New recursive estimators of the time-average variance constant

نویسندگان

  • Chun Yip Yau
  • Kin Wai Chan
چکیده

Estimation of the time-average variance constant (TAVC) of a stationary process plays a fundamental role in statistical inference for the mean of a stochastic process. Wu (2009) proposed an efficient algorithm to recursively compute the TAVC with O(1) memory and computational complexity. In this paper, we propose two new recursive TAVC estimators that can compute TAVC estimate with O(1) computational complexity. One of them is uniformly better than Wu’s estimator in terms of asymptotic mean squared error (MSE) at a cost of slightly higher memory complexity. The other preserves the O(1) memory complexity and is better then Wu’s estimator in most situations. Moreover, the first estimator is nearly optimal in the sense that its asymptotic MSE is 23 ≒ 1.12 times that of the optimal off-line TAVC estimator.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The Ratio-type Estimators of Variance with Minimum Average Square Error

The ratio-type estimators have been introduced for estimating the mean and total population, but in recent years based on the ratio methods several estimators for population variance have been proposed. In this paper two families of estimators have been suggested and their approximation mean square error (MSE) have been developed. In addition, the efficiency of these variance estimators are com...

متن کامل

Parametric Estimation of Diffusion Processes Sampled at First Exit Times

This paper introduces a family of recursively defined estimators of the parameters of a diffusion process. We use ideas of stochastic algorithms for the construction of the estimators. Asymptotic consistency of these estimators and asymptotic normality of an appropriate normalization are proved. The results are applied to two examples from the financial literature; viz., Cox-Ingersoll-Ross’ mod...

متن کامل

Square-Root Algorithms of Recursive Least-Squares Wiener Estimators in Linear Discrete-Time Stochastic Systems

This paper addresses the QR decomposition and UD factorization based square-root algorithms of the recursive least-squares (RLS) Wiener fixed-point smoother and filter. In the RLS Wiener estimators, the Riccati-type difference equations for the auto-variance function of the filtering estimate are included. Hence, by the roundoff errors, in the case of the small value of the observation noise va...

متن کامل

Some Improvment in the Estimation of Population Mean in Cluster Sampling

Gupta and Shabbir (2008) have suggested an alternative form of ratio-type estimator for estimating the population mean. In this paper, we introduced new estimators by mixing two, stratified and cluster sampling method. Then we improved these estimators by using auxiliary variables and introducing new estimators. For sampling in infinite populations with a high geographic dispersion, the populat...

متن کامل

An Empirical Comparison of Performance of the Unified Approach to Linearization of Variance Estimation after Imputation with Some Other Methods

Imputation is one of the most common methods to reduce item non_response effects. Imputation results in a complete data set, and then it is possible to use naϊve estimators. After using most of common imputation methods, mean and total (imputation estimators) are still unbiased. However their variances (imputation variances) are underestimated by naϊve variance estimators. Sampling mechanism an...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • Statistics and Computing

دوره 26  شماره 

صفحات  -

تاریخ انتشار 2016