In this study, three classes of generalized and more efficient combined regression-cum-ratio estimators are presented to estimate the population mean of the study variable in stratified two-phase sampling considering non-response and measurement error are present jointly. The expressions for the bias and mean square error of the three proposed generalized combined regression-cum-ratio estimators have been obtained. Optimal conditions which make the proposed generalized regression-cum-ratio estimators more efficient than modified combined regression estimator are discussed. The performance of the proposed generalized combined regression-cum-ratio estimators has been compared theoretically as well as empirically with various combined type estimators in stratified two-phase sampling including usual combined ratio estimator, usual combined exponential ratio estimator, usual combined regression estimator, and modified combined regression estimator. An empirical study shows that the proposed generalized combined regression-cum-ratio estimators perform more efficiently than all combined type ratio, exponential ratio, and regression estimators discussed in the study.

‎‎‎Performance measures are essential for evaluating portfolio performance in the risk management and fund industries‎, ‎with the Sharpe ratio being a widely adopted risk-adjusted metric‎. ‎This ratio compares the excess expected return to its standard deviation‎, ‎enabling investors to assess the returns of risk-taking activities against risk-free options‎. ‎Its popularity stems from its ease of calculation and straightforward interpretation‎. ‎However‎, ‎the actual Sharpe ratio value is often unavailable and must be estimated empirically based on the assumption of normality of asset returns‎. ‎In practice‎, ‎financial assets typically exhibit non-normal distributions and nonlinear dependencies‎, ‎which can compromise the accuracy of the Sharpe ratio estimation when normality is assumed‎. ‎This paper challenges the normality assumption‎, ‎aiming to enhance the accuracy of Sharpe ratio estimates‎. ‎We investigate the impact of dependency on the Sharpe ratio of a two-asset portfolio using copulas‎. ‎Theoretical findings and extensive simulations demonstrate the effectiveness of the proposed copula-based approach to the classic Sharpe ratio‎.

‎‎‎Performance measures are essential for evaluating portfolio performance in the risk management and fund industries‎, ‎with the Sharpe ratio being a widely adopted risk-adjusted metric‎. ‎This ratio compares the excess expected return to its standard deviation‎, ‎enabling investors to assess the returns of risk-taking activities against risk-free options‎. ‎Its popularity stems from its ease of calculation and straightforward interpretation‎. ‎However‎, ‎the actual Sharpe ratio value is often unavailable and must be estimated empirically based on the assumption of normality of asset returns‎. ‎In practice‎, ‎financial assets typically exhibit non-normal distributions and nonlinear dependencies‎, ‎which can compromise the accuracy of the Sharpe ratio estimation when normality is assumed‎. ‎This paper challenges the normality assumption‎, ‎aiming to enhance the accuracy of Sharpe ratio estimates‎. ‎We investigate the impact of dependency on the Sharpe ratio of a two-asset portfolio using copulas‎. ‎Theoretical findings and extensive simulations demonstrate the effectiveness of the proposed copula-based approach to the classic Sharpe ratio‎.

This article introduces a dual problem of widely used calibration ratio-type estimators for estimating population mean of the study variable considering auxiliary information under dual constraints using stratified systematic sampling design. Under large sample approximations, the expression for bias and variance of the proposed estimator are derived. In addition, the optimality condition for the proposed estimator and hence optimum variance expression is also obtained for the same. Moreover, a study based on real-life data is carried out to judge the performance of the proposed calibration estimator in terms of minimum relative bias and relative root mean squared error criterion. The study reveals that the calibration ratio-type estimator under dual constraints may be preferred in practice as it provides consistent and more precise parameter estimates.

This paper presents a new estimator for the speech enhancement using codebook. Codebook-based speech enhancement method separates the noise and speech from each other and synthesizes the enhanced speech signal by optimally selecting the speech codebook indexes. This method can enhance the noisy speech with signal to noise ratio of less than zero decibel. In this method it is very important to select the correct codebook indexes. Therefore, in this paper, the maximum likelihood estimator is proposed for speech and noise by applying auditory quality-enhancing weights. The relation of this estimator is also used as a distance function in the design of codebooks. This method is simulated for different speakers and noises. The results show the proposed maximum likelihood estimator leads to better speech enhancement than the euclidean distance estimator. The proposed method is also more successful in dealing with non-stationary or stationary noises and negative or positive SNRs than other methods. The cost of the superior quality enhancement in this method is the requirement to a relatively time-consuming signal processing.

In this study, we suggest a family of ratio estimators for the population mean parameter using various robust regression techniques. These robust regressions techniques are Huber MM, LTS, and LMS estimates. We evaluate the performance of estimators in terms of the mean square error (MSE), and we compare the efficiency of our proposed robust-regression-ratio-type estimators with existing estimators under the optimal conditions. These comparisons show that our robust ratio-type estimators give more efficient results than the existing estimators under double sampling. In addition, the simulation and the empirical studies based on a data set that includes unusual observations show that our proposed estimators have a lower MSE than the existing estimators.

In this paper we propose an estimator of the entropy of a continuous random variable. The estimator is obtained by modifying the estimator proposed by Vasicek (1976). Consistency of estimator is proved, and comparisons are made with Vasicek’s estimator (1976), van Es’s estimator (1992), Ebrahimi et al.’s estimator (1994) and Correa’s estimator (1995). The results indicate that the proposed estimator has smaller mean squared error than above estimators.

In this paper, we show that the unbiased estimator of the certion Parameter of the selected population does not exist. First, we give a new proof of this fact for the selected normal population. We then extend the result to some other distributions belonging to one-parameteric exponential family. Whenever an unbiased estimator exists, it is shown to be a function of order statiscs.

This paper considers the problem of estimating the population mean ybar of the study variate y using information on different parameters such as population mean (X), coefficient of variation (Cx), kurtosis (b2(x)), standard deviation (Sx) of the auxiliary variate x and on the correlation coefficient, r, between the study variate y and the auxiliary variate x through transformation. A class of estimators on the lines of Kadilar and Cingi (2003) has been defined and its properties are studied to the first degree of approximation. It has been shown that the proposed class of estimators is better than usual unbiased estimator y, ratio estimator y R, ratio-type estimator tR and Kadilar and Cingi (2003) estimator y C under some realistic conditions. Numerical illustration is given in support of the present study.