Techniques　used　to　analyze　exceedances　over　a　high　threshold　are　in　great　demand　for　research　in　economics,　environmental　science,　and　other　fields.　The　generalized　Pareto　distribution　(GPD)　has　been　widely　used　to　fit　observations　exceeding　the　tail　threshold　in　the　peaks　over　threshold　(POT)　framework.　Parameter　estimation　and　threshold　selection　are　two　critical　issues　for　threshold-based　GPD　inference.　In　this　work,　we　propose　a　new　GPD-based　estimation　approach　by　combining　the　method　of　moments　and　likelihood　moment　techniques　based　on　the　least　squares　concept,　in　which　the　shape　and　scale　parameters　of　the　GPD　can　be　simultaneously　estimated.　To　analyze　extreme　data,　the　proposed　approach　estimates　the　parameters　by　minimizing　the　sum　of　squared　deviations　between　the　theoretical　GPD　function　and　its　expectation.　Additionally,　we　introduce　a　recently　developed　stopping　rule　to　choose　the　suitable　threshold　above　which　the　GPD　asymptotically　fits　the　exceedances.　Simulation　studies　show　that　the　proposed　approach　performs　better　or　similar　to　existing　approaches,　in　terms　of　bias　and　the　mean　square　error,　in　estimating　the　shape　parameter.　In　addition,　the　performance　of　three　threshold　selection　procedures　is　assessed　by　estimating　the　value-at-risk　(VaR)　of　the　GPD.　Finally,　we　illustrate　the　utilization　of　the　proposed　method　by　analyzing　air　pollution　data.　In　this　analysis,　we　also　provide　a　detailed　guide　regarding　threshold　selection.