Wavelet based Multi-scale Auto-Regressive (MAR) Model: An Application for Prediction of Coconut Price in Kerala Author: Sandipan Sarkar, Ranjit Kumar Paul, A.K. Paul and L.M. Bhar Pages: 1-10
In recent times, forecasting of agricultural commodity price becomes a major issue. But in the context of forecasting of time series data exhibiting Long-Range Dependence (LRD) becomes more complex with the fractional differencing value. In general, Autoregressive Fractionally Integrated Moving Average (AFRIMA) model is widely used for time-series forecasting having long range dependency. It has been observed that in many cases forecasting performance with ARFIMA model is not satisfactory. Therefore, Multi-scale Autoregressive (MAR) model based on wavelets decomposition at level 6. Here, an attempt has been made to improve the forecasting performance of MAR model by inclusion of some extra regressors (modified MAR model). Daily wholesale price data on coconut of Kerala market has been used for the illustration purpose. A comparative study has been made for ARFIMA, MAR and modified MAR model in terms of Mean Squared Error (MSE) and Root Mean Squared Error (RMSE). The empirical study reveals that forecasting ability of modified MAR model outperforms the other two methodologies in terms of lower MSE and RMSE values. Keywords: ARFIMA, Long Range Dependence (LRD), Multi-scale Auto-Regressive (MAR) model, Wavelet transformation.
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A Note on Effects on the Eigenstructure of a Data Matrix when Deleting a Subset of Observations Author: Ravindra Khattree Pages: 11-17
We provide a result which elegantly helps us identify influential observations in a data matrix based on the eigenstructure of a specific matrix which measures the effect of one or more influential observations. The theorem suggests that the corresponding statistic is easily computable. We illustrate its usefulness in data cleaning prior to modeling using a classical data of Graybill and Iyer and provide its implementation using a short SAS code. This approach is especially useful for large data, where model-free approach to identification of influential observations is a natural choice. Keywords: Data cleaning, Data processing, Eigenstructure, Eigenvalues, Emphasis measure, Influential observations.
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Calibration Approach for Estimation of Population Ratio under Double Sampling Author: Sadikul Islam, Hukum Chandra, U.C. Sud, Saurav Guha and Pradip Basak Pages: 19-25
Ratio estimator is widely used survey estimation method for estimating the finite population mean (or total) using auxiliary variable which is linearly related to study variable. However, this method requires the availability of aggregate level population information for auxiliary variable which may not be always available. As a result, in many practical situations, the ratio method of estimation cannot be applied. Alternatively, the double (or two-phase) sampling approach is often applied in such cases. This paper develops the calibration approach based finite population ratio estimator using the double sampling. It is assumed that the ratio of the total of auxiliary variables is available for the first phase sample only. The expression for variance and estimator of the variance of the proposed estimator is also developed. In addition, optimum sample sizes for the first and second phase samples are also suggested for a fixed cost. Monte Carlo simulations based on real population show that the proposed estimator is efficient than the existing alternative. Keywords: Calibration, Cost function, Double sampling, Population ratio.
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Construction of Balanced Sampling Plans Excluding Adjacent Units Author: Rajeev Kumar, B.N. Mandal and Rajender Parsad Pages: 27-32
Balanced sampling plans excluding adjacent units are useful for sampling from populations in which the nearer units provide similar observations due to natural ordering of the units in time or space. The ordering of units in the population may be circular or linear. For these plans, all the first order inclusion probabilities are equal whereas second order inclusion probabilities for pairs of adjacent units at a distance less than or equal to ? are zero and constant for all other pairs of non-adjacent units which are at a distance greater than ?. In this article, we present 13 new balanced sampling plans excluding adjacent units for one dimensional population with circular and 111 with linear ordering of units in the parametric range N ? 50, n ? 7, ? ? 7, ? ? 5. Keywords: Balanced sampling plans excluding adjacent units, Linear programming approach, Polygonal designs.
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Preliminary Test Regression type Estimator of Finite Population Mean in Survey Sampling Author: Dhyanesh Shukla and B.V.S. Sisodia Pages: 33-40
A preliminary test regression type estimator (PTRE) of population mean in survey sampling has been developed when prior value of correlation coefficient between study variable and an auxiliary variable is available. It has been demonstrated that PTRE performs well as compared to the usual difference and regression estimators. Keywords: Difference estimator, Regression estimator, Preliminary test of significance, Mellin transform, Legendre function.
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Unbiased Class of Product Estimators in Circular Systematic Sampling (C.S.S.) Scheme Author: Kuldeep Rajpoot and K.S. Kushwaha Pages: 53-57
An unbiased class of product type estimators in circular systematic sampling (C.S.S.) scheme is proposed to estimate the population mean Ny of a response variables y. Jack-knife technique pioneered by Quenouille (1949,1956) has been applied to make the class unbiased. An explicit expression for the sampling variance of the class T?PUis derived to the terms of order o(n-1). An empirical study is provided to examine the applied usefulness of the result derived. Key Words: Product estimator, Jack-knife technique, Circular systematic sampling, M.V.U. estimator.
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Small Domain Inference Combining Data from Two Independent Surveys Author: Sadikul Islam and Hukum Chandra Pages: 59-69
Many often two surveys conducted independently, may have some auxiliary variables in common along with a set of extra variables that are not common to both the surveys. One survey, which is small in sample size but collects both variable of interest as well as a set of auxiliary variables. The another survey which is relatively larger in sample size, does not collects variable of interest but collects a set of auxiliary variables, common to the small survey. In addition, the large survey collects multiple response variables as well as set of auxiliary variables not common to the small survey. A small area predictor for small domain (or area) means is proposed by combining data from these two surveys using multipurpose weights. Empirical results from model-based as well as design-based simulations indicate that the proposed small area predictor that incorporates the additional auxiliary variables of the large survey along with the common auxiliary variables, provide better efficiency gain. Keyewords: Combining data; Empirical predictor; Independent surveys; Non-sample area; Small domain; Multipurpose weight; Variable specific EBLUP weight.
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Hindi Supplement Author: ISAS Pages: 4
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Scrambled Response Techniques in Two Wave Rotation Sampling for Estimating Population Mean of Sensitive Characteristics with Case Study Author: Kumari Priyanka, Pidugu Trisandhya and Richa Mittal Pages: 41-52
Present work is an attempt to use non-sensitive auxiliary variable and scrambled response techniques (SRT) to estimate population mean of a sensitive variable. A class of estimator is proposed to estimate the population mean of a sensitive variable in sampling over two successive waves. Various members of the proposed class of estimators has been discussed. The proposed class of estimator has been analysed theoretically as well as empirically. It has been compared with modified general successive sampling estimator and with some of members of its own class. Simulation study has also been discussed. A case study of drug usage by students in a college on two successive waves has also been carried out. Keywords: Randomized response technique, Scrambled response technique, Sensitive variable, Scrambling variable, Exponential ratio type estimators, Successive sampling, Optimum rotation rate, Non-sensitive auxiliary variable, Mean squared error, Bias.
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Efficient and Cost Effective Partial Three-Way Cross Designs for Breeding Experiments with Scarce Resources Author: Mohd Harun, Cini Varghese, Seema Jaggi, Anindita Datta and Eldho Varghese Pages: 71-78
Three-way cross plans find a vital role in breeding experiments due to uniformity, stability and the relative simplicity of selecting and testing. Here, methodology has been developed for obtaining information matrices pertaining to general combining ability effects of full parents and half parents after eliminating specific combining ability effects. A new, efficient and cost effective series of designs involving three-way crosses for breeding experiments has been introduced and general expressions of information matrices, eigenvalues, variance factors, efficiency factor and degree of fractionation have been derived. The developed series has small degree of fractionation and high efficiency factor making them cost effective and suitable for scarce resource conditions. Keywords: Degree of fractionation, Efficiency factor, General combining ability, Partial three-way cross, Triangular association scheme, Variance factor.