A Two-Stage Plug-In Bandwidth Selection and Its Implementation in Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation

The performance of a kernel HAC estimator depends on the accuracy of the estimation of the normalized curvature, an unknown quantity in the optimal bandwidth represented as the spectral density and its derivative. This paper proposes to estimate it with a general class of kernels. The AMSE of the kernel estimator and the AMSE-optimal bandwidth are derived. It is shown that the optimal bandwidth for the kernel estimator should grow at a much slower rate than the one for the HAC estimator with the same kernel. A solve-the-equation implementation method is also proposed. Finite sample performances are assessed through simulations.Covariance matrix estimation, Kernel estimator, Bandwidth selection, Spectral density, Asymptotic mean squared error

"A Two-Stage Plug-In Bandwidth Selection and Its Implementation for Covariance Estimation"

The two most popular bandwidth choice rules for kernel HAC estimation have been proposed by Andrews (1991) and Newey and West (1994). This paper suggests an alternative approach that estimates an unknown quantity in the optimal bandwidth for the HAC estimator (called normalized curvature) using a general class of kernels, and derives the optimal bandwidth that minimizes the asymptotic mean squared error of the estimator of normalized curvature. It is shown that the optimal bandwidth for the kernel-smoothed normalized curvature estimator should diverge at a slower rate than that of the HAC estimator using the same kernel. An implementation method of the optimal bandwidth for the HAC estimator, which is analogous to the one for probability density estimation by Sheather and Jones (1991), is also developed. The finite sample performance of the new bandwidth choice rule is assessed through Monte Carlo simulations.

"Time Series Nonparametric Regression Using Asymmetric Kernels with an Application to Estimation of Scalar Diffusion Processes"

This paper considers a nonstandard kernel regression for strongly mixing processes when the regressor is nonnegative. The nonparametric regression is implemented using asymmetric kernels [Gamma (Chen, 2000b), Inverse Gaussian and Reciprocal Inverse Gaussian (Scaillet, 2004) kernels] that possess some appealing properties such as lack of boundary bias and adaptability in the amount of smoothing. The paper investigates the asymptotic and finite-sample properties of the asymmetric kernel Nadaraya-Watson, local linear, and re-weighted Nadaraya-Watson estimators. Pointwise weak consistency, rates of convergence and asymptotic normality are established for each of these estimators. As an important economic application of asymmetric kernel regression estimators, we reexamine the problem of estimating scalar diffusion processes.

Nonparametric Estimation of Scalar Diffusion Processes of Interest Rates Using Asymmetric Kernels

This paper proposes a nonparametric regression using asymmetric kernel functions for nonnegative, absolutely regular processes, and specializes this technique to estimating scalar diffusion models of spot interest rate. We illustrate the advantages of asymmetric kernel estimators for bias correction and efficiency gains. The finite-sample properties and the practical relevance of the proposed estimators are evaluated in the context of bond and option pricing. We also present estimation results from empirical analysis of the term structure of U.S. interest rates.Nonparametric regression; Gamma kernel; diffusion estimation; spot interest rate; derivative pricing

The views of university-level Japanese instructors on incoming students for university-level Japanese classes

Prior to this study, research on articulation in Japanese Language in America was scarce. Thus, this study was designed to identify how college-level Japanese instructors view their students who have previous learning experience in Japanese.Sixteen questionnaires (Japanese Articulation Survey)developed by the principal investigator were sent to instructors who are teaching Japanese at The University of Tennessee and its peer institutions. Nine responses were received, and the results were tabulated and analyzed by the principal investigator.A condensed summary of the findings are as follows:1. None of the respondents had experience in teachingJapanese in pre-college level.2. Less than one third of the college students benefited from studying Japanese in high school by exceeding the first year of Japanese at the college level.3. There was diversity in evaluation of these students in their weakness and strength by the college-level instructors 4. There was little consistency in college-level instructors\u27 views of which skills are most important for these students to possess when entering college

Consistent Estimation of Linear Regression Models Using Matched Data

Economists often use matched samples, especially when dealing with earnings data where a number of missing observations need to be imputed. In this paper, we demonstrate that the ordinary least squares estimator of the linear regression model using matched samples is inconsistent and has a non-standard convergence rate to its probability limit. If only a few variables are used to impute the missing data then it is possible to correct for the bias. We propose two semi-parametric bias-corrected estimators and explore their asymptotic properties. The estimators have an indirectinference interpretation and their convergence rates depend on the number of variables used in matching. We can attain the parametric convergence rate if that number is no greater than three. Monte Carlo simulations confirm that the bias correction works very well in such cases

Least Squares Estimators for Unit Root Processes with Locally Stationary Disturbance

The random walk is used as a model expressing equitableness and the effectiveness of various finance phenomena. Random walk is included in unit root process which is a class of nonstationary processes. Due to its nonstationarity, the least squares estimator (LSE) of random walk does not satisfy asymptotic normality. However, it is well known that the sequence of partial sum processes of random walk weakly converges to standard Brownian motion. This result is so-called functional central limit theorem (FCLT). We can derive the limiting distribution of LSE of unit root process from the FCLT result. The FCLT result has been extended to unit root process with locally stationary process (LSP) innovation. This model includes different two types of nonstationarity. Since the LSP innovation has time-varying spectral structure, it is suitable for describing the empirical financial time series data. Here we will derive the limiting distributions of LSE of unit root, near unit root and general integrated processes with LSP innovation. Testing problem between unit root and near unit root will be also discussed. Furthermore, we will suggest two kind of extensions for LSE, which include various famous estimators as special cases

Consistent Estimation of Linear Regression Models Using Matched Data

Economists often use matched samples, especially when dealing with earnings data where a number of missing observations need to be imputed. In this paper, we demonstrate that the ordinary least squares estimator of the linear regression model using matched samples is inconsistent and has a non-standard convergence rate to its probability limit. If only a few variables are used to impute the missing data then it is possible to correct for the bias. We propose two semi-parametric bias-corrected estimators and explore their asymptotic properties. The estimators have an indirectinference interpretation and their convergence rates depend on the number of variables used in matching. We can attain the parametric convergence rate if that number is no greater than three. Monte Carlo simulations confirm that the bias correction works very well in such cases

Consistent Estimation of Linear Regression Models Using Matched Data

Economists often use matched samples, especially when dealing with earnings data where a number of missing observations need to be imputed. In this paper, we demonstrate that the ordinary least squares estimator of the linear regression model using matched samples is inconsistent and has a nonstandard convergence rate to its probability limit. If only a few variables are used to impute the missing data, then it is possible to correct for the bias. We propose two semiparametric bias-corrected estimators and explore their asymptotic properties. The estimators have an indirect-inference interpretation and they attain the parametric convergence rate if the number of matching variables is no greater than three. Monte Carlo simulations confirm that the bias correction works very well in such cases