Title
Unbiased Ratio Estimation for Finite Populations: Generalized Hartely and Ross Estimator to Unequal Probability Sampling Designs,Used
Delivery time: 8-12 business days (International)
In this work, the Hartely and Ross (1954) estimator is generalized to unequalprobability sampling designs, under the condition of measurability. Two distinct versions are considered. The first builds on the Horvitz and Thompson( 1952) estimator. This GHR estimator is unbiased and an exact variance and an unbiased estimator for the exact variance are obtained. The second version of GHR is derived using a Hansen and Hurwitz (1943) type estimator for withreplacement sampling. This estimator is unbiased. This estimator is discussed under two different asymptotic scenarios; a CLT is established and the asymptotic variance and a consistent estimator for the variance are given. An important problem in applications is estimation of the population total t_y under a stratified sampling design when stratum x totals are known, particularly in the case of small stratum sizes. If biased estimators are used to estimate withinstratum population y totals, the bias may accumulate across strata. The unbiased GHR estimators can be used effectively in dealing with such situations by introducing a separate GHR estimator, analogous to the classic separate ratio estimator of survey statistics.
By changing our most important processes and
products, we have already made a big leap forward. This ranges from the
increased use of more sustainable fibers to the use of more
environmentally friendly printing processes to the development of
efficient waste management in our value chain.
Shipping & Returns
Shipping
We ship your order within 2–3 business days for USA deliveries and 5–8 business days for international shipments. Once your package has been dispatched from our warehouse, you'll receive an email confirmation with a tracking number, allowing you to track the status of your delivery.
Returns
To facilitate a smooth return process, a Return Authorization (RA) Number is required for all returns. Returns without a valid RA number will be declined and may incur additional fees. You can request an RA number within 15 days of the original delivery date. For more details, please refer to our Return & Refund Policy page.
Shipping & Returns
Shipping
We ship your order within 2–3 business days for USA deliveries and 5–8 business days for international shipments. Once your package has been dispatched from our warehouse, you'll receive an email confirmation with a tracking number, allowing you to track the status of your delivery.
Returns
To facilitate a smooth return process, a Return Authorization (RA) Number is required for all returns. Returns without a valid RA number will be declined and may incur additional fees. You can request an RA number within 15 days of the original delivery date. For more details, please refer to our Return & Refund Policy page.
Warranty
We provide a 2-year limited warranty, from the date of purchase for all our products.
If you believe you have received a defective product, or are experiencing any problems with your product, please contact us.
This warranty strictly does not cover damages that arose from negligence, misuse, wear and tear, or not in accordance with product instructions (dropping the product, etc.).
Warranty
We provide a 2-year limited warranty, from the date of purchase for all our products.
If you believe you have received a defective product, or are experiencing any problems with your product, please contact us.
This warranty strictly does not cover damages that arose from negligence, misuse, wear and tear, or not in accordance with product instructions (dropping the product, etc.).
Secure Payment
Your payment information is processed securely. We do not store credit card details nor have access to your credit card information.
We accept payments with :
Visa, MasterCard, American Express, Paypal, Shopify Payments, Shop Pay and more.
Secure Payment
Your payment information is processed securely. We do not store credit card details nor have access to your credit card information.
We accept payments with :
Visa, MasterCard, American Express, Paypal, Shopify Payments, Shop Pay and more.