A simple but efficient method has been proposed to select variables in heteroscedastic regression models. It is shown that the pseudo empirical wavelet coefficients corresponding to the significant explanatory variabl...A simple but efficient method has been proposed to select variables in heteroscedastic regression models. It is shown that the pseudo empirical wavelet coefficients corresponding to the significant explanatory variables in the regression models are clearly larger than those nonsignificant ones, on the basis of which a procedure is developed to select variables in regression models. The coefficients of the models are also estimated. All estimators are proved to be consistent.展开更多
Wavelets are applied to detect the jumps in a heteroscedastic regression model. It is shown that the wavelet coefficients of the data have significantly large absolute values across fine scale levels near the jump poi...Wavelets are applied to detect the jumps in a heteroscedastic regression model. It is shown that the wavelet coefficients of the data have significantly large absolute values across fine scale levels near the jump points. Then a procedure is developed to estimate the jumps and jump heights. All estimators are proved to be consistent.展开更多
Heteroscedasticity and multicollinearity are serious problems when they exist in econometrics data. These problems exist as a result of violating the assumptions of equal variance between the error terms and that of i...Heteroscedasticity and multicollinearity are serious problems when they exist in econometrics data. These problems exist as a result of violating the assumptions of equal variance between the error terms and that of independence between the explanatory variables of the model. With these assumption violations, Ordinary Least Square Estimator</span><span style="font-family:""> </span><span style="font-family:""><span style="font-family:Verdana;">(OLS) will not give best linear unbiased, efficient and consistent estimator. In practice, there are several structures of heteroscedasticity and several methods of heteroscedasticity detection. For better estimation result, best heteroscedasticity detection methods must be determined for any structure of heteroscedasticity in the presence of multicollinearity between the explanatory variables of the model. In this paper we examine the effects of multicollinearity on type I error rates of some methods of heteroscedasticity detection in linear regression model in other to determine the best method of heteroscedasticity detection to use when both problems exist in the model. Nine heteroscedasticity detection methods were considered with seven heteroscedasticity structures. Simulation study was done via a Monte Carlo experiment on a multiple linear regression model with 3 explanatory variables. This experiment was conducted 1000 times with linear model parameters of </span><span style="white-space:nowrap;"><em><span style="font-family:Verdana;">β</span></em><sub><span style="font-family:Verdana;">0</span></sub><span style="font-family:Verdana;"> = 4 , </span><em><span style="font-family:Verdana;">β</span></em><sub><span style="font-family:Verdana;">1</span></sub><span style="font-family:Verdana;"> = 0.4 , </span><em><span style="font-family:Verdana;">β</span></em><sub><span style="font-family:Verdana;">2</span></sub><span style="font-family:Verdana;">= 1.5</span></span></span><span style="font-family:""><span style="font-family:Verdana;"> and </span><em style="font-family展开更多
Consider the heteroscedastic regression model Yi = g（xi） ＋ σiei, 1 ≤ i ≤ n, where σi^2 = f（ui）, here （xi, ui） being fixed design points, g and f being unknown functions defined on [0, 1], ei being independe...Consider the heteroscedastic regression model Yi = g（xi） ＋ σiei, 1 ≤ i ≤ n, where σi^2 = f（ui）, here （xi, ui） being fixed design points, g and f being unknown functions defined on [0, 1], ei being independent random errors with mean zero. Assuming that Yi are censored randomly and the censored distribution function is known or unknown, we discuss the rates of strong uniformly convergence for wavelet estimators of g and f, respectively. Also, the asymptotic normality for the wavelet estimators of g is investigated.展开更多
Chaos theory has taught us that a system which has both nonlinearity and random input will most likely produce irregular data. If random errors are irregular data, then random error process will raise nonlinearity （K...Chaos theory has taught us that a system which has both nonlinearity and random input will most likely produce irregular data. If random errors are irregular data, then random error process will raise nonlinearity （Kantz and Schreiber （1997））. Tsai （1986） introduced a composite test for autocorrelation and heteroscedasticity in linear models with AR（1） errors. Liu （2003） introduced a composite test for correlation and heteroscedasticity in nonlinear models with DBL（p, 0, 1） errors. Therefore, the important problems in regression model axe detections of bilinearity, correlation and heteroscedasticity. In this article, the authors discuss more general case of nonlinear models with DBL（p, q, 1） random errors by score test. Several statistics for the test of bilinearity, correlation, and heteroscedasticity are obtained, and expressed in simple matrix formulas. The results of regression models with linear errors are extended to those with bilinear errors. The simulation study is carried out to investigate the powers of the test statistics. All results of this article extend and develop results of Tsai （1986）, Wei, et al （1995）, and Liu, et al （2003）.展开更多
基金Zhou's research was partially supported by the foundations of NatioiMd Natural Science (10471140) and (10571169) of China.
文摘A simple but efficient method has been proposed to select variables in heteroscedastic regression models. It is shown that the pseudo empirical wavelet coefficients corresponding to the significant explanatory variables in the regression models are clearly larger than those nonsignificant ones, on the basis of which a procedure is developed to select variables in regression models. The coefficients of the models are also estimated. All estimators are proved to be consistent.
文摘Wavelets are applied to detect the jumps in a heteroscedastic regression model. It is shown that the wavelet coefficients of the data have significantly large absolute values across fine scale levels near the jump points. Then a procedure is developed to estimate the jumps and jump heights. All estimators are proved to be consistent.
文摘Heteroscedasticity and multicollinearity are serious problems when they exist in econometrics data. These problems exist as a result of violating the assumptions of equal variance between the error terms and that of independence between the explanatory variables of the model. With these assumption violations, Ordinary Least Square Estimator</span><span style="font-family:""> </span><span style="font-family:""><span style="font-family:Verdana;">(OLS) will not give best linear unbiased, efficient and consistent estimator. In practice, there are several structures of heteroscedasticity and several methods of heteroscedasticity detection. For better estimation result, best heteroscedasticity detection methods must be determined for any structure of heteroscedasticity in the presence of multicollinearity between the explanatory variables of the model. In this paper we examine the effects of multicollinearity on type I error rates of some methods of heteroscedasticity detection in linear regression model in other to determine the best method of heteroscedasticity detection to use when both problems exist in the model. Nine heteroscedasticity detection methods were considered with seven heteroscedasticity structures. Simulation study was done via a Monte Carlo experiment on a multiple linear regression model with 3 explanatory variables. This experiment was conducted 1000 times with linear model parameters of </span><span style="white-space:nowrap;"><em><span style="font-family:Verdana;">β</span></em><sub><span style="font-family:Verdana;">0</span></sub><span style="font-family:Verdana;"> = 4 , </span><em><span style="font-family:Verdana;">β</span></em><sub><span style="font-family:Verdana;">1</span></sub><span style="font-family:Verdana;"> = 0.4 , </span><em><span style="font-family:Verdana;">β</span></em><sub><span style="font-family:Verdana;">2</span></sub><span style="font-family:Verdana;">= 1.5</span></span></span><span style="font-family:""><span style="font-family:Verdana;"> and </span><em style="font-family
基金the National Natural Science Foundation of China(10571136)a Wonkwang University Grant in 2007
文摘Consider the heteroscedastic regression model Yi = g（xi） ＋ σiei, 1 ≤ i ≤ n, where σi^2 = f（ui）, here （xi, ui） being fixed design points, g and f being unknown functions defined on [0, 1], ei being independent random errors with mean zero. Assuming that Yi are censored randomly and the censored distribution function is known or unknown, we discuss the rates of strong uniformly convergence for wavelet estimators of g and f, respectively. Also, the asymptotic normality for the wavelet estimators of g is investigated.
文摘Chaos theory has taught us that a system which has both nonlinearity and random input will most likely produce irregular data. If random errors are irregular data, then random error process will raise nonlinearity （Kantz and Schreiber （1997））. Tsai （1986） introduced a composite test for autocorrelation and heteroscedasticity in linear models with AR（1） errors. Liu （2003） introduced a composite test for correlation and heteroscedasticity in nonlinear models with DBL（p, 0, 1） errors. Therefore, the important problems in regression model axe detections of bilinearity, correlation and heteroscedasticity. In this article, the authors discuss more general case of nonlinear models with DBL（p, q, 1） random errors by score test. Several statistics for the test of bilinearity, correlation, and heteroscedasticity are obtained, and expressed in simple matrix formulas. The results of regression models with linear errors are extended to those with bilinear errors. The simulation study is carried out to investigate the powers of the test statistics. All results of this article extend and develop results of Tsai （1986）, Wei, et al （1995）, and Liu, et al （2003）.
基金Supported by the National Natural Science Foundation of China(71171003)Provincial Natural Science Research Project of Anhui Colleges(KJ2011A032)+2 种基金Anhui Polytechnic University Foundation for Recruiting Talent(2011YQQ004)Anhui Provincial Natural Scienice Foundation(1208085QA04)Anhui Normal University postdoctoral positions funded
