR(p) process , where {ɛt} is a sequence of i.i.d. random variables lying in the domain of attraction of a stable law with index 0

This paper investigates the asymptotic theory of the least squares estimators (LSE) for a long-memory nearly unstable model when the innovation sequences are functionals of moving averages. It is shown that the limit distribution of the LSE is a functional of the Hermite Ornstein–Uhlenbeck process. This result not only generalizes the result of Buchmann and Chan [Ann. Statist. 35 (2007), 2001–2017], but also that of Wu [Economet. Theory 22 (2006), 1–14].

An empirical likelihood–based confidence interval is proposed for interval estimations of the autoregressive coefficient of a first-order autoregressive model via weighted score equations. Although the proposed weighted estimate is less efficient than the usual least squares estimate, its asymptotic limit is always normal without assuming stationarity of the process. Unlike the bootstrap method or the least squares procedure, the proposed empirical likelihood–based confidence interval is applicable regardless of whether the underlying autoregressive process is stationary, unit root, near-integrated, or even explosive, thereby providing a unified approach for interval estimation of an AR(1) model to encompass all situations. Finite-sample simulation studies confirm the effectiveness of the proposed method.

The maximum likelihood estimate (MLE) of the autoregressive coefficient of a near-unit root autoregressive process Yt = ?nYt-1 + ?t with a-stable noise {?t} is studied in this paper. Herein ?n = 1 - ?/n, ? = 0 is a constant, Y0 is a fixed random variable and et is an a-stable random variable with characteristic function f(t,?) for some parameter ?. It is shown that when 0 1 and E?1 = 0, the limit distribution of the MLE of ?n and ? are mixtures of a stable process and Gaussian processes. On the other hand, when a > 1 and E?1 ? 0, the limit distribution of the MLE of ?n and ? are normal. A Monte Carlo simulation reveals that the MLE performs better than the usual least squares procedures, particularly for the case when the tail index a is less than 1.

It is known that the tail index of a GARCH model is determined by a moment equation, which involves the underlying unknown parameters of the model. A tail index estimator can therefore be constructed by solving the sample moment equation with the unknown parameters being replaced by its quasi-maximum likelihood estimates (QMLE). To construct a confidence interval for the tail index, one needs to estimate the non-trivial asymptotic variance of the QMLE. In this paper, an empirical likelihood method is proposed for interval estimation of the tail index. One advantage of the proposed method is that interval estimation can still be achieved without having to estimate the complicated asymptotic variance. A simulation study confirms the advantage of the proposed method.

Consider the nonparametric heteroscedastic regression model Y = m ( X ) + σ ( X ) ɛ , where m ( · ) is an unknown conditional mean function and σ ( · ) is an unknown conditional scale function. In this paper, the limit distribution of the quantile estimate for the scale function σ ( X ) is derived. Since the limit distribution depends on the unknown density of the errors, an empirical likelihood ratio statistic based on quantile estimator is proposed. This statistics is used to construct confidence intervals for the variance function. Under certain regularity conditions, it is shown that the quantile estimate of the scale function converges to a Brownian motion and the empirical likelihood ratio statistic converges to a chi-squared random variable. Simulation results demonstrate the superiority of the proposed method over the least squares procedure when the underlying errors have heavy tails.

Parameters estimation for a FIGARCH(p, d, q )m odel is studied in this paper. By constructing a compact parameter space Θ satisfying the non-negativity constraints for the FI- GARCH model, it is shown that the results of Robinson and Zaffaroni (2006) can be applied to establish the strong con- sistency and asymptotic normality of the quasi-maximum likelihood (QML) estimator of the FIGARCH model. AMS 2000 subject classifications: Primary 62F12, 62E20; secondary 91B84. Keywords and phrases: Asymptotic normality, Con- sistency, Fractionally-integrated GARCH model, Non- negativity, Quasi-maximum likelihood estimator. To apply the results of Robinson and Zaffaroni (2006), a compact searching region Θ satisfying the assumption NN has to be constructed. In this note, we show under certain conditions that the assumptions A-H of Robinson and Zaf- faroni (2006) are fulfilled for θ ∈ Θ. In this way, the asymp- totic behavior of the QMLE of the FIGARCH models within Θ can then be directly established. It should be noted that due to the difficulties of explicitly expressing Θ, in practice, we have to search for the stationary points of the quasi-log likelihood function globally. The link between these station- ary points and the QMLE in Θ is furnished in Proposition 2. Throughout this paper, the assumptions A to H of Robin- son and Zaffaroni (2006) are denoted by RZ-A to RZ-H. Consider the FIGARCH model, X 2 t = σ 2 � 2

This paper studies the goodness-of-fit test of the residual empirical process of a nearly unstable long-memory time series. Chan and Ling (2008) showed that the usual limit distribution of the Kolmogorov–Smirnov test statistics does not hold for an unstable autoregressive model. A key question of interest is what happens when this model has a near unit root, that is, when it is nearly unstable. In this paper, it is established that the statistics proposed by Chan and Ling can be generalized to encompass nearly unstable long-memory models. In particular, the limit distribution is expressed as a functional of an Ornstein–Uhlenbeck process that is driven by a fractional Brownian motion. Simulation studies demonstrate that the limit distribution of the statistic possesses desirable finite sample properties and power.

Fan and Yao (1998) proposed an efficient method to estimate the conditional variance of heteroskedastic regression models. Chen, Cheng, and Peng (2009) applied variance reduction techniques to the estimator of Fan and Yao (1998) and proposed a new estimator for conditional variance to account for the skewness of financial data. In this paper, we apply empirical likelihood methods to construct confidence intervals for the conditional variance based on the estimator of Fan and Yao (1998) and the reduced variance modification of Chen et al. (2009). Simulation studies and data analysis demonstrate the advantage of the empirical likelihood method over the normal approximation method.

Bandwidth selection has been an important topic in nonparametric density estimation. In this paper an effective method for local bandwidth selection is proposed. For local bandwidth selection, due to data sparsity and other reasons, extremely small bandwidths are sometimes selected, which lead to severe undersmoothing. To circumvent this difficulty, the main idea behind the proposed method is to choose the largest bandwidth that still achieves the optimal rate. When coupled with practical bias reduction techniques, the bandwidth selected from this method can be applied simultaneously to conduct both local point and interval estimation. Simulation studies demonstrate the effectiveness of the proposed approach, which compares favorably with other existing approaches.