This paper is concerned with the consistency of nonparametric regression model. For the weighted estimator of unknown regression function, the strong consistency, the complete consistency and the convergence rate of t...
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This paper is concerned with the consistency of nonparametric regression model. For the weighted estimator of unknown regression function, the strong consistency, the complete consistency and the convergence rate of the complete consistency are investigated under some mild conditions. These results extend or improve the corresponding ones of Yang et al. (2018) for extended negatively dependent (END, for short) random variables to asymptotically almost negatively associated random variables. Also, the simulation study of the finite samples provided in this paper shows the validity of our results.
This article is concerned with the estimating problem of nonparametric regression model. Under certain regularity conditions, we derive the Berry-Esseen bound for wavelet estimators of the unknown regression function ...
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This article is concerned with the estimating problem of nonparametric regression model. Under certain regularity conditions, we derive the Berry-Esseen bound for wavelet estimators of the unknown regression function with asymptotically negatively associated assumptions. Also, we present a numerical simulation study to verify the validity of the results established here.
In this paper, the nonparametric regression model with repeated measurements based on phi-mixing errors is considered. Therth mean consistency, strong consistency, strong convergence rate, complete consistency and the...
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In this paper, the nonparametric regression model with repeated measurements based on phi-mixing errors is considered. Therth mean consistency, strong consistency, strong convergence rate, complete consistency and the asymptotic normality of the wavelet estimator are established under some mild conditions on moments and mixing coefficients.
In this paper, we establish the pth mean consistency, complete consistency, and the rate of complete consistency for the wavelet estimator in a nonparametric regression model with m-extended negatively dependent rando...
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In this paper, we establish the pth mean consistency, complete consistency, and the rate of complete consistency for the wavelet estimator in a nonparametric regression model with m-extended negatively dependent random errors. We show that the best rates can be nearly O(n(-1/3)) under some general conditions. The results obtained in the paper markedly improve and extend some corresponding ones to a much more general setting.
In this paper, we mainly study the consistency for the estimator of nonparametric regression model based on asymptotically almost negatively associated (AANA, in short) errors. Firstly, the Bernstein type inequality f...
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In this paper, we mainly study the consistency for the estimator of nonparametric regression model based on asymptotically almost negatively associated (AANA, in short) errors. Firstly, the Bernstein type inequality for AANA random variables is established. By using the Bernstein type inequality and moment inequalities, we investigate the complete consistency and convergence rate for the estimator of nonparametric regression model based on AANA errors. As applications, the complete consistency and convergence rate for the nearest neighbor estimator are obtained.
Consider the nonparametric regression model Y-ni = g(t(ni)) + epsilon(i), i = 1, 2, horizontal ellipsis , n, n >= 1, where epsilon(i), 1 <= i <= n, are asymptotically negatively associated (ANA, for short) ra...
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Consider the nonparametric regression model Y-ni = g(t(ni)) + epsilon(i), i = 1, 2, horizontal ellipsis , n, n >= 1, where epsilon(i), 1 <= i <= n, are asymptotically negatively associated (ANA, for short) random variables. Under some appropriate conditions, the Berry-Esseen bound of the wavelet estimator of g(.) is established. In addition, some numerical simulations are provided in this paper. The results obtained in this paper generalize some corresponding ones in the literature.
High-frequency financial data is more difficult to predict than low-frequency data because it possesses nonlinearity, nonstationarity, higher volatility, and long memory and is frequently accompanied by the jump pheno...
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High-frequency financial data is more difficult to predict than low-frequency data because it possesses nonlinearity, nonstationarity, higher volatility, and long memory and is frequently accompanied by the jump phenomena. In this paper, the nonparametricregression (NR) model based on kernel function is used to fit the nonlinear relationship between the nonstationary series Yt and its lagging series to model the trend of high frequency financial time series. Furthermore, the deep learning LSTM (long short-term memory) model is applied to capture the high volatility and frequent jumps of high frequency financial data and to improve the forecasting accuracy of the residual series. The results demonstrate that the hybrid NR and LSTM model has greatly improved the forecasting accuracy in several evaluation criteria. In comparison to NR, support vector machine (SVM), LSTM, ARIMA and NR-SVM models, the mean absolute error (MAE) of NR-LSTM has reduced by 89.78%, 97.85%, 86.48%, 32.47% and 89%, respectively. In addition, we have constructed the trading strategy for the Shanghai-Shenzhen 300 index by using the NR-LSTM model. The NR-LSTM model can continue to provide good returns even during a bear market, which can serve as a guide for investors. Furthermore, the NR-LSTM model also exhibits the best forecasting effect when we model the high-frequency data of Ping An bank in China, the FTSE 100 index in the UK, and the S&P 500 index in the US.
Consider the following nonparametricmodel: Yni=g(xni)+epsilon ni,1 = 1, g(center dot) is a real valued function defined on A, and epsilon(n1),..., epsilon(nn) are rho(-)-mixing random errors with zero mean and finite...
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Consider the following nonparametricmodel: Yni=g(xni)+epsilon ni,1 <= i <= n,where x(ni) is an element of Aare the nonrandom design points and A is a compact set of R-m for some m >= 1, g(center dot) is a real valued function defined on A, and epsilon(n1),..., epsilon(nn) are rho(-)-mixing random errors with zero mean and finite variance. We obtain the Berry-Esseen bounds of the weighted estimator of g(center dot). The rate can achieve nearly O((n-1)/4) when the moment condition is appropriate. Moreover, we carry out some simulations to verify the validity of our results.
In this paper, the Berry-Esseen bound for rho-mixing random variables with the rate of normal approximation O(n(-1/6) logn) is established under some suitable conditions. By using the Berry-Esseen bound, we further in...
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In this paper, the Berry-Esseen bound for rho-mixing random variables with the rate of normal approximation O(n(-1/6) logn) is established under some suitable conditions. By using the Berry-Esseen bound, we further investigate the Berry-Esseen bound of sample quantiles for rho-mixing random variables. The rate of normal approximation is shown to be O(n(-1/6) logn) under some suitable conditions. In addition, the asymptotic normality of the linear weighted estimator for the nonparametric regression model based on rho-mixing errors is studied by using the Berry-Esseen bound that we established. Some new results are obtained in the paper under much weaker dependent structures.
In this paper, we establish the strong consistency and complete consistency of the Priestley-Chao estimator in nonparametric regression model with widely orthant dependent errors under some general conditions. We also...
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In this paper, we establish the strong consistency and complete consistency of the Priestley-Chao estimator in nonparametric regression model with widely orthant dependent errors under some general conditions. We also obtain the rates of strong consistency and complete consistency. We show that the rates can approximate to under appropriate conditions. The results obtained in the paper improve or extend the corresponding ones to widely orthant dependent assumptions.
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