In this simulation study, five correlation coefficients, namely, Pearson, Spearman, Kendal Tau, Permutation-based, and Winsorized were compared in terms of Type I error rate and power under different scenarios where t...In this simulation study, five correlation coefficients, namely, Pearson, Spearman, Kendal Tau, Permutation-based, and Winsorized were compared in terms of Type I error rate and power under different scenarios where the underlying distributions of the variables of interest, sample sizes and correlation patterns were varied. Simulation results showed that the Type I error rate and power of Pearson correlation coefficient were negatively affected by the distribution shapes especially for small sample sizes, which was much more pronounced for Spearman Rank and Kendal Tau correlation coefficients especially when sample sizes were small. In general, Permutation-based and Winsorized correlation coefficients are more robust to distribution shapes and correlation patterns, regardless of sample size. In conclusion, when assumptions of Pearson correlation coefficient are not satisfied, Permutation-based and Winsorized correlation coefficients seem to be better alternatives.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:""><span style="font-family:Verdana;">β</span><span style="font-family:Verdana;"><sub>3 </sub></span></em><span style="font-family:Verdana;">= 3.6</span><span style="font-family:Verdana;">. </span><span style="font-family:Verdana;">Five (5) </span><span style="font-family:Verdana;"></span><span style="font-family:Verdana;">levels of</span><span style="white-space:nowrap;font-family:Verdana;"> </span><span style="font-family:Verdana;"></span><span style="font-family:Verdana;">mulicollinearity </span></span><span style="font-family:Verdana;">are </span><span style="font-family:Verdana;">with seven</span><span style="font-family:""> </span><span style="font-family:Verdana;">(7) different sample sizes. The method’s performances were compared with the aids of set confidence interval (C.I</span><span style="font-family:Verdana;">.</span><span style="font-family:Verdana;">) criterion. Results showed that whenever multicollinearity exists in the model with any forms of heteroscedasticity structures, Breusch-Godfrey (BG) test is the best method to determine the existence of heteroscedasticity at all chosen levels of significance.展开更多
To improve the bit error rate(BER) performance of multiple input multiple output(MIMO) systems with low complexity, a three-branch transmission scheme employing 8-weighted-type fractional Fourier transform(8-WFRFT) mo...To improve the bit error rate(BER) performance of multiple input multiple output(MIMO) systems with low complexity, a three-branch transmission scheme employing 8-weighted-type fractional Fourier transform(8-WFRFT) module is proposed. In the proposed scheme, the original signal is first decomposed into eight sub-signals and then merged into three component signals by the same carrier pattern. The three signals have mathematical constraint relations among themselves that can counteract the channel fading. They are simultaneously transmitted via three independent antennas after delay regulating. At the receiver, an inverse 8-WFRFT module is employed to obtain the estimated original signal by processing the received signal. Then, the bit error rate(BER) performance, transmitting power, transmission rate, power spectrum and computational complexity of the proposed scheme are analysed in detail. Numerical results show that the proposed scheme has a superior performance compared to STBC based three-antenna transmission scheme, in terms of BER performance.展开更多
文摘In this simulation study, five correlation coefficients, namely, Pearson, Spearman, Kendal Tau, Permutation-based, and Winsorized were compared in terms of Type I error rate and power under different scenarios where the underlying distributions of the variables of interest, sample sizes and correlation patterns were varied. Simulation results showed that the Type I error rate and power of Pearson correlation coefficient were negatively affected by the distribution shapes especially for small sample sizes, which was much more pronounced for Spearman Rank and Kendal Tau correlation coefficients especially when sample sizes were small. In general, Permutation-based and Winsorized correlation coefficients are more robust to distribution shapes and correlation patterns, regardless of sample size. In conclusion, when assumptions of Pearson correlation coefficient are not satisfied, Permutation-based and Winsorized correlation coefficients seem to be better alternatives.
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:""><span style="font-family:Verdana;">β</span><span style="font-family:Verdana;"><sub>3 </sub></span></em><span style="font-family:Verdana;">= 3.6</span><span style="font-family:Verdana;">. </span><span style="font-family:Verdana;">Five (5) </span><span style="font-family:Verdana;"></span><span style="font-family:Verdana;">levels of</span><span style="white-space:nowrap;font-family:Verdana;"> </span><span style="font-family:Verdana;"></span><span style="font-family:Verdana;">mulicollinearity </span></span><span style="font-family:Verdana;">are </span><span style="font-family:Verdana;">with seven</span><span style="font-family:""> </span><span style="font-family:Verdana;">(7) different sample sizes. The method’s performances were compared with the aids of set confidence interval (C.I</span><span style="font-family:Verdana;">.</span><span style="font-family:Verdana;">) criterion. Results showed that whenever multicollinearity exists in the model with any forms of heteroscedasticity structures, Breusch-Godfrey (BG) test is the best method to determine the existence of heteroscedasticity at all chosen levels of significance.
基金supported by the National Basic Research Program of China (2013CB329003)the National Natural Science Foundation Program of China (No. 61671179)Funds for Science and Technology on Information Transmission and Dissemination in Communication Networks Laboratory (EX156410046)
文摘To improve the bit error rate(BER) performance of multiple input multiple output(MIMO) systems with low complexity, a three-branch transmission scheme employing 8-weighted-type fractional Fourier transform(8-WFRFT) module is proposed. In the proposed scheme, the original signal is first decomposed into eight sub-signals and then merged into three component signals by the same carrier pattern. The three signals have mathematical constraint relations among themselves that can counteract the channel fading. They are simultaneously transmitted via three independent antennas after delay regulating. At the receiver, an inverse 8-WFRFT module is employed to obtain the estimated original signal by processing the received signal. Then, the bit error rate(BER) performance, transmitting power, transmission rate, power spectrum and computational complexity of the proposed scheme are analysed in detail. Numerical results show that the proposed scheme has a superior performance compared to STBC based three-antenna transmission scheme, in terms of BER performance.
