In this paper, we examine the estimation for trend functions in a time series model with Gaussian dependent residues with the aid of wavelet techniques. Using the simulations on the five different test functions and the process and taking into account the desired function, the factors affecting the error in our estimation have been discussed. The results show that the error rate of the wavelet method depends on the long-term dependence length. Finally, according to our simulations, the wavelet estimator method is compared with the so called classical methods of Kernel estimation and the results revealed that Wavelet estimations are more efficient.

Despite the physicians and nutritionists recommendations to consume the fruits and vegetables, they point much less on how to choose fruits and vegetables in daily meals. In this study, with a novel approach, fruits and vegetables have been classified on the basis of their similar characteristics and the amount of certain nutrients. One of the goals of diet is the diversity and balance of nutrition; therefore the classification of fruits and vegetables on the basis of their nutritional value makes balancing the nutritional intake of these important food groups and also finding a suitable replacement for them feasible. In order to meet the nutritional needs, using principal component analysis and cluster analysis, fruits and vegetables are classified into several groups. MATLAB software was used for doing this classification.

In this paper, the estimation of the scale parameter of a two-parameter Weibull distribution based on the Progressive Type II censoring samples has been considered. The E-Bayesian and Hierarchical Bayesian estimators for the scale parameter of the Weibull distribution based on the symmetric and asymmetric loss functions, such as the squared error (SE), general entropy (GE) and Linear exponential (LINEX) loss functions, are provided. Then, with the use of mean square error and absolute bias and through Monte Carlo simulation study, these methods are compared with each other and with E-Bayesian estimator.

In this paper we study the problem of estimation of population mean in the presence of measurement error simultaneously using information on a single auxiliary variable. We have developed a new estimator of population mean and compared it with some existing estimators under the situations when measurement errors occur simultaneously. The proposed estimators are theoretically compared with existing estimators. Empirical and simulation study is also conducted to assess the performance of proposed estimator.

Additive noise channels are the most commonly used channels in signal processing. In these channels the received signal, random variable Y, is composed of a transmitted signal, random variable X, and an additive noise, random variable Z. One of the important problems studied on the received signal is the entropy of random variable Y. When additive noise Z is an independent Gaussian random variable with zero mean and unit variance, the elegant algebraic connection between differential entropy of output signal Y and Fisher information is stated through a relation known as the De Bruijn’s identity. In this paper, we first obtain a general relation for differentials of conditional distribution of output signal and use it to prove the relationship between the first derivative of differential entropy of output signal and its Fisher information. This method can be used for extending De Bruijn’s identity when the additive noise is distributed as another useful statistical distributions.

Wavelets are one of the newest achievements of mathematical science, which have many applications in other sciences especially statistics. In this paper, after introducing wavelet transforms, the nonparametric estimator of the density function is expressed by the nuclear wavelet and threshold wavelet method. Also variance-covariance of wavelet coefficient are investigated. At the end we survey the theoretical outcomes with numerical computation by using R software to compare purpose estimators.