In most situations the best estimator of a function of the parameter exists, but sometimes it has a complex form and we cannot compute its variance explicitly. Therefore, a lower bound for the variance of an estimator is one of the fundamentals in the estimation theory, because it gives us an idea about the accuracy of an estimator. It is well-known in statistical inference that the Cram&eac...

we develop a two phase sampling procedure to determine the sample size necessary to estimatethe population mean of a normally distributed random variable and show that the resulting estimator has preassigned variance and is unbiased under a regular condition. we present a necessary and sufficient condition under which the final sample mean is an unbiased estimator for the population mean.

Objective: This paper aims to introduce a modified kernel-type ridge estimator for partially linear models under randomly-right censored data. Such models include two main issues that need to be solved: multi-collinearity and censorship. To address these issues, we improved the kernel estimator based on synthetic data transformation and kNN imputation techniques. The key idea of this paper is t...

This paper deals with nonparametric estimators of the drift function b computed from independent continuous observations, on a compact time interval, solution stochastic differential equation driven by fractional Brownian motion (fSDE). First, risk bound is established Skorokhod’s integral based least squares oracle $${\widehat{b}}$$ b. Thanks to relationship between fSDE and its derivative res...

This note focuses on estimating the quantile function based on the kernel smooth estimator under a truncated dependent model. The Bahadurtype representation of the kernel smooth estimator is established, and from the Bahadur representation it can be seen that this estimator is strongly consistent.

Given random variables X ∈ IR and Y such that E[Y |X = x] = m(x), the average derivative δ0 is defined as δ0 = E[∇m(X)], i.e., as the expected value of the gradient of the regression function. Average derivative estimation has several applications in econometric theory (Stoker, 1992) and thus it is crucial to have a fast implementation of this estimator for practical purposes. We present such a...