Generalized Ratio-cum-Product Estimator for Finite Population Mean under Two-Phase Sampling Scheme

A method to lower the MSE of a proposed estimator relative to the MSE of the linear regression estimator under two-phase sampling scheme is developed. Estimators are developed to estimate the mean of the variate under study with the help of auxiliary variate (which are unknown but it can be accessed conveniently and economically). The mean square errors equations are obtained for the proposed estimators. In addition, optimal sample sizes are obtained under the given cost function. The comparison study has been done to set up conditions for which developed estimators are more effective than other estimators with novelty. The empirical study is also performed to supplement the claim that the developed estimators are more efficient.

UNIFORM-IN-SUBMODEL BOUNDS FOR LINEAR REGRESSION IN A MODEL-FREE FRAMEWORK

For the last two decades, high-dimensional data and methods have proliferated throughout the literature. Yet, the classical technique of linear regression has not lost its usefulness in applications. In fact, many high-dimensional estimation techniques can be seen as variable selection that leads to a smaller set of variables (a “submodel”) where classical linear regression applies. We analyze linear regression estimators resulting from model selection by proving estimation error and linear representation bounds uniformly over sets of submodels. Based on deterministic inequalities, our results provide “good” rates when applied to both independent and dependent data. These results are useful in meaningfully interpreting the linear regression estimator obtained after exploring and reducing the variables and also in justifying post-model-selection inference. All results are derived under no model assumptions and are nonasymptotic in nature.

A Crowd Monitoring Methodology based on the Analysis of the Electromagnetic Spectrum

In this work, a system able to monitor the crowd density detecting mobile phone communications through the analysis of the electromagnetic spectrum is proposed and experimentally assessed. The variations of the electromagnetic spectrum are collected with a low-cost spectrum analyzer, and a high gain log-periodic directive antenna (LPDA). The objective is to relate the spectral power density in a given frequency band to estimate the connections present and the number of people in a given area. In particular, a linear regression estimator, whose parameters have been calculated with the least square method modeled considering experimental data in a controlled environment, permits us to infer the number of customers detected on a given frequency band. The obtained experimental results demonstrated the efficacy of the method, which can be used not only to monitoring the number of people in a given scenario, but it also be used for commercial activities to detect the presence and pervasiveness of different mobile phone companies.

Two-Way Fixed Effects Estimators with Heterogeneous Treatment Effects

Linear regressions with period and group fixed effects are widely used to estimate treatment effects. We show that they estimate weighted sums of the average treatment effects (ATE ) in each group and period, with weights that may be negative. Due to the negative weights, the linear regression coefficient may for instance be negative while all the ATEs are positive. We propose another estimator that solves this issue. In the two applications we revisit, it is significantly different from the linear regression estimator. (JEL C21, C23, D72, J31, J51, L82)

An Analog Approach for Weather Estimation Using Climate Projections and Reanalysis Data

General circulation models (GCMs) are essential for projecting future climate; however, despite the rapid advances in their ability to simulate the climate system at increasing spatial resolution, GCMs cannot capture the local and regional weather dynamics necessary for climate impacts assessments. Temperature and precipitation, for which dense observational records are available, can be bias corrected and downscaled, but many climate impacts models require a larger set of variables such as relative humidity, cloud cover, wind speed and direction, and solar radiation. To address this need, we develop and demonstrate an analog-based approach, which we call a “weather estimator.” The weather estimator employs a highly generalizable structure, utilizing temperature and precipitation from previously downscaled GCMs to select analogs from a reanalysis product, resulting in a complete daily gridded dataset. The resulting dataset, constructed from the selected analogs, contains weather variables needed for impacts modeling that are physically, spatially, and temporally consistent. This approach relies on the weather variables’ correlation with temperature and precipitation, and our correlation analysis indicates that the weather estimator should best estimate evaporation, relative humidity, and cloud cover and do less well in estimating pressure and wind speed and direction. In addition, while the weather estimator has several user-defined parameters, a sensitivity analysis shows that the method is robust to small variations in important model parameters. The weather estimator recreates the historical distributions of relative humidity, pressure, evaporation, shortwave radiation, cloud cover, and wind speed well and outperforms a multiple linear regression estimator across all predictands.

A Class of Ratio-Type Estimator Using Two Auxiliary Variables for Estimating The Population Mean With Some Known Population Parameters

In this paper, we have suggested a class of ratio type estimators with a linear combination using two auxiliary variables with some known population mean of the study variable. The bias and the mean square error of the proposed estimators are derived. We identified sub-members of the class of ratio type estimators. The condition for which the the proposed the proposed estimators perform better than the sample mean per unit, Olkin (1958) multivariate ratio, classical linear regression estimator, Singh(1965), Mohanty (1967) and Swain (2012) are derived. From the analysis, it is observed that the proposed estimators perform better than the sample mean per unit and other existing ratio type estimators considered in this study.

Estimating Linear Trends: Simple Linear Regression versus Epoch Differences

Two common approaches for estimating a linear trend are 1) simple linear regression and 2) the epoch difference with possibly unequal epoch lengths. The epoch difference estimator for epochs of length M is defined as the difference between the average value over the last M time steps and the average value over the first M time steps divided by N − M, where N is the length of the time series. Both simple linear regression and the epoch difference are unbiased estimators for the trend; however, it is demonstrated that the variance of the linear regression estimator is always smaller than the variance of the epoch difference estimator for first-order autoregressive [AR(1)] time series with lag-1 autocorrelations less than about 0.85. It is further shown that under most circumstances if the epoch difference estimator is applied, the optimal epoch lengths are equal and approximately one-third the length of the time series. Additional results are given for the optimal epoch length at one end when the epoch length at the other end is constrained.