what is the relationship between the point estimate and confidence intervals?

In statistics, point estimation involves the use of sample data to calculate a single value (known as a statistic) which is to serve as a "best guess" or "best estimate" of an unknown (fixed or random) population parameter. More formally, it is the application of a point estimator to the data. In general, point estimation should be contrasted with interval estimation: such interval estimates are typically either confidence intervals in the case of frequentist inference, or credible intervals in the case of Bayesian inference. Point estimators minimum-variance mean-unbiased estimator (MVUE), minimizes the risk (expected loss) of the squared-error loss-function. best linear unbiased estimator (BLUE) minimum mean squared error (MMSE) median-unbiased estimator, minimizes the risk of the absolute-error loss function maximum likelihood (ML) method of moments, generalized method of moments Bayesian point-estimation Bayesian inference is based on the posterior distribution. Many Bayesian point-estimators are the posterior distribution's statistics of central tendency, e.g., its mean, median, or mode: Posterior mean, which minimizes the (posterior) risk (expected loss) for a squared-error loss function; in Bayesian estimation, the risk is defined in terms of the posterior distribution. Posterior median, which minimizes the posterior risk for the absolute-value loss function. maximum a posteriori (MAP), which finds a maximum of the posterior distribution; for a uniform prior probability, the MAP estimator coincides with the maximum-likelihood estimator; The MAP estimator has good asymptotic properties, even for many difficult problems, on which the maximum-likelihood estimator has difficulties. For regular problems, where the maximum-likelihood estimator is consistent, the maximum-likelihood estimator ultimately agrees with the MAP estimator.[1][2][3] Bayesian estimators are admissible, by Wald's theorem.[4][2] Special cases of Bayesian estimators are important: Kalman filter Wiener filter Several methods of computational statistics have close connections with Bayesian analysis: particle filter Markov chain Monte Carlo (MCMC)

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A point estimate in a normal distribution may fall in the range of confidence interval or may fall outside the confidence interval. if it falls in the Null Hypothesis (inside the interval) we fail to reject the null hypothesis. if it falls on the alternate hypothesis. We will reject the null hypothesis More on null hypothesis from investopedia <a rel="nofollow" target="_blank" href="http://www.investopedia.com/terms/n/null_hypothesis.asp" style='word-wrap:break-word;'>http://www.investopedia.com/terms/n/null_hypothesis.asp</a>

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